mit phd qualifying exam physics

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Well-being - inclusion - collaboration - mentorship - respect, search form, graduate coursework and qualifying exams, on this page:.

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• Advice about the oral exam

Official academic information

Department webpages about academic requirements.

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• Core course and oral exam information
• Requirements for the interdisciplinary PhD in Physics, Statistics, and Data Science

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• Cross-registration instructions
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Advising and Support Services

Your Academic and Research Advisors:  Every graduate student is assigned an academic advisor in addition to their primary research advisor. You'll have an academic advising meeting on Registration Day at the beginning of every semester, but you can email this person for advice any time during the year. 

Graduate Student Advocate:    A person you can go to outside of your advisors is  Claude Canizares , the department's Graduate Student Advocate. He works with graduate students to connect them to resources in the Department and around MIT, and to help them progress towards their degrees and develop professionally. Prof. Canizares is an X-ray astrophysicist who led the Center for Space Research (now the MIT Kavli Institute), served as Vice President for Research, and is deeply connected around MIT. His email address is crc at mit dot edu.

APO Staff:   The staff of the Physics Academic Programs Office supports every aspect of the Physics education program at MIT. We are a friendly, welcoming team of professionals dedicated to the success of all students in MIT Physics degree programs or taking an MIT Physics course. From inquiries about the undergraduate major or questions about admission to our doctoral program, to overseeing degree completion and celebrating graduates, we are available at every step of the Physics education journey: providing information, interpreting academic policy, administering advising, organizing classes, and solving problems. As a part of your extended support network, we’re also available to help with non-academic issues as well, pointing you towards opportunities and resources of all kinds. If you have a question about any aspect of academic life at MIT, ask the Academic Programs Office and we’ll help you find the answers you need.

GradSupport:   GradSupport in the Office of Graduate Education (OGE)  is a place you can go to outside the department for advice and counsel about academic matters. It is the rough equivalent of the undergrads' S3 . 

Core Course Tips

Resources and advice.

• From PGSC  - the most comprehensive info you'll find!
• From the Department  
• From physREFS

Astrophysics

• Students are provided with the  180 questions  they could be asked in advance

Atomic, Molecular, and Optical Physics

• Generally speaking, the exam covers all the material in Wolfgang Ketterle's two classes on Atomic Physics: 8.421 and 8.422 .
• Students typically take the exam during spring of their 2nd year or fall of their 3rd year and often will spend a full two to three months preparing.
• Students will be given a topic one week ahead of their scheduled exam.
• Students are expected to prepare a ~15 minute chalk-talk without any notes on their assigned topic.
• During the roughly one hour and forty-five minute exam, the committee (made up of three AMO faculty, not including the student's research advisor) will interrupt and ask questions about the topic, the student's research, and/or other unrelated AMO topics.
• See this document for the official list of topics students should be familiar with before the exam and a general description of the exam.
• 1st-3rd year AMO students have a bi-weekly study group for students to practice giving presentations on AMO topics to their peers. Contact Alyssa Rudelis at [email protected] to be added to the mailing list for this study group.
• Study guide currently posted on the PhysREFS website

Condensed matter experiment

• Students give a presentation about a topic they are assigned 1 month before the exam
• The rest of the exam consists of questions from the committee
• Expected to know the material in Introduction to Solid State Physics by Kittel
• Graduate students in the division keep an archive of past oral exam questions, study materials, and guides - ask students who have completed their oral exam for more information

Condensed matter theory

• General information on oral exams webpage
• Your research advisor gives you one problem in advance and the rest are from the committee
• Expected to know the material in textbooks:  Solid State Physics by Ashcroft and Mermin, Introduction to Solid State Physics by Kittel, and Intro to Stat Mec h by Kerson Huang

Nuclear/particle experiment

• According to the  department website  as of fall 2019:
• "The NUPAX oral exam consists of three parts: (a) a question prepared in advance based on a relevant topic in nuclear and particle physics, (b) a portion focusing on the student’s current research program, and (c) a broad set of questions in nuclear and particle physics.  Passing of the exam will depend on the student’s performance in the assigned question, as well as their proficiency in  nuclear physics ,  particle physic s,  and   detectors and experimental techniques .   The topics and questions are drawn primarily from material covered in the NUPAX required graduate classes (8.701, 8.711, and 8.811). The exam is a total of 90 minutes in duration and results are communicated to the student at the completion of the exam."

Nuclear/particle theory

• Students give a short presentation about a topic they are assigned a few weeks before the exam
• The rest of the exam is questions from three professors
• "The topics and questions are drawn primarily from material covered in NUPAT graduate classes, with emphasis on 8.325 and Field Theory of the Standard Model." - from 2019 CTP graduate student handbook
• The graduate students in the division keep an archive of old oral exam questions, study materials, and guides in a shared Dropbox folder. Ask a friend or officemate for access!

Plasma physics

• Students give a ~30-minute presentation on a topic (often a paper) assigned a few weeks before the exam by the student's official (senior) supervisor
• The committee often asks questions about the presentation for ~30 minutes, then general questions (total time of the exam is ~2 hours)
• Expected to know the material in  Introduction to Plasma Physics  by F. Chen; additional material from Hutchinson's Principles of Plasma Diagnonstics , Friedberg's Ideal MHD or Fusion Energy may be requested depending on the breadth of courses the student has taken
• Senior graduate students in the division can share notes and tips from past oral exams - get in touch with one of them to rehearse your presentation and answer some practice questions on the blackboard!

Quantum information

• Students give a short presentation on a topic assigned 2+ weeks before the exam
• According to the 2019 CTP graduate student handbook , "The topics and questions are drawn primarily from material covered in the textbook by Nielsen and Chuang."

Qualifying Exam

The qualifying exam requires that students progress through a two-step process:.

• Technical Qualifying Examination (TQE) : Students demonstrate technical competence based on coursework. The TQE is typically completed in the first three or four regular semesters of registration.
• Oral Qualifying Examination (OQE) : After successful completion of the TQE, students take an oral qualifying exam. It is desirable to complete the OQE by the end of the fourth regular semester of registration. Students must successfully complete the OQE by the end of the sixth regular semester of registration; explicit permission from the QuEHST committee is required to continue in the program beyond six semesters without passing the OQE.

Technical Qualifying Examination (TQE) Class Requirement

• TQE Form (Contract Form and Subject Grid)
• TQE Approved Subjects  (Subject Grid and titles)

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During their first year, students choose a technical concentration area in which to develop a focused engineering/physics skill set. Students must select a set of advanced technical subjects — minimum of 4 classes and 42 units — from a single concentration area. All students must also take Human Pathology (HST030/031 or HST034/035) and HST500: Frontiers in (Bio)Medical Engineering and Medical Physics  as part of their TQE.

Each student, with the assistance of his/her academic advisor, should construct a plan for satisfying the TQE course requirement. In constructing their TQE plans, students should consider the following:

• A thorough grounding in a classical engineering or physical sciences discipline is one of the fundamental underpinnings of the MEMP program. Many MEMP students have undergraduate backgrounds that were not structured this way, but we believe that such training is an important part of the preparation for interdisciplinary research. Selecting a technical concentration area provides students with the opportunity to focus their general technical interests and acquire a solid technical foundation in a specific discipline.
• It is often useful to enroll in undergraduate classes in preparation for some of the advanced technical subjects.

Students must register their plans by submitting a signed Contract for TQE form  to Traci Anderson in E25-518, by Spring term Registration Day of their first year in the program. Changing the TQE concentration area at a later time requires a written petition to the QuEHST committee.

Changing TQE classes.  Students may “shop” classes at the start of each term and make changes to TQE class selections – via an email to Traci Anderson with cc to the academic advisor – until Add Date of the term in which they are enrolled in the class being added. Please make sure that the email is clear with respect to which class(es) are being added to the TQE plan and which class(es) are being removed. Under no circumstances will students be permitted to add a class to the TQE plan after earning a grade in the class.

Click here for sample schedules that fulfill TQE requirements

Students pass the TQE portion of the qualifying exam by demonstrating competence in the chosen concentration area and by earning a grade of "satisfactory" or better in pathology. Competence in the chosen technical concentration area is demonstrated by:

• Earning at least three A grades and one B grade in the four selected TQE classes.
• Earning two A grades and two B grades in the four selected TQE classes, and subsequently earning an A grade in an alternate, fifth TQE class.
• When five classes are required to meet the 42-unit minimum: Earning at least 30 units of A and no more than 12 units of B in the five selected TQE classes.
• Applies only to Biological Engineering, Chemical Engineering, and Material Science and Engineering TQE areas: Earning at least two A grades and two B grades in the four selected TQE classes. 

When a student does not initially meet the criteria above, the QuEHST committee will review the student's academic performance and decide on a remediation plan individualized to the circumstances. The student is welcome to submit a written statement explaining any circumstances impacting their performance and proposing a specific remediation. Remediation plans could potentially include:

• Taking (or retaking) one or more specific classes to achieve mastery of the material.
• After suitable preparation, retaking the final exam and earning a grade (specified by instructor) that is indicative of a firm grasp of the subject matter. 
• After suitable preparation, taking an oral exam with a pass/fail outcome in a specific topic area.
• Communication between HST and the instructor(s) of those class(s) in which students received a B to determine the class rank of the candidate and the minimum rank indicating mastery of the subject material according to the instructor. (This approach is necessary because of the uneven grading policies - percent A's - in graduate subjects across different departments.) Under no circumstances should students approach instructors directly to discuss remediation.

Successful completion of the TQE is a prerequisite for taking the OQE.

Oral Qualifying Examination (OQE) Requirement

Students should identify a  research project  during the first year, and should conduct full-time research during their first summer. This research experience is essential as part of the preparation for the oral qualifying exam, but need not be the basis of the doctoral thesis.

The purpose of the OQE is to evaluate whether the student can integrate information from diverse sources into a well thought out and coherent research proposal - a skill essential for successful scholarship. The ability to defend this proposal during an oral presentation is a central part of the qualifying process. The qualifying exam explores students’ ability to formulate coherent research questions and to explain the relevance of their proposed research to clinical medicine.  In addition, students should be prepared to demonstrate how they think on their feet. It is not possible to anticipate every question that might be asked during the OQE, but students should be prepared to show how they approach technical questions even when they do not immediately know the answer.

Each OQE is administered by an OQE committee composed of the student's Qualifying Exam (QE) chair and two additional faculty members. The student's research advisor may not be a member of the OQE committee. A member of the QuEHST committee will be assigned as a QE chair upon successful completion of the TQE (or in those cases where a student has all As in the TQE subjects with one only remaining subject and thus eligible to schedule the OQE in the term of the final TQE subject registration.)

The OQE is offered twice each year, in January and Spring (May/June). Students indicate their intent to take the exam by submitting an OQE Scheduling form to Traci Anderson in the IMES/HST Academic Office by November 1 for January exams or by March 1 for Spring exams. The student and their QE chair must both sign the OQE scheduling form. Students may not submit the OQE scheduling form until they have successfully completed the TQE, with the following exceptions:

• Students may submit the OQE scheduling form during the term in which they are taking Human Pathology and/or HST.500;
• When three A’s and one B are required, students who have received A's in three TQE courses may submit the OQE scheduling form during the term in which they are taking their fourth TQE course.
• When two A’s and two B's are required, students who have received A's in two TQE courses and a B in one TQE course may submit the OQE scheduling form during the term in which they are taking their fourth TQE course.
• When five classes are required to meet the 42-unit minimum, students who have received A’s in TQE courses totaling at least 30 units may submit the OQE scheduling form during the term in which they are taking their remaining TQE course(s).

Three weeks prior to the exam date, the student must ensure that the the following items have been submitted to Traci Anderson in the IMES/HST Academic Office: 

• A recommendation letter from the research advisor. The letter should address the student's potential for conducting independent research and their progress in the laboratory to date. It is the student's responsibility to ensure that the research advisor's letter is received in a timely fashion. However, the letter should be sent from the research advisor directly to tanderso [at] mit.edu (Traci Anderson) rather than submitted by the student.
• Overall Goals and Specific Aims 
• Background and Significance 
• Preliminary Data (As in HST500, students may use their own preliminary data or data from the literature or sponsoring laboratory supporting the feasibility of the proposed work.) 
• Research Design and Methods 
• References (not included in 10 page limit)

The OQE normally consists of a 30-minute oral presentation by the student, followed by questions from the OQE committee. However, the precise format of the exam is determined by the QE chair and therefore questions/interruptions may be allowed during the student's presentation. Two hours are allotted for the OQE.

While the written research proposal should be at a detailed scientific level, expectations for the oral presentation differ. Committee members will judge the oral presentation based on the student’s ability to present their research to a broad scientific audience, for example, readers of Scientific American . Students should avoid jargon and should not assume that the committee members possess detailed knowledge about their field of specialization. In preparing their oral presentation, students are encouraged to seek help and advice from their research advisor, lab mates, fellow MEMP students, and other knowledgeable parties.

At the conclusion of the exam, the OQE committee makes a recommendation to the QuEHST committee. This recommendation is based on the student's performance on the oral exam, the written research proposal, and the research advisor's recommendation letter. The QuEHST committee determines the final outcome, which is one of the following:

• Qualified: No further testing/evaluation is required. The student is qualified to proceed with thesis research.
• Not Yet Qualified: Additional tasks are required to pass the OQE. This may include additional coursework and/or a repeat oral exam. Each student is permitted a maximum of two attempts at the oral exam.
• Not Qualified: The student is not qualified to continue his/her pursuit of a degree in Medical Engineering and Medical Physics.

Petitions to the QuEHST Committee requesting exceptions to any of these policies may be submitted to tanderso [at] MIT.EDU (Traci Anderson) in the IMES/HST Academic Office, E25-518.

QuEHST Committee

The doctoral qualifying examination is administered by the Qualifying Exam in HST (QuEHST) Committee, comprised of HST Faculty Members:

• Sangeeta Bhatia , chair
• Elfar Adalsteinsson
• Kwanghun Chung
• Martha Gray
• Ellen Roche
• Alex Shalek
• Mehmet Toner

2025 Oral Exam Dates

• Winter: Monday, January 27 - Tuesday, January 28, 2025
• Spring: Monday, June 2 - Tuesday, June 3, 2025

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Information on Graduate Course Requirements

Choosing first year graduate subjects.

The Department does not require PhD students to take any subjects other than those needed to satisfy the specialty and breadth requirements described below. However, many students begin by taking some combination of graduate Classical Mechanics ( 8.309 ), graduate Quantum Mechanics ( 8.321 and 8.322 ), graduate Electricity and Magnetism ( 8.311 ), and graduate Statistical Mechanics ( 8.333 ). Not only have these subjects been proven to give students a broad view of basic physics, but each of them (with the exception of 8.322) may be used to satisfy the related part of the Written General Exam.

First-year students concerned with the level of their undergraduate preparation are encouraged to consider taking senior-level undergraduate subjects such as Electricity and Magnetism ( 8.07 ), Statistical Mechanics ( 8.08 ) and Classical Mechanics ( 8.09 ). Some first-year students may wish to sample basic graduate subjects in specialty areas: Atomic and Optical Physics ( 8.421 or 8.422 ), Solid State Physics ( 8.511 ), Systems Biology ( 8.591J ), Plasma Physics ( 8.613J ), Introduction to Nuclear and Particle Physics ( 8.701 ), and Astrophysics ( 8.901 or 8.902 ). These subjects may later be counted towards one’s specialty or breadth requirements. While planning their first year program, students should keep in mind that the normal subject load for those with full time RAs is two academic subjects, or about 24 units. A student with an RA will also register for Pre-Thesis Research ( 8.391 in the fall; 8.392 in the spring and summer terms), for 12 or more units, depending on the rest of the course load.

NUPAX Graduate Student Classes

Graduate students who belong to the NUPAX division are required to take three specialty classes ( effective Fall 2023 ) and two breadth requirements. The full academic responsibilities for graduate students are discussed in greater detail on the main Physics website ( http://web.mit.edu/physics/current/graduate/doctoral.html ). Students are encouraged to visit the website for more information about these requirements.

NuPAX offers three courses in experimental nuclear and particle physics: 8.701 , 8.811 , and 8.711 . The graduate courses 8.811 and 8.711 assume that students have completed a rigorous introductory course in nuclear and particle physics. The level of undergraduate particle and nuclear physics varies greatly depending on institution and instructor. Students should review the example final for 8.701 to determine placement. The purpose of each of the three courses is summarized, and detailed topics are outlined, below.

Introduction to Particle and Nuclear Physics – 8.701

• Graduate or advanced undergraduate introduction to particle and nuclear physics.
• Satisfies breadth requirement for graduate students not in NuPAT or NuPAX.
• Prepares undergraduates for Physics GRE subject exam.
• NuPAX students should take this course in the fall of their first year.

Nuclear Physics – 8.711

• Graduate overview of topics in nuclear physics.
• Satisfies breadth requirement for NuPAT.
• Undergraduates should have completed 8.701 before taking 8.711.
• NuPAX students should take this course in the spring of their first year.

Particle Physics – 8.811

• Graduate overview of topics in particle physics.
• Undergraduates should have completed 8.701 before taking 8.811.
• NuPAX students should take this course in the fall of their second year or in consultation with the instructor and their graduate advisor.

Subjects and Topics

Course Overview: Introduction to Nuclear and Particle Physics

• Properties of particles and nuclei
• Development of standard model
• Feynman calculations
• Experimental techniques
• Relativity Review
• Relativistic kinematics
• Lagrangians
• Noether’s Theorem
• Fermi’s Golden Rule
• Decay Rates
• Cross-sections

Electromagnetism

• Dirac Equation
• Feynman diagram calculations

Weak Interactions

• P Violation and Wu Experiment
• Flavor and CKM
• CP Violation and Cronin & Fitch
• Higgs Mechanism

Strong Interaction

• Properties of mesons, baryons, quarkonia
• QCD, color, asymptotic freedom
• Parton distribution functions, sum rules
• PDF connection to experiment

Nuclear Physics

• Nuclei basics
• Shell model
• Alpha Decay, quantum tunnelling
• Beta Decay, Fermi theory
• Solar cycle, binding per nucleon
• Nuclear reactors and weapons
• Accelerators
• Spectroscopy, Partial Wave, Dalitz plots
• electron-proton scattering, GE & GM, structure functions
• Deep in-elastic scattering

Course Overview: Experimentalist’s top down view of nuclei

• Fundamental particles and interactions
• Modern NP (quarks, nucleons, Nuclei, Astro)
• Pions, isospin and NN interaction
• Low energy properties of nuclei and nuclear saturation
• Nuclear Decays

Effective Many Body Methods

• Nuclear properties and observables (excited states, spins, parities, EM moments, …)
• Mean-field approximation and the Shell-Model
• Single particle excited states and EM transitions
• Bohr-Mottelson collective model
• Phonons, nuclear deformations, rotational modes
• Nuclei far from stability, pairing interactions and modification of magic numbers

Nuclear Astrophysics

• History of the universe,
• Big Bang Nucleosynthesis
• Solar Fusion
• Element production via s-process and r-process in neutron stars.

NN Interaction and Ab-Initio Many-Body Methods

• The Deuteron
• Phenomenological potentials (AV18)
• NN scattering and phase shifts
• QCD and chiral EFT
• Many-body methods [MC, CC, SRG, Corr. Operators]
• Beyond the mean-field approximation (long and short-range correlations, clustering)

Electron Scattering

• Elastic scattering
• Continued  …..
• Quasi-Elastic scattering
• Polarization observables
• Deep Inelastic Scattering
• Parity violation

Nucleon Structure

• Form Factors
• Structure functions
• Spin structure
• TMD / GPD etc
• Nuclear medium modification

Nuclear Decay and Fundamental Symmetries

• Beta decay and electron capture (nuclear modeling and standard model tests)
• Neutrino Oscillations
• Double-Beta decay (emphasis on gA quenching and matrix elements)

Heavy Ion Collisions

• Anisotropic flow
• QCD phase diagram

Nuclear Energy

• Nuclear reactors
• Nuclear weapons

Detectors (Integrated as appropriate in the above topics)

• Interactions of particle with matter
• Nuclear detectors

Course Overview: Particle Physics at the Energy, Intensity and Cosmology Frontiers

Standard Model

• Detectors and Accelerators
• Particle Astrophysics
• Advanced Feynman diagrams
• Extending the SM with GUTs

Neutrino Physics

• Sterile Neutrinos
• Matter Effects
• See-saw Models
• Basic formalism
• CMB, Supernova, Lensing, LSS

Dark Matter

• Dark Matter and Structure
• Model building

Cosmic Rays

• Origin of Cosmic Rays
• Propagation and GZK cutoff
• Neutrino Production

Experiment (Some presented with above topics)

• Detectors at colliders
• Specialized detectors

Requirements for a Doctorate in Physics

An advanced degree in physics at Caltech is contingent upon an extensive research achievement. Students in the program are expected to join a research group, carry out independent research, and write publications for peer-reviewed journals as well as a thesis. The thesis work proposed to a Caltech candidacy committee then presented and evaluated by a Caltech thesis committee in a public defense. Initially, students are required to consolidate their knowledge by taking advanced courses in at least three subfields of physics. Students must also pass a written candidacy exam in both classical physics and quantum mechanics in order to progress into the research phase of the degree.

Graduates of our program are expected to have extensive experience with modern research methods, a broad knowledge of contemporary physics, and the ability to perform as independent researchers at the highest intellectual and technical levels.

The PhD requirements are below and are also available in the Caltech Catalog, Section 4: Information for Graduate Students .

Plan of Study

The plan of study is the set of courses that a student will take to complete the Advance Physics Requirement and any courses needed as preparation to pass the Written Candidacy Exams (see below). Any additional courses the student plans to take as part of their graduate curriculum may be included in the plan of study but are not required. Students should consult with their Academic Advisor on their Plan of Study and discuss any exception or special considerations with the Option Representative. 

Log in to REGIS and navigate to the Ph. D. Candidacy Tab of your Graduate Degree Progress page. Add you courses into the Plan of Study section. When complete, click the "Submit Plan of Study to Option Rep" button. This will generate a notice to the Option Rep to approve your plan of study. Once you complete the courses in the Plan of Study, the Advanced Physics Requirement is completed.

Written Candidacy Exams

Physics students must demonstrate proficiency in all areas of basic physics, including classical mechanics (including continuum mechanics), electricity and magnetism, quantum mechanics, statistical physics, optics, basic mathematical methods of physics, and the physical origin of everyday phenomena. A solid understanding of these fundamental areas of physics is considered essential, so proficiency will be tested by written candidacy examinations.

No specific course work is required for the basic physics requirement, but some students may benefit from taking several of the basic graduate courses, such as Ph 106 and Ph 125. In addition, the class Ph 201 will provide additional problem solving training that matches the basic physics requirement.

Exam I: Classical Mechanics and Electromagnetism       Topics include: TBA

Exam 2: Quantum Mechanics, Statistical Mechanics and Thermodynamics      Topics include: TBA

Both exams are offered twice each year (July and October) Email  [email protected]  to sign up

Nothing additional. Sign up for the exam by emailing Mika Walton. The Student Programs Office will update your REGIS record once you pass the exams.

Advanced Physics Requirement

Students must establish a broad understanding of modern physics through study in six graduate courses. The courses must be spread over at least three of the following four areas of advanced physics. Many courses in physics and related areas may be allowed to count toward the Advanced Physics requirements.  Below are some popular examples.  Contact the Physics Option Representative to find out if any particular course not listed here can be used for this requirement. 

Physics of elementary particles and fields (Nuclear Physics, High Energy Physics, String Theory)

                 Ph 139 Intro to Particle Physics                 Ph 205abc Relativistic Quantum Field Theory                 Ph 217 Intro to the Standard Model                 Ph 230 Elementary Particle Theory (offered every two years)                 Ph 250 Intro to String Theory (offered every two years)

Quantum Information and Matter (Atomic/Molecular/Optical Physics, Condensed-Matter Physics, Quantum Information)   

                Ph 127ab Statistical Physics                 Ph 135a Intro to Condensed Matter Physics                 Ph 136a Applications of Classical Physics (Stat Mech, Optics) (offered every two years)                 Ph 137abc Atoms and Photons                 Ph 219abc Quantum Computation                 Ph 223ab Advanced Condensed Matter Physics

Physics of the Universe (Gravitational Physics, Astrophysics, Cosmology)             

                Ph 136b Applications of Classical Physics (Elasticity, Fluid Dynamics) (offered every two years)                 Ph 136c Applications of Classical Physics (Plasma, GR) (offered every two years)                 Ph 236ab Relativity                 Ph 237 Gravitational Waves (offered every two years)                 Ay 121 Radiative Processes

Interdisciplinary Physics (e.g. Biophysics, Applied Physics, Chemical Physics, Mathematical Physics, Experimental Physics)

                Ph 77 Advanced Physics Lab                   Ph 101 Order of magnitude (offered every two years)                 Ph 118 Physics of measurement                 Ph 129 Mathematical Methods of Physics                 Ph 136a Applications of Classical Physics (Stat Mech, Optics) (offered every two years)                 Ph 136b Applications of Classical Physics (Elasticity, Fluid Dynamics) (offered every two years)                 Ph 229 Advanced Mathematical Methods of Physics

Nothing additional. Once you complete the courses in your approved Plan of Study, the Advanced Physics Requirement is complete.

Oral Candidacy Exam

The Oral Candidacy Exam is primarily a test of the candidate's suitability for research in his or her chosen field. Students should consult with the executive officer to assemble their oral candidacy committee. The chair of the committee should be someone other than the research adviser.

The candidacy committee will examine the student's knowledge of his or her chosen field and will consider the appropriateness and scope of the proposed thesis research during the oral candidacy exam. This exam represents the formal commitment of both student and adviser to a research program.

See also the Physics Candidacy FAQs

After the exam, your committee members will enter their result and any comments they may have. Non-Caltech committee members are instructed to send their results and comments to the physics graduate office who will enter the information on their behalf. Once all "pass" results have been entered, the Option Rep will be prompted to recommend you for admission to candidacy. The recommendation goes to the Dean of Graduate Studies who has the final approval to formally admit you to candidacy.

Teaching Requirement

Thesis advisory committee (tac).

After the oral candidacy exam, students will hold annual meetings with their Thesis Advisory Committee (TAC). The TAC will review the research progress and provide feedback and guidance towards completion of the degree. Students should consult with the executive officer to assemble their oral candidacy committee and TAC by the end of their third year. The TAC is normally constituted from the candidacy examiners, but students may propose variations or changes at any time to the option representative. The TAC chair should be someone other than the research Adviser. The TAC chair will typically also serve as the thesis defense chair, but changes may be made in consultation with the Executive Officer and the Option Rep.

What to do in REGIS?

Login to Regis, navigate to the Ph. D. Examination Tab of your Graduate Degree Progress page, and scroll down to the Examination Committee section. Enter the names of your Thesis Advisory Committee members. Click the "Submit Examination Committee for Approval" button and this will automatically generate notifications for the Option Rep and the Dean of Graduate Studies to approve your committee. Enter the date, time and location of your TAC meeting and click "Submit Details." Your committee members will automatically be sent email reminders with the meeting details.

PhD Defense

The final thesis examination will cover the thesis topic and its relation to the general body of knowledge of physics. The candidate should send the thesis document to the defense committee and graduate office at least two weeks prior to the defense date. The defense must take place at least three weeks before the degree is to be conferred. Please refer to the  Graduate Office  and  Library  webpages for thesis guidelines, procedures, and deadlines.

• Date, time, and location of your exam and click the "Submit Examination Details" button. You committee members will automatically be sent email reminders with the exam details. 
• Commencement Information and click the "Submit Commencement Information" button (at least 2 weeks prior to defense)
• Marching Information and click the "Submit your Marching Information" button (at least 2 weeks prior to commencement)

PhD Qualifying Exam: by end of G2 year

[Part of the Policies of the CHD, last updated fall 2021; see also area-specific exam guidelines for Applied Math , Applied Physics , Bioengineering , Computer Science , Electrical Engineering , Environmental Science & Engineering , and Materials Science & Mechanical Engineering ]

The qualifying examination should be taken no later than the end of May of the fourth semester (or the end of the Reading Period if the fourth semester is in the fall).  An extension of this deadline will be granted only if the chair of the qualifying committee makes a specific request to the CHD via the “ Request to Delay the Qualifying Exam " form.  If a student is transferring between advisors and does not have a chair of their qualifying committee, the student can make the extension request to the DGS. A recommendation that the examination be held within a few weeks after that deadline as a matter of mutual convenience, or for good and sufficient reasons during the period June through September following the second year of graduate study, will normally be routinely approved, provided the student has a cumulative average grade better than 3.00 (“B”). Marginal students, or postponement beyond the end of September in the fifth semester, will receive careful scrutiny as to the reasons behind the recommendation.

If a student has not received approval for an extension and does not complete the qualifying examination by the deadline of end of May of the fourth semester (or the end of the Reading Period if the fourth semester is in the fall), SEAS may put the student in unsatisfactory (UNSAT) progress status with GSAS. At that time the CHD will determine whether the student should lose their monthly research funding support, and whether tuition for the following semester is not to be paid, potentially blocking registration for the following semester.

Exam Committee and Scheduling

The qualifying committee is comprised of four committee members: the research advisor, the research advisor’s nominee, the student’s nominee, and the Dean’s Nominee (assigned by the CHD).  The members of the qualifying committee should be Harvard faculty members, but on occasion MIT faculty members or other technical professionals of comparable stature may serve in this capacity with the approval of the CHD.  The qualifying committee so constituted should include at least two SEAS faculty members, at least one of whom should be a senior faculty member (i.e., a full professor).  Usually, the research advisor serves as chair of the qualifying committee; but if the research advisor is not a Harvard faculty member, the research advisor will serve as co-chair with a SEAS faculty member.  Area-specific exam guidelines may specify that the Dean's Nominee is to chair the exam.

[Ed. note: students, be sure to ask your hoped-for advisor's and student's nominees whether they're willing to serve on your qualifying committee before listing them on your Program Plan.]

Approval of the final program plan and the identification of the Dean’s nominee by the CHD will permit the student to schedule the qualifying examination.  Once the student has agreed upon a time for the examination with all members of the qualifying committee, the student is responsible for contacting the Office of Academic Programs ( [email protected] ) at least two weeks in advance in order to prepare the exam paperwork, and, if needed, to schedule a room. 

The Qualifying Exam is a major milestone en route to the PhD and an important opportunity for the student to engage with their faculty committee and receive formal feedback on their progress. As such, SEAS expects the student and committee to meet together in person for the exam. If after attempting to schedule a time for the full committee to meet together in person it appears that no such time can be found, the student should consult with the Office of Academic Programs about alternatives, possibly including that one or more committee members attend remotely. In all cases the student should take the exam in a classroom or seminar room that includes a blackboard or whiteboard that they can use while answering questions, with sufficient videoconferencing for any remote-attending committee member to view it clearly.

Specifics of the Exam

The qualifying examination has the dual purpose of verifying the adequacy of the student's preparation for undertaking research in his/her chosen field, and of assessing his/her ability to synthesize the technical knowledge already acquired.  The purpose of the examination is not to reassess the student's performance in formal courses; however, evaluation of the student's general knowledge in the major field is appropriate.  The basic judgment to be made is whether the student has demonstrated sufficient mastery of the intellectual skills necessary to conduct research so that a confident prediction can be made that an acceptable doctoral dissertation will be forthcoming in timely fashion.  These skills include the ability to pull together scientific ideas, to formulate technical questions, to recognize answers thereto and to make reasonable judgments on how to seek answers to such questions.

The format of the qualifying examination ordinarily is a two-hour oral examination devoted to the presentation and discussion of one or more potential dissertation topics and to more general questions.  The intent is to test the student's comprehension of his/her chosen research field and to probe the limits of the student's technical knowledge in related areas.  Various groups within SEAS have different customs with regard to the detailed nature of the qualifying examination.  For area-specific exam guidelines, see the Graduate Program Degree Requirements page in each academic area. One role of the Dean's nominee is to assure that comparable standards are applied throughout SEAS.  The qualifying committee should agree among themselves as to what is expected of the student, who should reach out to the committee members in advance of the examination regarding the committee’s expectations.

The qualifying committee may pass or fail the student, or may judge the performance to be inconclusive.  Within its discretion, the committee may stipulate further requirements, such as additional course work, a written examination or presentation of a research proposal, as conditions that must be satisfied.  The research committee (see below) will determine whether these conditions have been met, and so report to the CHD.  Failure means that the student may not re-register, thus terminating degree candidacy.  In the case of an inconclusive performance, after consultation with his/her potential research advisor, the student may schedule a second examination, which must be conclusive. The qualifying committee should explain to the student and report to the CHD its reasons for judging the performance to be inadequate and for granting a second examination.

Students who change degree areas

Students who chose to switch degree areas within SEAS after completing their qualifying exam are ordinarily required to take a qualifying exam in the new area (for example, within Engineering Sciences from Bioengineering to Electrical Engineering or between degrees such as from Engineering Sciences to Applied Physics).  The qualifying exam committee for this exam should appropriately reflect the new degree path. Students must first seek approval of the Director of Graduate Studies and the CHD in the area they wish to transfer and must submit a final program plan for the new degree area to be reviewed and approved by the CHD.

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Department of Physics

You are here, qualifying exam - past exams.

2023 Exam - Solutions: Part 1 , Part 2 , Part 3 , and Part 4

2022 Exam - Solutions: Part 1 , Part 2 , Part 3 , and Part 4

2021 Exam - Solutions: Part 1 , Part 2 , Part 3 , and Part 4

2019 Exam - Solutions:  Part 1 ,  Part 2 ,  Part 3 , and  Part 4

2018 Exam - Solutions:  Part 1 ,  Part 2 ,  Part 3 , and  Part 4

2017 Exam - Solutions:  Part 1  and  Part 2

2016 Exam - Solutions:  Part 1  and  Part 2

2015 Exam - Solutions:  Part 1  and  Part 2

2014 Exam - Solutions:  Part 1  and  Part 2

2013 Exam - Solutions:  Part 1  and  Part 2

2012 Exam - Solutions:  Part 1  and  Part 2

2011 Exam - Solutions:  Part 1  and  Part 2

2010 Exam - Solutions: Part 1 and Part 2

77 Massachusetts Avenue Building 4-315 Cambridge MA, 02139

617-253-4841 [email protected]

Website: Physics

Application Opens: September 15

Deadline: December 15 at 11:59 PM Eastern Time

Fee: $90.00

Terms of Enrollment

Doctor of Science (ScD)

*The Master’s Degree in Physics is available in special cases only (e.g., US military officers).

Interdisciplinary Programs

Interdisciplinary Doctoral Program in Statistics (IDPS)

Standardized Tests

Graduate Record Examination (GRE)

• General test and subject test will be optional for applications due 12/15/2023.

International English Language Testing System (IELTS)

• Minimum score required: 7
• Electronic scores send to: MIT Graduate Admissions

Test of English as a Foreign Language (TOEFL)

• Minimum score required: 100 (iBT) 600 (PBT)
• Institute code: 3514
• Department code: 76

Waiver of TOEFL/IELTS may be available.

Areas of Research

• Astrophysics, Space and Planetary Physics
• Atomic and Optical Physics
• Biophysics, Medical Physics
• Condensed Matter Physics
• High Energy and Nuclear Physics
• Plasma Physics, Nuclear Fusion Research, Relativistic Beam Physics
• Quantum Information Science
• Plasma Physics, Nuclear Fusion Research, Plasma Astrophysics
• Theoretical Astrophysics

Financial Support

Our PhD students are fully supported financially throughout the duration of their program, provided that they make satisfactory progress. Funding is provided from Fellowships (internal and external) and/or Assistantships (research and teaching) and covers tuition, health insurance, and a living stipend. Read more about funding at the Physics website.

Application Requirements

• Online application
• Statement of objectives
• Three letters of recommendation
• Transcripts
• English proficiency exam scores, if required
• GRE scores are optional for applications due 12/15/2023

Special Instructions

Official transcripts should be scanned and uploaded to your online application. You must provide one uploaded copy of the official academic transcript from each college you have attended. A hard copy of your transcript may be requested later if additional processing is required; please do not send a hard copy of your transcript until we ask that you do so.

Applicants are required to complete Subjects Taken section of the online application. Please list physics, mathematics, and other science courses only; group courses by subject area, and complete each column.

Fee waivers may be available on a limited basis for qualifying applicants. Please see the Physics website for more information.

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Graduate Womxn in Physics

A group for transgender women, cisgender women, non-binary people, and gender diverse physics graduate students at MIT

General Exam Guidelines

These guidelines were compiled from the suggestions of several people. Please feel free to contact us if you have anything to add. [Note: In August 2015, the Physics Department changed the structure of the general exams. There is now only a single written exam rather than Part I and Part II. The current written exam is most similar to the old Part II exam, but the resources below for Part I may be useful for general study.]

See also the Official Physics Department general exams webpage and the MIT Physics REFS Gerneral Exam Preparation Site .

Preparation

By far the best way to study is to do old exams. While the exams have been recently revised, they are still the best guide to the sorts of topics and problems that professors in this department consider relevant. The exams have a tendency to creep upward in difficulty over the years and then get revised downwards in a sudden jump. Try not to be too surprised (or worried) about fluctuations in difficulty between different exams. It happens, and the passing scores fluctuate along with the difficulty.

Useful References

It's important to understand the level of the exam and not overshoot (or undershoot). It's overkill to read Jackson or Landau and Lifshitz for Part I (and even Part II) -- spend your mental energy elsewhere. We have compiled a list of books that we have found useful in preparing for the exams:

For Part I:

• Halliday and Resnick (yes, really: general memory refresher, optics, hydrodynamics, phasors)
• Griffiths, Introduction to Electrodynamics
• Griffiths, Quantum Mechanics
• Kittel and Kroemer, Thermal Physics
• Kleppner and Kolenkow, Classical Mechanics

For Part II:

• Bransden and Joachaim, Introduction to Quantum Mechanics
• Sakurai, Quantum Mechanics
• Marion and Heald, Classical Electromagnetic Radiation
• Kardar, Statistical Physics of Particles
• Pathria, Statistical Mechanics
• Marion and Thornton, Classical dynamics of particles and systems

There are also several sets of books of general exam problems which can be very useful:

• Cahn and Nadgorny, A Guide to Physics Problems Part I (mechanics, relativity, and electrodynamics) and Part II (thermodynamics, statistical physics, and quantum mechanics)
• Lim Yung-kuo et al., Problems and Solutions on (Mechanics, Electromagnetism, Thermodynamics and Statistical Mechanics)

Finally, here are some books that have some interesting problems but cover a broader scope of subjects than appear on our qualifying exams:

• Cronin, Greenberg, and Telegdi, UChicago Graduate Problems in Physics with Solutions
• Newbury, Newman, Ruhl, Staggs, and Thorsett, Princeton Problems in Physics with Solutions

It's a good idea to make sure you can not only do the problems but do the problems under test conditions. Speed counts, and so does endurance. You may find that sitting an exam for five hours straight is difficult in itself. You may wish to save a few days at the end of your studying to do practice exams in real time.

And here's some common sense: studying can be stressful and miserable. Take some time to be nice to yourself. Don't isolate yourself. Don't flip out. Remember: everyone has to go through this, nobody likes it, and you're even getting paid to study.

Taking the Exam

First and most importantly, get a good night's sleep.

So You Didn't Pass?

Okay, yeah, it's not fun. But try not to feel too bad about it: these exams are hardly a reliable indicator of how good a physicist you will be, especially if you are an experimentalist. Qualifiers are not why you came to graduate school, and in the big picture they are the least important part of your graduate experience: research and classes are much more important.

It can be useful to go look at your exam paper to get a clear assessment of where you went wrong and which subject areas you need the most practice in. Your advisor may also be able to discuss your exam with you.

Finally, if you've failed all of your attempts of the written exam, you will have to take...

The Special Oral

These guidelines are courtesy of Jon Miller

In memoriam Mike Piv, PhD 2000, may your hair always grow red

0 Realize: they don't have to give you this exam. If you had really flopped the exam, and they thought you should go, they'd call your advisor and say so, and then you'd be having a talk with your advisor instead of taking the exam. In giving you this exam, they are looking for an excuse to keep you, because they want you here and believe that you can do it. The only other time they convene 3 profs for anything except cookies is for a thesis defense, and it is hard enough to get 3 profs together for THAT, so be aware that they are really trying to keep you.

1 Your special oral should be on only the topics where they feel you did not demonstrate sufficient ability on the exam. This means that you can study ONLY those things which they mention, and not all four areas. So you get to focus.

2 ASAP: find out who is on your committee. Go talk with them. Tell them how badly you want to succeed. Tell them honestly what you feel your strengths and weaknesses are. Ask their advice. You can only win here: a) it's harder to fail someone you know, b) you can demonstrate that you took them seriously and used their advice when you take the exam, and c) it might actually help you study. But go and talk. Email is not enough. Not even close. Go and sit down and talk.

3 Do all of your studying standing-up at a chalkboard. Learn how to use the space well. Talk aloud. I know it's stupid. People looked at me funny. But look -- half of the committee's task is to get you nervous, to push you, to fluster you -- and then to see "Does his/her thinking go back to sound physics, or back to 2nd grade?" To the extent to which you can write clearly, talk clearly, and walk the committee through every step like you were literally teaching a recitation to freshman, you limit their ability to take any issue with you or to fluster you. The more YOU talk and the more YOU state your assumptions, the more YOU think aloud and show that you are using sound reasoning, the less THEY can try to do it for you. I cannot stress this enough. Really, do tons of problems standing up at a chalkboard and talking. I did them for anyone that would listen at any opportunity, even during commercials at home in front of my TV-addicted housemates.

4 Take at least 2, and preferrably 3, practice special oral exams. Have grad students sit down and play committee for you in a conference room and give you a practice oral exam. They need to be nasty. They need to try to get you off track. You need to make sure that they forget they are your friends, and instead really give it to you good. The first practice exam I took, they really did manage to get me nervous and angry and flustered. Thank god. Then I knew what it felt like. The next two were much better. But as with number (3) above, it's about learning to revert to solid physics when you get upset.

5 Go look at the exams you failed with someone who did well on them. Make sure you can do those problems in your sleep. Try to think of twists and tangents. Try to make them harder. Try altering the assumptions and doing it again. See how many methods you can use to get to a correct answer. And know them all. I promise you, they WILL ask these questions in the oral exam. They will tell you to study these when you go talk to them. So these serve as GIMME's. So you better know them inside and out. Do these in your practice orals, too.

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Department of Physics

The Department of Physics offers undergraduate, graduate, and postgraduate training, with a wide range of options for specialization.

The emphasis of both the undergraduate curriculum and the graduate program is on understanding the fundamental principles that appear to govern the behavior of the physical world, including space and time and matter and energy in all its forms, from the subatomic to the cosmological and from the elementary to the complex.

The Department of Physics strives to be at the forefront of many areas where new physics can be found. Consequently, the department works on problems where extreme conditions may reveal new behavior: from clusters of galaxies or the entire universe to elementary particles or the strings that may be the substructure of these particles; from collisions of nuclei at relativistic velocities that make droplets of matter hotter than anything since the Big Bang to laser-cooled atoms so cold that their wave functions overlap, resulting in a macroscopic collective state, the Bose-Einstein condensate; and from individual atoms to unusual materials, such as high-temperature superconductors and those that are important in biology. Pushing the limits provides the opportunity to observe new general principles and test theories of the structure and behavior of matter and energy.

Bachelor of Science in Physics (Course 8)

Minor in physics, minor in astronomy, undergraduate study.

An undergraduate degree in physics provides an excellent basis not only for graduate study in physics and related fields, but also for professional work in such fields as astrophysics, biophysics, engineering and applied physics, geophysics, management, law, or medicine. The undergraduate curriculum offers students the opportunity to acquire a deep conceptual understanding of fundamental physics. The core departmental requirements begin this process. The student then chooses one of two options to complete the degree: the focused option is designed for students who plan to pursue physics as a career, and is an excellent choice for students who want to experience as deep an engagement as possible with physics; the flexible option also provides a very strong physics framework, and gives students who may want to pursue additional academic interests the flexibility to do so. Both programs prepare students very well for graduate studies in physics, as well as for a variety of academic or research-related careers. Either option provides a considerable amount of time for exploration through electives. Students proceed at the pace and degree of specialization best suited to their individual capacities. Both options lead to the same degree: the Bachelor of Science in Physics.

Physics: Focused Option

This option—which includes three terms of quantum mechanics, 36 units of laboratory experience, and a thesis—is ideal preparation for a career in physics.

In the second year, students take:

Important skills for experimentation in physics may be acquired by starting an Undergraduate Research Opportunities Program (UROP)  project.

In the third year, students normally take laboratory subjects:

Students should also begin to take the restricted elective subjects, one in mathematics and at least two in physics. The mathematics subjects 18.04 Complex Variables with Applications , 18.075 Methods for Scientists and Engineers , and 18.06 Linear Algebra are particularly popular with physics majors. Topical elective subjects in astrophysics, biological physics, condensed matter, plasma, and nuclear and particle physics allow students to gain an appreciation of the forefronts of modern physics. Students intending to go on to graduate school in physics are encouraged to take the theoretical physics sequence:

An important component of this option is the thesis, which is a physics research project carried out under the guidance of a faculty member. Many thesis projects grow naturally out of UROP projects. Students should have some idea of a thesis topic by the middle of the junior year. A thesis proposal must be submitted before registering for thesis units and no later than Add Date of the fall term of the senior year.

A relatively large amount of elective time usually becomes available during the fourth year and can be used either to deepen one's background in physics or to explore other disciplines.

Physics: Flexible Option

This option is designed for students who wish to develop a strong background in the fundamentals of physics and then build on this foundation as they prepare for career paths that may or may not involve a graduate degree in physics. Many students find an understanding of the basic concepts of physics and an appreciation of the physicist's approach to problem solving an excellent preparation for the growing spectrum of nontraditional, technology-related career opportunities, as well as for careers in business, law, medicine, or engineering. Additionally, the flexible option makes it more possible for students with diverse intellectual interests to pursue a second major in another department.

The option begins with the core subjects:

Students round out their foundation material with either an additional quantum mechanics subject ( 8.05 Quantum Physics II ) or a subject in relativity ( 8.20 Introduction to Special Relativity or 8.033 Relativity ). There is an experimental requirement of 8.13 Experimental Physics I or, with the approval of the department, a laboratory subject of similar intensity in another department, an experimental research project or senior thesis, or an experimentally oriented summer externship. An exploration requirement consists of one elective subject in physics. Students can satisfy the departmental portion of the Communication Requirement by taking two of the following subjects:

The department and the Subcommittee on the Communication Requirement may accept substitution of one of the department's two required CI-M subjects with a CI-M subject in another department if it forms a natural part of the student's physics program.

Students following this option must also complete a focus requirement—three subjects forming one intellectually coherent unit in some area (not necessarily physics), subject to the approval of the department and separate from those used by the student to satisfy the HASS requirement. Areas of focus chosen by students have included astronomy, biology, computational physics, theoretical physics, nanotechnology, history of science, science and technology policy, philosophy, and science teaching. Some students may choose to satisfy their experimental and exploration requirements in the same area as their focus; others may opt for greater breadth by choosing other fields to fulfill these requirements.

Although students may choose this option at any time in their undergraduate career, many decide on the flexible major during their sophomore year in order to have enough time to craft a program that best suits their individual needs. Specific subject choices for the experimental and focus requirements require the written approval of the Flexible Program coordinator, Dr. Sean P. Robinson.

The Minor in Physics provides a solid foundation for the pursuit of a broad range of professional activities in science and engineering. The requirements for a Minor in Physics are as follows: 

Students should submit a completed Minor Application Form to Physics Academic Programs, Room 4-315. The Physics Department's minor coordinator is Shannon Larkin. See Undergraduate Education for more information on minor programs .

The Minor in Astronomy , offered jointly with the Department of Earth, Atmospheric, and Planetary Sciences, covers the observational and theoretical foundations of astronomy. For a description of the minor, see Interdisciplinary Programs.

Additional information concerning degree programs and research activities may be obtained by contacting the department office , Room 4-315, 617-253-4841.

Master of Science in Physics

Doctor of philosophy, graduate study.

The Physics Department offers programs leading to the degrees of Master of Science in Physics and Doctor of Philosophy.

Admission Requirements for Graduate Study

Students intending to pursue graduate work in physics should have as a background the equivalent of the requirements for the Bachelor of Science in Physics from MIT. However, students may make up some deficiencies over the course of their graduate work.

The normal degree program in the department leads to a PhD in Physics. Admission to a master's degree program in Physics is available only in special cases (e.g., US military officers). The requirements for the Master of Science in Physics are the same as the General Degree Requirements listed under Graduate Education. A master's thesis must represent a piece of independent research work in any of the fields described below, and must be carried out under the supervision of a department faculty member. No fixed time is set for the completion of a master's program; two years of work is a rough guideline. There is no language requirement for this degree.

Candidates for the Doctor of Philosophy or Doctor of Science are expected to enroll in those basic graduate subjects that prepare them for the general examination, which must be passed no later than in the seventh term after initial enrollment. Students are required to take two subjects in the candidate's doctoral research area (specialty requirement) and two subjects outside the candidate's field of specialization (breadth requirement). In addition, all students in the first year of the PhD program must enroll in two semesters of 8.398, a seminar specifically for first-year students. Half of the breadth requirement may be satisfied through a departmentally approved industrial internship. The doctoral thesis must represent a substantial piece of original research, carried out under the supervision of a department faculty member.

The Physics Department faculty members offer subjects of instruction and are engaged in research in a variety of fields in experimental and theoretical physics. This broad spectrum of activities is organized in the divisional structure of the department, presented below. Graduate students are encouraged to contact faculty members in the division of their choice to inquire about opportunities for research, and to pass through an apprenticeship (by signing up for Pre-Thesis Research) as a first step toward an engagement in independent research for a doctoral thesis.

Research Divisions

Faculty and students in the Department of Physics are generally affiliated with one of several research divisions:

• Astrophysics
• Experimental Nuclear and Particle Physics
• Atomic Physics, Biophysics, Condensed Matter Physics, and Plasma Physics
• Theoretical Nuclear and Particle Physics

Much of the research in the department is carried out as part of the work of various interdisciplinary laboratories and centers, including the Center for Materials Science and Engineering, Francis Bitter Magnet Laboratory, Haystack Observatory, Laboratory for Nuclear Science, Microsystems Technology Laboratories, MIT Kavli Institute for Astrophysics and Space Research, Plasma Science and Fusion Center, Research Laboratory of Electronics, and Spectroscopy Laboratory. Additional information about interdisciplinary laboratories and centers can be found under Research and Study . These facilities provide close relationships among the research activities of a number of MIT departments and give students opportunities for contact with research carried out in disciplines other than physics.

Additional information on degree programs, research activities, admissions, financial aid, teaching and research assistantships may be obtained by contacting the department office , Room 4-315, 617-253-4851.

Faculty and Teaching Staff

Deepto Chakrabarty, PhD

Professor of Physics

Head, Department of Physics

Lindley Winslow, PhD

Associate Head, Department of Physics

Raymond Ashoori, PhD

Edmund Bertschinger, PhD

Claude R. Canizares, PhD

Bruno B. Rossi Distinguished Professor Post-Tenure in Experimental Physics

Paola Cappellaro, PhD

Ford Professor of Engineering

Professor of Nuclear Science and Engineering

(On leave, spring)

Arup K. Chakraborty, PhD

John M. Deutch Institute Professor

Robert T. Haslam (1911) Professor in Chemical Engineering

Professor of Chemistry

Core Faculty, Institute for Medical Engineering and Science

Isaac Chuang, PhD

Professor of Electrical Engineering

Janet Conrad, PhD

William Detmold, PhD

(On leave, fall)

Matthew J. Evans, PhD

Mathworks Physics Professor

Peter H. Fisher, PhD

Thomas A. Frank (1977) Professor of Physics

Associate Vice President for Research Computing and Data

Joseph A. Formaggio, PhD

Anna L. Frebel, PhD

Liang Fu, PhD

Nuh Gedik, PhD

Donner Professor of Physics

Jeff Gore, PhD

Alan Guth, PhD

Victor F. Weisskopf Professor in Physics

Aram W. Harrow, PhD

Jacqueline N. Hewitt, PhD

Julius A. Stratton Professor

Scott A. Hughes, PhD

Robert L. Jaffe, PhD

Otto (1939) and Jane Morningstar Professor Post-Tenure of Science

Professor Post-Tenure of Physics

Pablo Jarillo-Herrero, PhD

Cecil and Ida Green Professor of Physics

John D. Joannopoulos, PhD

Francis Wright Davis Professor

Steven G. Johnson, PhD

Professor of Mathematics

David I. Kaiser, PhD

Germeshausen Professor of the History of Science

Mehran Kardar, PhD

Francis L. Friedman Professor of Physics

Wolfgang Ketterle, PhD

John D. MacArthur Professor

Patrick A. Lee, PhD

William and Emma Rogers Professor

Yen-Jie Lee, PhD

Class of 1958 Career Development Professor

Leonid Levitov, PhD

Hong Liu, PhD

Nuno F. Loureiro, PhD

Herman Feshbach (1942) Professor of Physics

Nergis Mavalvala, PhD

Curtis (1963) and Kathleen Marble Professor

Dean, School of Science

Richard G. Milner, PhD

Leonid A. Mirny, PhD

Richard J. Cohen (1976) Professor in Medicine and Biomedical Physics

Ernest J. Moniz, PhD

Cecil and Ida Green Distinguished Professor

Professor Post-Tenure of Engineering Systems

William D. Oliver, PhD

Henry Ellis Warren (1894) Professor

Professor of Electrical Engineering and Computer Science

Christoph M. E. Paus, PhD

Miklos Porkolab, PhD

David E. Pritchard, PhD

Cecil and Ida Green Professor Post-Tenure of Physics

Krishna Rajagopal, PhD

William A. M. Burden Professor of Physics

Gunther M. Roland, PhD

Sara Seager, PhD

Class of 1941 Professor of Planetary Sciences

Professor of Aeronautics and Astronautics

Robert A. Simcoe, PhD

Tracy Robyn Slatyer, PhD

Marin Soljačić, PhD

Iain Stewart, PhD

Otto (1939) and Jane Morningstar Professor of Science

Washington Taylor IV, PhD

Max Erik Tegmark, PhD

Jesse Thaler, PhD

Member, Institute for Data, Systems, and Society

Samuel C. C. Ting, PhD

Thomas D. Cabot Institute Professor

Senthil Todadri, PhD

Mark Vogelsberger, PhD

Vladan Vuletić, PhD

Lester Wolfe Professor

Xiao-Gang Wen, PhD

Cecil and Ida Green Professor in Physics

Frank Wilczek, PhD

Herman Feshbach (1942) Professor Post-Tenure of Physics

Michael Williams, PhD

Boleslaw Wyslouch, PhD

Barton Zwiebach, PhD

Martin Wolfram Zwierlein, PhD

Associate Professors

Joseph George Checkelsky, PhD

Associate Professor of Physics

Riccardo Comin, PhD

Netta Engelhardt, PhD

Nikta Fakhri, PhD

Thomas D. and Virginia W. Cabot Associate Professor of Physics

Daniel Harlow, PhD

Philip Harris, PhD

Or Hen, PhD

Erin Kara, PhD

Kiyoshi Masui, PhD

Michael McDonald, PhD

Max Metlitski, PhD

Phiala E. Shanahan, PhD

Class of 1957 Career Development Professor

Julien Tailleur, PhD

Salvatore Vitale, PhD

Assistant Professors

Soonwon Choi, PhD

Assistant Professor of Physics

Anna-Christina Eilers, PhD

Richard J. Fletcher, PhD

Ronald Garcia Ruiz, PhD

Long Ju, PhD

Sarah Millholland, PhD

Lina Necib, PhD

Shu-Heng Shao, PhD

Eluned Smith, PhD

Andrew Vanderburg, PhD

Visiting Associate Professors

Ibrahim I. Cissé, PhD

Visiting Associate Professor of Physics

Senior Lecturers

Peter Dourmashkin, PhD

Senior Lecturer in Physics

Erik Katsavounidis, PhD

Mohamed Abdelhafez, PhD

Lecturer in Physics

Byron Drury, PhD

Sean P. Robinson, PhD

Senior Technical Instructor of Physics

Alex Shvonski, PhD

Michelle Tomasik, PhD

Technical Instructors

Rosi Anderson, BS

Technical Instructor of Physics

Caleb C. Bonyun, MS

Aidan MacDonagh, BSE

Senior Technical Instructor of Digital Learning

Christopher Miller, BS

Aaron Pilarcik, MS

Joshua Wolfe, BS

Research Staff

Senior research scientists.

Earl S. Marmar, PhD

Senior Research Scientist of Physics

Jagadeesh Moodera, PhD

Richard J. Temkin, PhD

Professors Emeriti

John Winston Belcher, PhD

Class of 1922 Professor Emeritus

Professor Emeritus of Physics

George B. Benedek, PhD

Alfred H. Caspary Professor Emeritus of Physics

Professor Emeritus of Biological Physics

Ahmet Nihat Berker, PhD

William Bertozzi, PhD

Robert J. Birgeneau, PhD

Hale V. Bradt, PhD

Wit Busza, PhD

Min Chen, PhD

Bruno Coppi, PhD

Edward Farhi, PhD

Cecil and Ida Green Professor Emeritus of Physics

Daniel Z. Freedman, PhD

Professor Emeritus of Mathematics

Jerome I. Friedman, PhD

Institute Professor Emeritus

Jeffrey Goldstone, PhD

Thomas J. Greytak, PhD

Lester Wolfe Professor Emeritus of Physics

Lee Grodzins, PhD

Erich P. Ippen, PhD

Elihu Thomson Professor Emeritus

Professor Emeritus of Electrical Engineering

Paul Christopher Joss, PhD

Marc A. Kastner, PhD

Donner Professor of Science Emeritus

Vera Kistiakowsky, PhD

Professor Emerita of Physics

Daniel Kleppner, PhD

Lester Wolfe Professor Emeritus

Stanley B. Kowalski, PhD

J. David Litster, PhD

Earle L. Lomon, PhD

June Lorraine Matthews, PhD

John W. Negele, PhD

William A. Coolidge Professor Emeritus

Irwin A. Pless, PhD

Saul A. Rappaport, PhD

Robert P. Redwine, PhD

Lawrence Rosenson, PhD

Paul L. Schechter, PhD

William A. M. Burden Professor Emeritus in Astrophysics

Rainer Weiss, PhD

James E. Young, PhD

Undergraduate Subjects

8.006 exploring physics using python (new).

Prereq: None. Coreq: 6.100L ; or permission of instructor U (Fall) 2-0-1 units

Reviews and reinforces 6.100L topics, making connections and studying interesting physical systems (from abstract knowledge of concepts to modeling, coding, and evaluating results) that are relevant to physicists. Classes are active and interactive. Students apply programming skills to introductory physics problems and explore the role of simulations on physics. Limited to 12.

8.01 Physics I

Prereq: None U (Fall) 3-2-7 units. PHYSICS I Credit cannot also be received for 8.011 , 8.012 , 8.01L , ES.801 , ES.8012

Introduces classical mechanics. Space and time: straight-line kinematics; motion in a plane; forces and static equilibrium; particle dynamics, with force and conservation of momentum; relative inertial frames and non-inertial force; work, potential energy and conservation of energy; kinetic theory and the ideal gas; rigid bodies and rotational dynamics; vibrational motion; conservation of angular momentum; central force motions; fluid mechanics. Subject taught using the TEAL (Technology-Enabled Active Learning) format which features students working in groups of three, discussing concepts, solving problems, and doing table-top experiments with the aid of computer data acquisition and analysis.

J. Formaggio, P. Dourmashkin

8.011 Physics I

Prereq: Permission of instructor U (Spring) 5-0-7 units. PHYSICS I Credit cannot also be received for 8.01 , 8.012 , 8.01L , ES.801 , ES.8012

Introduces classical mechanics. Space and time: straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics. Designed for students with previous experience in 8.01 ; the subject is designated as 8.01 on the transcript.

8.012 Physics I

Prereq: None U (Fall) 5-0-7 units. PHYSICS I Credit cannot also be received for 8.01 , 8.011 , 8.01L , ES.801 , ES.8012

Elementary mechanics, presented in greater depth than in 8.01 . Newton's laws, concepts of momentum, energy, angular momentum, rigid body motion, and non-inertial systems. Uses elementary calculus freely; concurrent registration in a math subject more advanced than 18.01 is recommended. In addition to covering the theoretical subject matter, students complete a small experimental project of their own design. First-year students admitted via AP or Math Diagnostic for Physics Placement results.

M. Soljacic

8.01L Physics I

Prereq: None U (Fall, IAP) 3-2-7 units. PHYSICS I Credit cannot also be received for 8.01 , 8.011 , 8.012 , ES.801 , ES.8012

Introduction to classical mechanics (see description under 8.01 ). Includes components of the TEAL (Technology-Enabled Active Learning) format. Material covered over a longer interval so that the subject is completed by the end of the IAP. Substantial emphasis given to reviewing and strengthening necessary mathematics tools, as well as basic physics concepts and problem-solving skills. Content, depth, and difficulty is otherwise identical to that of 8.01 . The subject is designated as 8.01 on the transcript.

P. Jarillo-Herrero

8.02 Physics II

Prereq: Calculus I (GIR) and Physics I (GIR) U (Fall, Spring) 3-2-7 units. PHYSICS II Credit cannot also be received for 8.021 , 8.022 , ES.802 , ES.8022

Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric currents, magnetic fields and Ampere's law. Magnetic materials. Time-varying fields and Faraday's law of induction. Basic electric circuits. Electromagnetic waves and Maxwell's equations. Subject taught using the TEAL (Technology Enabled Active Learning) studio format which utilizes small group interaction and current technology to help students develop intuition about, and conceptual models of, physical phenomena.

J. Belcher, I. Cisse

8.021 Physics II

Prereq: Calculus I (GIR) , Physics I (GIR) , and permission of instructor U (Fall) 5-0-7 units. PHYSICS II Credit cannot also be received for 8.02 , 8.022 , ES.802 , ES.8022

Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric currents, magnetic fields and Ampere's law. Magnetic materials. Time-varying fields and Faraday's law of induction. Basic electric circuits. Electromagnetic waves and Maxwell's equations. Designed for students with previous experience in 8.02 ; the subject is designated as 8.02 on the transcript. Enrollment limited.

J. Checkelsky

8.022 Physics II

Prereq: Physics I (GIR) ; Coreq: Calculus II (GIR) U (Fall, Spring) 5-0-7 units. PHYSICS II Credit cannot also be received for 8.02 , 8.021 , ES.802 , ES.8022

Parallel to 8.02 , but more advanced mathematically. Some knowledge of vector calculus assumed. Maxwell's equations, in both differential and integral form. Electrostatic and magnetic vector potential. Properties of dielectrics and magnetic materials. In addition to the theoretical subject matter, several experiments in electricity and magnetism are performed by the students in the laboratory.

8.03 Physics III

Prereq: Calculus II (GIR) and Physics II (GIR) U (Fall, Spring) 5-0-7 units. REST

Mechanical vibrations and waves; simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations, and normal modes; vibrations of continuous systems; reflection and refraction; phase and group velocity. Optics; wave solutions to Maxwell's equations; polarization; Snell's Law, interference, Huygens's principle, Fraunhofer diffraction, and gratings.

Y-J. Lee, R. Comin

8.033 Relativity

Prereq: Calculus II (GIR) and Physics II (GIR) U (Fall) 5-0-7 units. REST

Einstein's postulates; consequences for simultaneity, time dilation, length contraction, and clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy, and mass; particle collisions. Relativity and electricity; Coulomb's law; magnetic fields. Brief introduction to Newtonian cosmology. Introduction to some concepts of general relativity; principle of equivalence. The Schwarzchild metric; gravitational red shift; particle and light trajectories; geodesics; Shapiro delay.

8.04 Quantum Physics I

Prereq: 8.03 and ( 18.03 or 18.032 ) U (Spring) 5-0-7 units. REST Credit cannot also be received for 8.041

Experimental basis of quantum physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, deBroglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials and introduction to hydrogenic systems.

8.041 Quantum Physics I

Prereq: 8.03 and ( 18.03 or 18.032 ) U (Fall) 2-0-10 units. REST Credit cannot also be received for 8.04

Blended version of 8.04 using a combination of online and in-person instruction. Covers the experimental basis of quantum physics: Mach-Zender interferometers, the photoelectric effect, Compton scattering, and de Broglie waves. Heisenberg uncertainty principle and momentum space. Introduction to wave mechanics: Schroedinger's equation, probability amplitudes, and wave packets. Stationary states and the spectrum of one-dimensional potentials, including the variational principle, the Hellmann-Feynman lemma, the virial theorem, and the harmonic oscillator. Basics of angular momentum, central potentials, and the hydrogen atom. Introduction to the Stern-Gerlach experiment, spin one-half, spin operators, and spin states.

8.044 Statistical Physics I

Prereq: 8.03 and 18.03 U (Spring) 5-0-7 units

Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third laws of thermodynamics. Numerous examples illustrating a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices. Concurrent enrollment in 8.04 is recommended.

8.05 Quantum Physics II

Prereq: 8.04 or 8.041 U (Fall) 5-0-7 units Credit cannot also be received for 8.051

Vector spaces, linear operators, and matrix representations.  Inner products and adjoint operators. Commutator identities. Dirac's Bra-kets. Uncertainty principle and energy-time version. Spectral theorem and complete set of commuting observables. Schrodinger and Heisenberg pictures.  Axioms of quantum mechanics. Coherent states and nuclear magnetic resonance. Multiparticle states and tensor products. Quantum teleportation, EPR and Bell inequalities. Angular momentum and central potentials. Addition of angular momentum. Density matrices, pure and mixed states, decoherence.

B. Zwiebach

8.051 Quantum Physics II

Prereq: 8.04 and permission of instructor U (Spring) 2-0-10 units Credit cannot also be received for 8.05

Blended version of 8.05 using a combination of online and in-person instruction. Together with 8.06 covers quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wave functions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen. Limited to 20.

Fall: Staff Spring: W. Detmold

8.06 Quantum Physics III

Prereq: 8.05 U (Spring) 5-0-7 units

Continuation of 8.05 . Units: natural units, scales of microscopic phenomena, applications. Time-independent approximation methods: degenerate and nondegenerate perturbation theory, variational method, Born-Oppenheimer approximation, applications to atomic and molecular systems. The structure of one- and two-electron atoms: overview, spin-orbit and relativistic corrections, fine structure, variational approximation, screening, Zeeman and Stark effects. Charged particles in a magnetic field: Landau levels and integer quantum hall effect. Scattering: general principles, partial waves, review of one-dimension, low-energy approximations, resonance, Born approximation. Time-dependent perturbation theory. Students research and write a paper on a topic related to the content of 8.05 and 8.06 .

8.07 Electromagnetism II

Prereq: 8.03 and 18.03 U (Fall) 4-0-8 units

Survey of basic electromagnetic phenomena: electrostatics, magnetostatics; electromagnetic properties of matter. Time-dependent electromagnetic fields and Maxwell's equations. Electromagnetic waves, emission, absorption, and scattering of radiation. Relativistic electrodynamics and mechanics.

8.08 Statistical Physics II

Prereq: 8.044 and 8.05 U (IAP) 4-0-8 units

Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations.

Staff, L. Fu

8.09 Classical Mechanics III

Subject meets with 8.309 Prereq: 8.223 U (Spring) 4-0-8 units

Covers Lagrangian and Hamiltonian mechanics, systems with constraints, rigid body dynamics, vibrations, central forces, Hamilton-Jacobi theory, action-angle variables, perturbation theory, and continuous systems. Provides an introduction to ideal and viscous fluid mechanics, including turbulence, as well as an introduction to nonlinear dynamics, including chaos. Students taking graduate version complete different assignments.

Undergraduate Laboratory and Special Project Subjects

8.10 exploring and communicating physics (and other) frontiers.

Prereq: None U (Fall) Not offered regularly; consult department 2-0-0 units

Features a series of 12 interactive sessions that span a wide variety of topics at the frontiers of science - e.g., quantum computing, dark matter, the nature of time - and encourage independent thinking. Discussions draw from the professor's published pieces in periodicals as well as short excerpts from his books.  Also discusses, through case studies, the process of writing and re-writing. Subject can count toward the 6-unit discovery-focused credit limit for first year students.

8.13 Experimental Physics I

Prereq: 8.04 U (Fall, Spring) 0-6-12 units. Institute LAB

First in a two-term advanced laboratory sequence in modern physics focusing on the professional and personal development of the student as a scientist through the medium of experimental physics. Experimental options cover special relativity, experimental foundations of quantum mechanics, atomic structure and optics, statistical mechanics, and nuclear and particle physics. Uses modern physics experiments to develop laboratory technique, systematic troubleshooting, professional scientific attitude, data analysis skills and reasoning about uncertainty. Provides extensive training in oral and written communication methods. Limited to 12 students per section.

J. Conrad, N. Fakhri, C. Paus, G. Roland

8.14 Experimental Physics II

Prereq: 8.05 and 8.13 U (Spring) 0-6-12 units

Second in a two-term advanced laboratory sequence in modern physics focusing on the professional and personal development of the student as a scientist through the medium of experimental physics. Experimental options cover special relativity, experimental foundations of quantum mechanics, atomic structure and optics, statistical mechanics, and nuclear and particle physics. Uses modern physics experiments to develop laboratory technique, systematic troubleshooting, professional scientific attitude, data analysis skills, and reasoning about uncertainty; provides extensive training in oral and written communication methods. Continues 8.13 practice in these skills using more advanced experiments and adds an exploratory project element in which students develop an experiment from the proposal and design stage to a final presentation of results in a poster session. Limited to 12 students per section.

8.16 Data Science in Physics

Subject meets with 8.316 Prereq: 8.04 and ( 6.100A , 6.100B , or permission of instructor) U (Spring) 3-0-9 units

Aims to present modern computational methods by providing realistic, contemporary examples of how these computational methods apply to physics research. Designed around research modules in which each module provides experience with a specific scientific challenge. Modules include: analyzing LIGO open data; measuring electroweak boson to quark decays; understanding the cosmic microwave background; and lattice QCD/Ising model. Experience in Python helpful but not required. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Students taking graduate version complete additional assignments.

8.18 Research Problems in Undergraduate Physics

Prereq: Permission of instructor U (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

Opportunity for undergraduates to engage in experimental or theoretical research under the supervision of a staff member. Specific approval required in each case.

Consult N. Mavalvala

8.19 Readings in Physics

Prereq: None U (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

Supervised reading and library work. Choice of material and allotment of time according to individual needs. For students who want to do work not provided for in the regular subjects. Specific approval required in each case.

Undergraduate Elective Subjects

8.20 introduction to special relativity.

Prereq: Calculus I (GIR) and Physics I (GIR) U (IAP) 2-0-7 units. REST

Introduces the basic ideas and equations of Einstein's special theory of relativity. Topics include Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of general relativity. Intended for freshmen and sophomores. Not usable as a restricted elective by Physics majors. Credit cannot be received for 8.20 if credit for 8.033 is or has been received in the same or prior terms.

8.21 Physics of Energy

Prereq: Calculus II (GIR) , Chemistry (GIR) , and Physics II (GIR) U (Spring) 5-0-7 units. REST

A comprehensive introduction to the fundamental physics of energy systems that emphasizes quantitative analysis. Focuses on the fundamental physical principles underlying energy processes and on the application of these principles to practical calculations. Applies mechanics and electromagnetism to energy systems; introduces and applies basic ideas from thermodynamics, quantum mechanics, and nuclear physics. Examines energy sources, conversion, transport, losses, storage, conservation, and end uses. Analyzes the physics of side effects, such as global warming and radiation hazards. Provides students with technical tools and perspective to evaluate energy choices quantitatively at both national policy and personal levels.

8.223 Classical Mechanics II

Prereq: Calculus II (GIR) and Physics I (GIR) U (IAP) 2-0-4 units

A broad, theoretical treatment of classical mechanics, useful in its own right for treating complex dynamical problems, but essential to understanding the foundations of quantum mechanics and statistical physics. Generalized coordinates, Lagrangian and Hamiltonian formulations, canonical transformations, and Poisson brackets. Applications to continuous media. The relativistic Lagrangian and Maxwell's equations.

8.224 Exploring Black Holes: General Relativity and Astrophysics

Prereq: 8.033 or 8.20 Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Fall) 3-0-9 units

Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat space-time; the metric; curvature of space-time near rotating and nonrotating centers of attraction; trajectories and orbits of particles and light; elementary models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the term is reserved for collaborative research projects on topics such as the Global Positioning System, solar system tests of relativity, descending into a black hole, gravitational lensing, gravitational waves, Gravity Probe B, and more advanced models of the cosmos. Subject has online components that are open to selected MIT alumni. Alumni wishing to participate should contact Professor Bertschinger at [email protected]. Limited to 40.

E. Bertschinger

8.225[J] Einstein, Oppenheimer, Feynman: Physics in the 20th Century

Same subject as STS.042[J] Prereq: None Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Spring) 3-0-9 units. HASS-H

See description under subject STS.042[J] . Enrollment limited.

D. I. Kaiser

8.226 Forty-three Orders of Magnitude

Prereq: ( 8.04 and 8.044 ) or permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Spring) 3-0-9 units

Examines the widespread societal implications of current scientific discoveries in physics across forty-three orders of magnitude in length scale. Addresses topics ranging from climate change to nuclear nonproliferation. Students develop their ability to express concepts at a level accessible to the public and to present a well-reasoned argument on a topic that is a part of the national debate. Requires diverse writing assignments, including substantial papers. Enrollment limited.

8.228 Relativity II

Prereq: 8.033 or permission of instructor U (IAP) 2-0-4 units

A fast-paced and intensive introduction to general relativity, covering advanced topics beyond the 8.033 curriculum. Provides students with a foundation for research relying on knowledge of general relativity, including gravitational waves and cosmology. Additional topics in curvature, weak gravity, and cosmology.

8.231 Physics of Solids I

Prereq: 8.044 ; Coreq: 8.05 U (Fall) 4-0-8 units

Introduction to the basic concepts of the quantum theory of solids. Topics: periodic structure and symmetry of crystals; diffraction; reciprocal lattice; chemical bonding; lattice dynamics, phonons, thermal properties; free electron gas; model of metals; Bloch theorem and band structure, nearly free electron approximation; tight binding method; Fermi surface; semiconductors, electrons, holes, impurities; optical properties, excitons; and magnetism.

8.241 Introduction to Biological Physics

Prereq: Physics II (GIR) and ( 8.044 or ( 5.601 and 5.602 )) Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Spring) 4-0-8 units Credit cannot also be received for 20.315 , 20.415

Introduces the main concepts of biological physics, with a focus on biophysical phenomena at the molecular and cellular scales. Presents the role of entropy and diffusive transport in living matter; challenges to life resulting from the highly viscous environment present at microscopic scales, including constraints on force, motion and transport within cells, tissues, and fluids; principles of how cellular machinery (e.g., molecular motors) can convert electro-chemical energy sources to mechanical forces and motion. Also covers polymer physics relevant to DNA and other biological polymers, including the study of configurations, fluctuations, rigidity, and entropic elasticity. Meets with 20.315 and 20.415 when offered concurrently.

8.245[J] Viruses, Pandemics, and Immunity

Same subject as 5.003[J] , 10.382[J] , HST.439[J] Subject meets with 5.002[J] , 10.380[J] , HST.438[J] Prereq: None U (Spring) Not offered regularly; consult department 2-0-1 units

See description under subject HST.439[J] . HST.438[J] intended for first-year students; all others should take HST.439[J] .

A. Chakraborty

8.251 String Theory for Undergraduates

Prereq: 8.033 , 8.044 , and 8.05 Acad Year 2024-2025: U (Spring) Acad Year 2025-2026: Not offered 4-0-8 units Credit cannot also be received for 8.821

Introduction to the main concepts of string theory, i.e., quantum mechanics of a relativistic string. Develops aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics, including the study of D-branes and string thermodynamics. Meets with 8.821 when offered concurrently.

8.276 Nuclear and Particle Physics

Prereq: 8.033 and 8.04 U (Spring) Not offered regularly; consult department 4-0-8 units

Presents a modern view of the fundamental structure of matter. Starting from the Standard Model, which views leptons and quarks as basic building blocks of matter, establishes the properties and interactions of these particles. Explores applications of this phenomenology to both particle and nuclear physics. Emphasizes current topics in nuclear and particle physics research at MIT. Intended for students with a basic knowledge of relativity and quantum physics concepts.

M. Williams

8.277 Introduction to Particle Accelerators

Prereq: ( 6.2300 or 8.07 ) and permission of instructor U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit.

Principles of acceleration: beam properties; linear accelerators, synchrotrons, and storage rings. Accelerator technologies: radio frequency cavities, bending and focusing magnets, beam diagnostics. Particle beam optics and dynamics. Special topics: measures of accelerators performance in science, medicine and industry; synchrotron radiation sources; free electron lasers; high-energy colliders; and accelerators for radiation therapy. May be repeated for credit for a maximum of 12 units.

W. Barletta

8.282[J] Introduction to Astronomy

Same subject as 12.402[J] Prereq: Physics I (GIR) U (Spring) 3-0-6 units. REST

Quantitative introduction to the physics of planets, stars, galaxies and our universe, from origin to ultimate fate, with emphasis on the physics tools and observational techniques that enable our understanding. Topics include our solar system, extrasolar planets; our Sun and other "normal" stars, star formation, evolution and death, supernovae, compact objects (white dwarfs, neutron stars, pulsars, stellar-mass black holes); galactic structure, star clusters, interstellar medium, dark matter; other galaxies, quasars, supermassive black holes, gravitational waves; cosmic large-scale structure, origin, evolution and fate of our universe, inflation, dark energy, cosmic microwave background radiation, gravitational lensing, 21cm tomography. Not usable as a restricted elective by Physics majors.

8.284 Modern Astrophysics

Prereq: 8.04 U (Fall) 3-0-9 units

Application of physics (Newtonian, statistical, and quantum mechanics; special and general relativity) to fundamental processes that occur in celestial objects. Includes main-sequence stars, collapsed stars (white dwarfs, neutron stars, and black holes), pulsars, galaxies, active galaxies, quasars, and cosmology. Electromagnetic and gravitational radiation signatures of astrophysical phenomena explored through examination of observational data. No prior knowledge of astronomy required.

8.286 The Early Universe

Prereq: Physics II (GIR) and 18.03 Acad Year 2024-2025: U (Fall) Acad Year 2025-2026: Not offered 3-0-9 units. REST

Introduction to modern cosmology. First half deals with the development of the big bang theory from 1915 to 1980, and latter half with recent impact of particle theory. Topics: special relativity and the Doppler effect, Newtonian cosmological models, introduction to non-Euclidean spaces, thermal radiation and early history of the universe, big bang nucleosynthesis, introduction to grand unified theories and other recent developments in particle theory, baryogenesis, the inflationary universe model, and the evolution of galactic structure.

8.287[J] Observational Techniques of Optical Astronomy

Same subject as 12.410[J] Prereq: 8.282[J] , 12.409 , or other introductory astronomy course U (Fall) 3-4-8 units. Institute LAB

See description under subject 12.410[J] . Limited to 18; preference to Course 8 and Course 12 majors and minors.

M. Person, R. Teague

8.290[J] Extrasolar Planets: Physics and Detection Techniques

Same subject as 12.425[J] Subject meets with 12.625 Prereq: 8.03 and 18.03 U (Fall) 3-0-9 units. REST

See description under subject 12.425[J] .

8.292[J] Fluid Physics

Same subject as 1.066[J] , 12.330[J] Prereq: 5.60, 8.044 , or permission of instructor U (Spring) 3-0-9 units

A physics-based introduction to the properties of fluids and fluid systems, with examples drawn from a broad range of sciences, including atmospheric physics and astrophysics. Definitions of fluids and the notion of continuum. Equations of state and continuity, hydrostatics and conservation of momentum; ideal fluids and Euler's equation; viscosity and the Navier-Stokes equation. Energy considerations, fluid thermodynamics, and isentropic flow. Compressible versus incompressible and rotational versus irrotational flow; Bernoulli's theorem; steady flow, streamlines and potential flow. Circulation and vorticity. Kelvin's theorem. Boundary layers. Fluid waves and instabilities. Quantum fluids.

L. Bourouiba

8.295 Practical Experience in Physics

Prereq: None U (Fall, IAP, Spring, Summer) 0-1-0 units Can be repeated for credit.

For Course 8 students participating in off-campus experiences in physics. Before registering for this subject, students must have an internship offer from a company or organization and must identify a Physics advisor. Upon completion of the project, student must submit a letter from the company or organization describing the work accomplished, along with a substantive final report from the student approved by the MIT advisor. Subject to departmental approval. Consult departmental academic office.

8.298 Selected Topics in Physics

Prereq: Permission of instructor U (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Presentation of topics of current interest, with content varying from year to year.

Consult I. Stewart

8.299 Physics Teaching

Prereq: None U (Fall, Spring) Units arranged [P/D/F] Can be repeated for credit.

For qualified undergraduate students interested in gaining some experience in teaching. Laboratory, tutorial, or classroom teaching under the supervision of a faculty member. Students selected by interview.

8.EPE UPOP Engineering Practice Experience

Engineering School-Wide Elective Subject. Offered under: 1.EPE , 2.EPE , 3.EPE , 6.EPE , 8.EPE , 10.EPE , 15.EPE , 16.EPE , 20.EPE , 22.EPE Prereq: None U (Fall, Spring) 0-0-1 units Can be repeated for credit.

See description under subject 2.EPE . Application required; consult UPOP website for more information.

K. Tan-Tiongco, D. Fordell

8.S014 Special Subject: Physics (New)

Prereq: None U (IAP) 2-0-4 units

Opportunity for group study of subjects in physics not otherwise included in the curriculum.

K. Rajagopal

8.S02 Special Subject: Physics

Prereq: None U (Spring) Not offered regularly; consult department 1-0-2 units

P. Dourmashkin

8.S198 Special Subject: Physics (New)

Prereq: None U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit.

8.S199 Special Subject: Physics (New)

Prereq: None U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged [P/D/F]

8.S227 Special Subject: Physics

Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units

8.S271 Special Subject: Physics

Prereq: None Acad Year 2024-2025: U (Spring) Acad Year 2025-2026: Not offered 2-0-4 units

8.S30 Special Subject: Physics

Prereq: None Acad Year 2024-2025: U (Fall, Spring) Acad Year 2025-2026: Not offered Units arranged

A. Bernstein, J. Walsh

8.S50 Special Subject: Physics

Prereq: None U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit.

8.UR Undergraduate Research

Research opportunities in physics. For further information, contact the departmental UROP coordinator.

N. Mavalvala

8.THU Undergraduate Physics Thesis

Prereq: None U (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Program of research leading to the writing of an S.B. thesis; to be arranged by the student under approved supervision.

Information: N. Mavalvala

Graduate Subjects

8.309 classical mechanics iii.

Subject meets with 8.09 Prereq: None G (Spring) 4-0-8 units

8.311 Electromagnetic Theory I

Prereq: 8.07 G (Spring) 4-0-8 units

Basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional emf and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. Subject uses appropriate mathematics but emphasizes physical phenomena and principles.

8.315[J] Mathematical Methods in Nanophotonics

Same subject as 18.369[J] Prereq: 8.07 , 18.303 , or permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

See description under subject 18.369[J] .

S. G. Johnson

8.316 Data Science in Physics

Subject meets with 8.16 Prereq: 8.04 and ( 6.100A , 6.100B , or permission of instructor) Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

8.321 Quantum Theory I

Prereq: 8.05 G (Fall) 4-0-8 units

A two-term subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron.

8.322 Quantum Theory II

Prereq: 8.07 and 8.321 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 4-0-8 units

8.323 Relativistic Quantum Field Theory I

Prereq: 8.321 G (Spring) 4-0-8 units

A one-term self-contained subject in quantum field theory. Concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics. Topics: classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields, spin fields, and Gauge bosons. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization.

8.324 Relativistic Quantum Field Theory II

Prereq: 8.322 and 8.323 G (Fall) 4-0-8 units

The second term of the quantum field theory sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: perturbation theory and Feynman diagrams, scattering theory, Quantum Electrodynamics, one loop renormalization, quantization of non-abelian gauge theories, the Standard Model of particle physics, other topics.

8.325 Relativistic Quantum Field Theory III

Prereq: 8.324 G (Spring) 4-0-8 units

The third and last term of the quantum field theory sequence. Its aim is the proper theoretical discussion of the physics of the standard model. Topics: quantum chromodynamics; Higgs phenomenon and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator products and effective theories; detailed structure of the standard model; spontaneously broken gauge theory and its quantization; instantons and theta-vacua; topological defects; introduction to supersymmetry.

8.333 Statistical Mechanics I

Prereq: 8.044 and 8.05 G (Fall) 4-0-8 units

First part of a two-subject sequence on statistical mechanics. Examines the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, microcanonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory.

8.334 Statistical Mechanics II

Prereq: 8.333 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 4-0-8 units

Second part of a two-subject sequence on statistical mechanics. Explores topics from modern statistical mechanics: the hydrodynamic limit and classical field theories. Phase transitions and broken symmetries: universality, correlation functions, and scaling theory. The renormalization approach to collective phenomena. Dynamic critical behavior. Random systems.

8.351[J] Classical Mechanics: A Computational Approach

Same subject as 6.5160[J] , 12.620[J] Prereq: Physics I (GIR) , 18.03 , and permission of instructor G (Fall) 3-3-6 units

See description under subject 12.620[J] .

J. Wisdom, G. J. Sussman

8.370[J] Quantum Computation

Same subject as 2.111[J] , 6.6410[J] , 18.435[J] Prereq: 8.05 , 18.06 , 18.700 , 18.701 , or 18.C06[J] G (Fall) 3-0-9 units

See description under subject 18.435[J] .

I. Chuang, A. Harrow, P. Shor

8.371[J] Quantum Information Science

Same subject as 6.6420[J] , 18.436[J] Prereq: 18.435[J] G (Spring) 3-0-9 units

Examines quantum computation and quantum information. Topics include quantum circuits, the quantum Fourier transform and search algorithms, the quantum operations formalism, quantum error correction, Calderbank-Shor-Steane and stabilizer codes, fault tolerant quantum computation, quantum data compression, quantum entanglement, capacity of quantum channels, and quantum cryptography and the proof of its security. Prior knowledge of quantum mechanics required.

I. Chuang, A. Harrow

8.372 Quantum Information Science III

Prereq: 8.371[J] Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

Third subject in the Quantum Information Science (QIS) sequence, building on 8.370[J] and 8.371[J] . Further explores core topics in quantum information science, such as quantum information theory, error-correction, physical implementations, algorithms, cryptography, and complexity. Draws connections between QIS and related fields, such as many-body physics, and applications such as sensing.

8.381, 8.382 Selected Topics in Theoretical Physics

Prereq: Permission of instructor G (Fall, Spring) Not offered regularly; consult department 3-0-9 units

Topics of current interest in theoretical physics, varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.391 Pre-Thesis Research

Prereq: Permission of instructor G (Fall) Units arranged [P/D/F] Can be repeated for credit.

Advanced problems in any area of experimental or theoretical physics, with assigned reading and consultations.

8.392 Pre-Thesis Research

Prereq: Permission of instructor G (Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

8.395[J] Teaching College-Level Science and Engineering

Same subject as 1.95[J] , 5.95[J] , 7.59[J] , 18.094[J] Subject meets with 2.978 Prereq: None G (Fall) 2-0-2 units

See description under subject 5.95[J] .

8.396[J] Leadership and Professional Strategies & Skills Training (LEAPS), Part I: Advancing Your Professional Strategies and Skills

Same subject as 5.961[J] , 9.980[J] , 12.396[J] , 18.896[J] Prereq: None G (Spring; second half of term) 2-0-1 units

Part I (of two parts) of the LEAPS graduate career development and training series. Topics include: navigating and charting an academic career with confidence; convincing an audience with clear writing and arguments; mastering public speaking and communications; networking at conferences and building a brand; identifying transferable skills; preparing for a successful job application package and job interviews; understanding group dynamics and different leadership styles; leading a group or team with purpose and confidence. Postdocs encouraged to attend as non-registered participants. Limited to 80.

8.397[J] Leadership and Professional Strategies & Skills Training (LEAPS), Part II: Developing Your Leadership Competencies

Same subject as 5.962[J] , 9.981[J] , 12.397[J] , 18.897[J] Prereq: None G (Spring; first half of term) 2-0-1 units

Part II (of two parts) of the LEAPS graduate career development and training series. Topics covered include gaining self awareness and awareness of others, and communicating with different personality types; learning about team building practices; strategies for recognizing and resolving conflict and bias; advocating for diversity and inclusion; becoming organizationally savvy; having the courage to be an ethical leader; coaching, mentoring, and developing others; championing, accepting, and implementing change. Postdocs encouraged to attend as non-registered participants. Limited to 80.

8.398 Doctoral Seminar in Physics

Prereq: None G (Fall, Spring) 1-0-2 units Can be repeated for credit.

A seminar for first-year PhD students presenting topics of current interest, with content varying from year to year. Open only to first-year graduate students in Physics.

Consult J. Thaler

8.399 Physics Teaching

Prereq: Permission of instructor G (Fall, Spring) Units arranged [P/D/F] Can be repeated for credit.

For qualified graduate students interested in gaining some experience in teaching. Laboratory, tutorial, or classroom teaching under the supervision of a faculty member. Students selected by interview.

Consult C. Paus

Physics of Atoms, Radiation, Solids, Fluids, and Plasmas

8.421 atomic and optical physics i.

Prereq: 8.05 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

The first of a two-term subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical phsyics. The interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.

M. Zwierlein

8.422 Atomic and Optical Physics II

Prereq: 8.05 Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

The second of a two-term subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical physics. Non-classical states of light- squeezed states; multi-photon processes, Raman scattering; coherence- level crossings, quantum beats, double resonance, superradiance; trapping and cooling- light forces, laser cooling, atom optics, spectroscopy of trapped atoms and ions; atomic interactions- classical collisions, quantum scattering theory, ultracold collisions; and experimental methods.

8.431[J] Nonlinear Optics

Same subject as 6.6340[J] Prereq: 6.2300 or 8.03 G (Spring) 3-0-9 units

See description under subject 6.6340[J] .

J. G. Fujimoto

8.481, 8.482 Selected Topics in Physics of Atoms and Radiation

Prereq: 8.321 G (Fall, Spring) Not offered regularly; consult department 3-0-9 units

Presentation of topics of current interest, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.511 Theory of Solids I

Prereq: 8.231 G (Fall) 3-0-9 units

First term of a theoretical treatment of the physics of solids. Concept of elementary excitations. Symmetry- translational, rotational, and time-reversal invariances- theory of representations. Energy bands- electrons and phonons. Topological band theory. Survey of electronic structure of metals, semimetals, semiconductors, and insulators, excitons, critical points, response functions, and interactions in the electron gas. Theory of superconductivity.

8.512 Theory of Solids II

Prereq: 8.511 G (Spring) 3-0-9 units

Second term of a theoretical treatment of the physics of solids. Interacting electron gas: many-body formulation, Feynman diagrams, random phase approximation and beyond. General theory of linear response: dielectric function; sum rules; plasmons; optical properties; applications to semiconductors, metals, and insulators. Transport properties: non-interacting electron gas with impurities, diffusons. Quantum Hall effect: integral and fractional. Electron-phonon interaction: general theory, applications to metals, semiconductors and insulators, polarons, and field-theory description. Superconductivity: experimental observations, phenomenological theories, and BCS theory.

8.513 Many-Body Theory for Condensed Matter Systems

Prereq: 8.033 , 8.05 , 8.08 , and 8.231 Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

Concepts and physical pictures behind various phenomena that appear in interacting many-body systems. Visualization occurs through concentration on path integral, mean-field theories and semiclassical picture of fluctuations around mean-field state. Topics covered: interacting boson/fermion systems, Fermi liquid theory and bosonization, symmetry breaking and nonlinear sigma-model, quantum gauge theory, quantum Hall theory, mean-field theory of spin liquids and quantum order, string-net condensation and emergence of light and fermions.

8.514 Strongly Correlated Systems in Condensed Matter Physics

Prereq: 8.322 and 8.333 Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

Study of condensed matter systems where interactions between electrons play an important role. Topics vary depending on lecturer but may include low-dimension magnetic and electronic systems, disorder and quantum transport, magnetic impurities (the Kondo problem), quantum spin systems, the Hubbard model and high-temperature superconductors. Topics are chosen to illustrate the application of diagrammatic techniques, field-theory approaches, and renormalization group methods in condensed matter physics.

8.581, 8.582 Selected Topics in Condensed Matter Physics

Prereq: Permission of instructor Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units Can be repeated for credit.

Presentation of topics of current interest, with contents varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.590[J] Topics in Biophysics and Physical Biology

Same subject as 7.74[J] , 20.416[J] Prereq: None Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 2-0-4 units

Provides broad exposure to research in biophysics and physical biology, with emphasis on the critical evaluation of scientific literature. Weekly meetings include in-depth discussion of scientific literature led by distinct faculty on active research topics. Each session also includes brief discussion of non-research topics including effective presentation skills, writing papers and fellowship proposals, choosing scientific and technical research topics, time management, and scientific ethics.

J. Gore, N. Fakhri

8.591[J] Systems Biology

Same subject as 7.81[J] Subject meets with 7.32 Prereq: ( 18.03 and 18.05 ) or permission of instructor G (Fall) 3-0-9 units

Introduction to cellular and population-level systems biology with an emphasis on synthetic biology, modeling of genetic networks, cell-cell interactions, and evolutionary dynamics. Cellular systems include genetic switches and oscillators, network motifs, genetic network evolution, and cellular decision-making. Population-level systems include models of pattern formation, cell-cell communication, and evolutionary systems biology. Students taking graduate version explore the subject in more depth.

8.592[J] Statistical Physics in Biology

Same subject as HST.452[J] Prereq: 8.333 or permission of instructor Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

A survey of problems at the interface of statistical physics and modern biology: bioinformatic methods for extracting information content of DNA; gene finding, sequence comparison, phylogenetic trees. Physical interactions responsible for structure of biopolymers; DNA double helix, secondary structure of RNA, elements of protein folding. Considerations of force, motion, and packaging; protein motors, membranes. Collective behavior of biological elements; cellular networks, neural networks, and evolution.

M. Kardar, L. Mirny

8.593[J] Biological Physics

Same subject as HST.450[J] Prereq: 8.044 recommended but not necessary G (Spring) Not offered regularly; consult department 4-0-8 units

Designed to provide seniors and first-year graduate students with a quantitative, analytical understanding of selected biological phenomena. Topics include experimental and theoretical basis for the phase boundaries and equation of state of concentrated protein solutions, with application to diseases such as sickle cell anemia and cataract. Protein-ligand binding and linkage and the theory of allosteric regulation of protein function, with application to proteins as stores as transporters in respiration, enzymes in metabolic pathways, membrane receptors, regulators of gene expression, and self-assembling scaffolds. The physics of locomotion and chemoreception in bacteria and the biophysics of vision, including the theory of transparency of the eye, molecular basis of photo reception, and the detection of light as a signal-to-noise discrimination.

8.613[J] Introduction to Plasma Physics I

Same subject as 22.611[J] Prereq: ( 6.2300 or 8.07 ) and ( 18.04 or Coreq: 18.075 ) G (Fall) 3-0-9 units

See description under subject 22.611[J] .

N. Loureiro, I. Hutchinson

8.614[J] Introduction to Plasma Physics II

Same subject as 22.612[J] Prereq: 22.611[J] Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

See description under subject 22.612[J] .

N. Loureiro

8.624 Plasma Waves

Prereq: 22.611[J] Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

Comprehensive theory of electromagnetic waves in a magnetized plasma. Wave propagation in cold and hot plasmas. Energy flow. Absorption by Landau and cyclotron damping and by transit time magnetic pumping (TTMP). Wave propagation in inhomogeneous plasma: accessibility, WKB theory, mode conversion, connection formulae, and Budden tunneling. Applications to RF plasma heating, wave propagation in the ionosphere and laser-plasma interactions. Wave propagation in toroidal plasmas, and applications to ion cyclotron (ICRF), electron cyclotron (ECRH), and lower hybrid (LHH) wave heating. Quasi-linear theory and applications to RF current drive in tokamaks. Extensive discussion of relevant experimental observations.

M. Porkolab

8.641 Physics of High-Energy Plasmas I

Prereq: 22.611[J] G (Fall) Not offered regularly; consult department 3-0-9 units

Physics of High-Energy Plasmas I and II address basic concepts of plasmas, with temperatures of thermonuclear interest, relevant to fusion research and astrophysics. Microscopic transport processes due to interparticle collisions and collective modes (e.g., microinstabilities). Relevant macroscopic transport coefficients (electrical resistivity, thermal conductivities, particle "diffusion"). Runaway and slide-away regimes. Magnetic reconnection processes and their relevance to experimental observations. Radiation emission from inhomogeneous plasmas. Conditions for thermonuclear burning and ignition (D-T and "advanced" fusion reactions, plasmas with polarized nuclei). Role of "impurity" nuclei. "Finite-β" (pressure) regimes and ballooning modes. Convective modes in configuration and velocity space. Trapped particle regimes. Nonlinear and explosive instabilities. Interaction of positive and negative energy modes. Each subject can be taken independently.

8.642 Physics of High-Energy Plasmas II

8.670[j] principles of plasma diagnostics.

Same subject as 22.67[J] Prereq: 22.611[J] Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 4-4-4 units

See description under subject 22.67[J] .

J. Hare, A. White

8.681, 8.682 Selected Topics in Fluid and Plasma Physics

Prereq: 22.611[J] G (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Presentation of topics of current interest, with content varying from year to year. Subject not routinely offered; given when interest is indicated.

Consult M. Porkolab

Nuclear and Particle Physics

8.701 introduction to nuclear and particle physics.

Prereq: None. Coreq: 8.321 G (Fall) 3-0-9 units

The phenomenology and experimental foundations of particle and nuclear physics; the fundamental forces and particles, composites. Interactions of particles with matter, and detectors. SU(2), SU(3), models of mesons and baryons. QED, weak interactions, parity violation, lepton-nucleon scattering, and structure functions. QCD, gluon field and color. W and Z fields, electro-weak unification, the CKM matrix. Nucleon-nucleon interactions, properties of nuclei, single- and collective- particle models. Electron and hadron interactions with nuclei. Relativistic heavy ion collisions, and transition to quark-gluon plasma.

8.711 Nuclear Physics

Prereq: 8.321 and 8.701 G (Spring) 4-0-8 units

Modern, advanced study in the experimental foundations and theoretical understanding of the structure of nuclei, beginning with the two- and three-nucleon problems. Basic nuclear properties, collective and single-particle motion, giant resonances, mean field models, interacting boson model. Nuclei far from stability, nuclear astrophysics, big-bang and stellar nucleosynthesis. Electron scattering: nucleon momentum distributions, scaling, olarization observables. Parity-violating electron scattering. Neutrino physics. Current results in relativistic heavy ion physics and hadronic physics. Frontiers and future facilities.

8.712 Advanced Topics in Nuclear Physics

Prereq: 8.711 or permission of instructor G (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Subject for experimentalists and theorists with rotation of the following topics: (1) Nuclear chromodynamics-- introduction to QCD, structure of nucleons, lattice QCD, phases of hadronic matter; and relativistic heavy ion collisions. (2) Medium-energy physics-- nuclear and nucleon structure and dynamics studied with medium- and high-energy probes (neutrinos, photons, electrons, nucleons, pions, and kaons). Studies of weak and strong interactions.

8.751[J] Quantum Technology and Devices

Same subject as 22.51[J] Subject meets with 22.022 Prereq: 22.11 G (Spring) 3-0-9 units

See description under subject 22.51[J] .

P. Cappellaro

8.781, 8.782 Selected Topics in Nuclear Theory

Prereq: 8.323 G (Fall, Spring) Not offered regularly; consult department 3-0-9 units

Presents topics of current interest in nuclear structure and reaction theory, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

Consult E. Farhi

8.811 Particle Physics

Prereq: 8.701 G (Fall) 3-0-9 units

Modern review of particles, interactions, and recent experiments. Experimental and analytical methods. QED, electroweak theory, and the Standard Model as tested in recent key experiments at ee and pp colliders. Mass generation, W, Z, and Higgs physics. Weak decays of mesons, including heavy flavors with QCD corrections. Mixing phenomena for K, D, B mesons and neutrinos. CP violation with results from B-factories. Future physics expectations: Higgs, SUSY, sub-structure as addressed by new experiments at the LHC collider.

8.812 Graduate Experimental Physics

Prereq: 8.701 G (IAP) Not offered regularly; consult department 1-8-3 units

Provides practical experience in particle detection with verification by (Feynman) calculations. Students perform three experiments; at least one requires actual construction following design. Topics include Compton effect, Fermi constant in muon decay, particle identification by time-of-flight, Cerenkov light, calorimeter response, tunnel effect in radioactive decays, angular distribution of cosmic rays, scattering, gamma-gamma nuclear correlations, and modern particle localization.

8.821 String Theory

Prereq: 8.324 Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units Credit cannot also be received for 8.251

An introduction to string theory. Basics of conformal field theory; light-cone and covariant quantization of the relativistic bosonic string; quantization and spectrum of supersymmetric 10-dimensional string theories; T-duality and D-branes; toroidal compactification and orbifolds; 11-dimensional supergravity and M-theory. Meets with 8.251 when offered concurrently.

8.831 Supersymmetric Quantum Field Theories

Prereq: Permission of instructor Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units Can be repeated for credit.

Topics selected from the following: SUSY algebras and their particle representations; Weyl and Majorana spinors; Lagrangians of basic four-dimensional SUSY theories, both rigid SUSY and supergravity; supermultiplets of fields and superspace methods; renormalization properties, and the non-renormalization theorem; spontaneous breakdown of SUSY; and phenomenological SUSY theories. Some prior knowledge of Noether's theorem, derivation and use of Feynman rules, l-loop renormalization, and gauge theories is essential.

8.851 Effective Field Theory

Prereq: 8.324 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units Credit cannot also be received for 8.S851

Covers the framework and tools of effective field theory, including: identifying degrees of freedom and symmetries; power counting expansions (dimensional and otherwise); field redefinitions, bottom-up and top-down effective theories; fine-tuned effective theories; matching and Wilson coefficients; reparameterization invariance; and advanced renormalization group techniques. Main examples are taken from particle and nuclear physics, including the Soft-Collinear Effective Theory.

8.871 Selected Topics in Theoretical Particle Physics

Prereq: 8.323 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-0-9 units Can be repeated for credit.

Presents topics of current interest in theoretical particle physics, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.872 Selected Topics in Theoretical Particle Physics

8.881, 8.882 selected topics in experimental particle physics.

Prereq: 8.811 G (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Presents topics of current interest in experimental particle physics, with content varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

Space Physics and Astrophysics

8.901 astrophysics i.

Prereq: Permission of instructor G (Spring) 3-0-9 units

Size and time scales. Historical astronomy. Astronomical instrumentation. Stars: spectra and classification. Stellar structure equations and survey of stellar evolution. Stellar oscillations. Degenerate and collapsed stars; radio pulsars. Interacting binary systems; accretion disks, x-ray sources. Gravitational lenses; dark matter. Interstellar medium: HII regions, supernova remnants, molecular clouds, dust; radiative transfer; Jeans' mass; star formation. High-energy astrophysics: Compton scattering, bremsstrahlung, synchrotron radiation, cosmic rays. Galactic stellar distributions and populations; Oort constants; Oort limit; and globular clusters.

8.902 Astrophysics II

Prereq: 8.901 G (Fall) 3-0-9 units

Galactic dynamics: potential theory, orbits, collisionless Boltzmann equation, etc. Galaxy interactions. Groups and clusters; dark matter. Intergalactic medium; x-ray clusters. Active galactic nuclei: unified models, black hole accretion, radio and optical jets, etc. Homogeneity and isotropy, redshift, galaxy distance ladder. Newtonian cosmology. Roberston-Walker models and cosmography. Early universe, primordial nucleosynthesis, recombination. Cosmic microwave background radiation. Large-scale structure, galaxy formation.

M. McDonald

8.913 Plasma Astrophysics I

Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units

For students interested in space physics, astrophysics, and plasma physics in general. Magnetospheres of rotating magnetized planets, ordinary stars, neutron stars, and black holes. Pulsar models: processes for slowing down, particle acceleration, and radiation emission; accreting plasmas and x-ray stars; stellar winds; heliosphere and solar wind- relevant magnetic field configuration, measured particle distribution in velocity space and induced collective modes; stability of the current sheet and collisionless processes for magnetic reconnection; theory of collisionless shocks; solitons; Ferroaro-Rosenbluth sheet; solar flare models; heating processes of the solar corona; Earth's magnetosphere (auroral phenomena and their interpretation, bowshock, magnetotail, trapped particle effects); relationship between gravitational (galactic) plasmas and electromagnetic plasmas. 8.913 deals with heliospheric, 8.914 with extra-heliospheric plasmas.

8.914 Plasma Astrophysics II

Prereq: Permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units

8.921 Stellar Structure and Evolution

Observable stellar characteristics; overview of observational information. Principles underlying calculations of stellar structure. Physical processes in stellar interiors; properties of matter and radiation; radiative, conductive, and convective heat transport; nuclear energy generation; nucleosynthesis; and neutrino emission. Protostars; the main sequence, and the solar neutrino flux; advanced evolutionary stages; variable stars; planetary nebulae, supernovae, white dwarfs, and neutron stars; close binary systems; and abundance of chemical elements.

8.942 Cosmology

Prereq: Permission of instructor Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units

Thermal backgrounds in space. Cosmological principle and its consequences: Newtonian cosmology and types of "universes"; survey of relativistic cosmology; horizons. Overview of evolution in cosmology; radiation and element synthesis; physical models of the "early stages." Formation of large-scale structure to variability of physical laws. First and last states. Some knowledge of relativity expected. 8.962 recommended though not required.

8.952 Particle Physics of the Early Universe

Prereq: 8.323 ; Coreq: 8.324 Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units

Basics of general relativity, standard big bang cosmology, thermodynamics of the early universe, cosmic background radiation, primordial nucleosynthesis, basics of the standard model of particle physics, electroweak and QCD phase transition, basics of group theory, grand unified theories, baryon asymmetry, monopoles, cosmic strings, domain walls, axions, inflationary universe, and structure formation.

8.962 General Relativity

Prereq: 8.07 , 18.03 , and 18.06 G (Spring) 4-0-8 units

The basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.

8.971 Astrophysics Seminar

Prereq: Permission of instructor G (Fall, Spring) Not offered regularly; consult department 2-0-4 units Can be repeated for credit.

Advanced seminar on current topics, with a different focus each term. Typical topics: astronomical instrumentation, numerical and statistical methods in astrophysics, gravitational lenses, neutron stars and pulsars.

Consult D. Chakrabarty

8.972 Astrophysics Seminar

Advanced seminar on current topics, with a different focus each term. Typical topics: gravitational lenses, active galactic nuclei, neutron stars and pulsars, galaxy formation, supernovae and supernova remnants, brown dwarfs, and extrasolar planetary systems. The presenter at each session is selected by drawing names from a hat containing those of all attendees. Offered if sufficient interest is indicated.

8.981, 8.982 Selected Topics in Astrophysics

Prereq: Permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit.

Topics of current interest, varying from year to year. Subject not routinely offered; given when sufficient interest is indicated.

8.995 Practical Experience in Physics

Prereq: None G (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit.

For Course 8 students participating in off-campus experiences in physics. Before registering for this subject, students must have an internship offer from a company or organization, must identify a Physics advisor, and must receive prior approval from the Physics Department. Upon completion of the project, student must submit a letter from the company or organization describing the work accomplished, along with a substantive final report from the student approved by the MIT advisor. Consult departmental academic office.

8.998 Teaching and Mentoring MIT Students

Prereq: None U (Fall, Spring) 2-0-1 units

Designed for first-time physics mentors and others interested in improving their knowledge and skills in teaching one-on-one and in small groups, particularly TEAL TAs and graduate student TAs. Topics include: cognition, metacognition, and the role of affect; communication skills (practice listening, questioning, and eliciting student ideas); the roles of motivation and mindset in learning; fostering belonging and self-efficacy through peer mentorship; facilitating small-group interactions to enhance peer instruction and learning; physics-specific learning strategies, such as how to teach/learn problem solving; research-based techniques for effective mentorship in STEM. Includes a one-hour class on pedagogy topics, a one-hour weekly Physics Mentoring Community of Practice meeting, and weekly assignments to read or watch material in preparation for class discussions, and written reflections before class.

8.S301 Special Subject: Physics

Prereq: Permission of instructor G (Spring) Units arranged

Covers topics in Physics that are not offered in the regular curriculum. Limited enrollment; preference to Physics graduate students.

A. Lightman

8.S308 Special Subject: Physics (New)

Prereq: None G (IAP) Units arranged

J. Tailleur

8.S372 Special Subject: Physics

Prereq: None G (Spring) Not offered regularly; consult department 3-0-9 units

Covers topics in Physics that are not offered in the regular curriculum.

8.S373 Special Subject: Physics

Prereq: None Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units

8.S421 Special Subject: Physics

Prereq: Permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) Units arranged Can be repeated for credit.

W. Ketterle

8.S998 Special Subject: Physics

Prereq: None U (Fall, Spring) Not offered regularly; consult department Units arranged [P/D/F]

8.THG Graduate Physics Thesis

Prereq: Permission of instructor G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.

Program of research leading to the writing of an SM, PhD, or ScD thesis; to be arranged by the student and an appropriate MIT faculty member.

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Physics Graduate Student Council

Recommendations

Pictured: a very intense sunset near Kresge auditorium

Known surveys and recommendations issued to the department:

• 2015 – summary report of the qualifying exam survey
• June 2020 –  Recommendations to the Physics Community about Justice, Equity, Diversity, and Inclusion  (PVC-hosted  progress scorecard )
• July 2020 – Endorsement of Physics and Statistics PhD
• August 2020 – recommendations on administration of the written qualifying exam during the pandemic
• September 2020 – PGSC-GAGA survey of students/faculty on metrics of graduate student success
• November 2020 – SPS and PGSC survey on student support and communication resources
• January 2021 – Endorsement of concerned graduate student recommendations
• February 2021 – Recommendation on the General Exams
• May 2021 – Oral Exam Survey 2021