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DEPARTMENT OF PHYSICS
DEPARTMENT OF PHYSICS
The Department of Physics oers undergraduate, graduate,and postgraduate training, with a wide range of options forspecialization.
The emphasis of both the undergraduate curriculum and thegraduate program is on understanding the fundamental principlesthat appear to govern the behavior of the physical world, includingspace and time and matter and energy in all its forms, from thesubatomic to the cosmological and from the elementary to thecomplex.
The Department of Physics strives to be at the forefront of manyareas where new physics can be found. Consequently, thedepartment works on problems where extreme conditions may revealnew behavior: from clusters of galaxies or the entire universe toelementary particles or the strings that may be the substructure ofthese particles; from collisions of nuclei at relativistic velocities thatmake droplets of matter hotter than anything since the Big Bangto laser-cooled atoms so cold that their wave functions overlap,resulting in a macroscopic collective state, the Bose-Einsteincondensate; and from individual atoms to unusual materials, such ashigh-temperature superconductors and those that are important inbiology. Pushing the limits provides the opportunity to observe newgeneral principles and test theories of the structure and behavior ofmatter and energy.
Undergraduate Study
Bachelor of Science in Physics (Course 8)An undergraduate degree in physics provides an excellent basisnot only for graduate study in physics and related elds, but alsofor professional work in such elds as astrophysics, biophysics,engineering and applied physics, geophysics, management,law, or medicine. The undergraduate curriculum oers studentsthe opportunity to acquire a deep conceptual understanding offundamental physics. The core departmental requirements beginthis process. The student then chooses one of two options tocomplete the degree: the focused option (http://catalog.mit.edu/degree-charts/physics-course-8/#focusedoptiontext) is designed forstudents who plan to pursue physics as a career, and is an excellentchoice for students who want to experience as deep an engagementas possible with physics; the flexible option (http://catalog.mit.edu/degree-charts/physics-course-8/#flexibleoptiontext) also providesa very strong physics framework, and gives students who may wantto pursue additional academic interests the flexibility to do so.Both programs prepare students very well for graduate studies inphysics, as well as for a variety of academic or research-relatedcareers. Either option provides a considerable amount of time forexploration through electives. Students proceed at the pace anddegree of specialization best suited to their individual capacities.
Both options lead to the same degree: the Bachelor of Science inPhysics.
Physics: Focused OptionThis option—which includes three terms of quantum mechanics, 36units of laboratory experience, and a thesis—is ideal preparation fora career in physics.
In the second year, students take:
8.03 Physics III 128.033 Relativity 128.04 Quantum Physics I 128.044 Statistical Physics I 128.223 Classical Mechanics II 6
Important skills for experimentation in physics may be acquiredby starting an Undergraduate Research Opportunities Program(UROP) (http://catalog.mit.edu/mit/undergraduate-education/academic-research-options/undergraduate-research-opportunities-program) project.
In the third year, students normally take laboratory subjects:
8.13& 8.14
Experimental Physics Iand Experimental Physics II
36
8.05& 8.06
Quantum Physics IIand Quantum Physics III
24
Students should also begin to take the restricted elective subjects,one in mathematics and at least two in physics. The mathematicssubjects 18.04 Complex Variables with Applications, 18.075Methods for Scientists and Engineers, and 18.06 Linear Algebra areparticularly popular with physics majors. Topical elective subjectsin astrophysics, biological physics, condensed matter, plasma, andnuclear and particle physics allow students to gain an appreciationof the forefronts of modern physics. Students intending to go on tograduate school in physics are encouraged to take the theoreticalphysics sequence:
8.07 Electromagnetism II 128.08 Statistical Physics II 128.09 Classical Mechanics III 12
An important component of this option is the thesis, which is aphysics research project carried out under the guidance of a facultymember. Many thesis projects grow naturally out of UROP projects.Students should have some idea of a thesis topic by the middleof the junior year. A thesis proposal must be submitted beforeregistering for thesis units and no later than Add Date of the fall termof the senior year.
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DEPARTMENT OF PHYSICS
A relatively large amount of elective time usually becomes availableduring the fourth year and can be used either to deepen one'sbackground in physics or to explore other disciplines.
Physics: Flexible OptionThis option is designed for students who wish to develop a strongbackground in the fundamentals of physics and then build onthis foundation as they prepare for career paths that may or maynot involve a graduate degree in physics. Many students nd anunderstanding of the basic concepts of physics and an appreciationof the physicist's approach to problem solving an excellentpreparation 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 makesit more possible for students with diverse intellectual interests topursue a second major in another department.
The option begins with the core subjects:
8.01 Physics I 128.02 Physics II 128.03 Physics III 128.04 Quantum Physics I 128.044 Statistical Physics I 128.21 Physics of Energy 12
or 8.223 Classical Mechanics II
Students round out their foundation material with either anadditional quantum mechanics subject (8.05 Quantum PhysicsII) or a subject in relativity (8.20 Introduction to Special Relativityor 8.033 Relativity). There is an experimental requirement of 8.13Experimental Physics I or, with the approval of the department, alaboratory subject of similar intensity in another department, anexperimental research project or senior thesis, or an experimentallyoriented summer externship. An exploration requirement consistsof one elective subject in physics. Students can satisfy thedepartmental portion of the Communication Requirement by takingtwo of the following subjects:
8.06 Quantum Physics III 128.13 Experimental Physics I 188.14 Experimental Physics II 188.225[J] Einstein, Oppenheimer, Feynman:
Physics in the 20th Century12
8.226 Forty-three Orders of Magnitude 128.287[J] Observational Techniques of Optical
Astronomy15
The department and the Subcommittee on the CommunicationRequirement may accept substitution of one of the department's tworequired CI-M subjects with a CI-M subject in another department if itforms a natural part of the student's physics program.
Students following this option must also complete a focusrequirement—three subjects forming one intellectually coherent unitin some area (not necessarily physics), subject to the approval of thedepartment and separate from those used by the student to satisfythe HASS requirement. Areas of focus chosen by students haveincluded astronomy, biology, computational physics, theoreticalphysics, nanotechnology, history of science, science and technologypolicy, philosophy, and science teaching. Some students maychoose to satisfy their experimental and exploration requirements inthe same area as their focus; others may opt for greater breadth bychoosing other elds to fulll these requirements.
Although students may choose this option at any time in theirundergraduate career, many decide on the flexible major during theirsophomore year in order to have enough time to cra a program thatbest suits their individual needs. Specic subject choices for theexperimental and focus requirements require the written approval ofthe Flexible Program coordinator, Dr. Sean P. Robinson.
Minor in PhysicsThe Minor in Physics provides a solid foundation for the pursuit ofa broad range of professional activities in science and engineering.The requirements for a Minor in Physics are as follows:
18.03 Dierential Equations 1 12Select ve Course 8 subjects beyond the GeneralInstitute Requirements
57-60
Total Units 69-72
1 18.032 Dierential Equations is also acceptable.
Students should submit a completed Minor Application Form toPhysics Academic Programs, Room 4-315. The Physics Department'sminor coordinator is Catherine Modica. See UndergraduateEducation for more information on minor programs (http://catalog.mit.edu/mit/undergraduate-education/academic-programs/minors).
Minor in AstronomyThe Minor in Astronomy (http://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/astronomy), oered jointly withthe Department of Earth, Atmospheric, and Planetary Sciences,covers the observational and theoretical foundations of astronomy.For a description of the minor, see Interdisciplinary Programs.
InquiriesAdditional information concerning degree programs and researchactivities may be obtained by contacting the department oce([email protected]), Room 4-315, 617-253-4841.
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DEPARTMENT OF PHYSICS
Graduate Study
The Physics Department oers programs leading to the degrees ofMaster of Science in Physics and Doctor of Philosophy.
Admission Requirements for Graduate StudyStudents intending to pursue graduate work in physics should haveas a background the equivalent of the requirements for the Bachelorof Science in Physics from MIT. However, students may make upsome deciencies over the course of their graduate work.
Master of Science in PhysicsThe normal degree program in the department leads to a PhDin Physics. Admission to a master's degree program in Physicsis available only in special cases (e.g., US military ocers). Therequirements for the Master of Science in Physics are the sameas the General Degree Requirements (http://catalog.mit.edu/mit/graduate-education/general-degree-requirements) listed underGraduate Education. A master's thesis must represent a piece ofindependent research work in any of the elds described below,and must be carried out under the supervision of a departmentfaculty member. No xed time is set for the completion of a master'sprogram; two years of work is a rough guideline. There is nolanguage requirement for this degree.
Doctor of PhilosophyCandidates for the Doctor of Philosophy or Doctor of Science areexpected to enroll in those basic graduate subjects that preparethem for the general examination, which must be passed no laterthan in the seventh term aer initial enrollment. No specic subjectsof study are prescribed, except for the requirement of two subjectsin the candidate's doctoral research area and two subjects outsidethe candidate's eld of specialization (breadth requirement). Half ofthe breadth requirement may be satised through a departmentallyapproved industrial internship. The doctoral thesis must representa substantial piece of original research, carried out under thesupervision of a department faculty member.
The Physics Department faculty members oer subjects ofinstruction and are engaged in research in a variety of elds inexperimental and theoretical physics. This broad spectrum ofactivities is organized in the divisional structure of the department,presented below. Graduate students are encouraged to contactfaculty members in the division of their choice to inquire aboutopportunities for research, and to pass through an apprenticeship(by signing up for Pre-Thesis Research) as a rst step toward anengagement in independent research for a doctoral thesis.
Research DivisionsFaculty and students in the Department of Physics are generallyaliated 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 ofthe work of various interdisciplinary laboratories and centers,including the Center for Materials Science and Engineering, FrancisBitter Magnet Laboratory, Haystack Observatory, Laboratory forNuclear Science, Microsystems Technology Laboratories, MIT KavliInstitute for Astrophysics and Space Research, Plasma Science andFusion Center, Research Laboratory of Electronics, and SpectroscopyLaboratory. Additional information can be found under Research andStudy (http://catalog.mit.edu/mit/research). These facilities provideclose relationships among the research activities of a number ofMIT departments and give students opportunities for contact withresearch carried out in disciplines other than physics.
InquiriesAdditional information on degree programs, research activities,admissions, nancial aid, teaching and research assistantshipsmay be obtained by contacting the department oce ([email protected]), Room 4-315, 617-253-4851.
Faculty and Teaching Sta
Peter H. Fisher, PhDProfessor of PhysicsHead, Department of Physics
Nergis Mavalvala, PhDCurtis (1963) and Kathleen Marble ProfessorProfessor of PhysicsAssociate Head, Department of Physics
ProfessorsRaymond Ashoori, PhDProfessor of Physics
John Winston Belcher, PhDClass of 1922 ProfessorProfessor of Physics
Edmund Bertschinger, PhDProfessor of Physics
Wit Busza, PhDProfessor of Physics
Claude R. Canizares, PhDBruno B. Rossi Distinguished Professor in Experimental Physics
Department of Physics | 5
DEPARTMENT OF PHYSICS
Deepto Chakrabarty, PhDProfessor of Physics
Arup K. Chakraborty, PhDRobert T. Haslam (1911) Professor in Chemical EngineeringProfessor of Biological EngineeringProfessor of ChemistryProfessor of PhysicsCore Faculty, Institute for Medical Engineering and Science
Min Chen, PhDProfessor of Physics
Isaac L. Chuang, PhDProfessor of Electrical EngineeringProfessor of Physics
Janet Conrad, PhDProfessor of Physics
Bruno Coppi, PhDProfessor of Physics
Joseph A. Formaggio, PhDProfessor of Physics
Nuh Gedik, PhDProfessor of Physics
Alan Guth, PhDVictor F. Weisskopf Professor in Physics
Jacqueline N. Hewitt, PhDJulius A. Stratton ProfessorProfessor of Physics
Scott A. Hughes, PhDProfessor of Physics
Robert L. Jae, PhDOtto (1939) and Jane Morningstar Professor of ScienceProfessor of Physics
Pablo Jarillo-Herrero, PhDCecil and Ida Green Professor of Physics
John D. Joannopoulos, PhDFrancis Wright Davis ProfessorProfessor of Physics
Steven G. Johnson, PhDProfessor of MathematicsProfessor of Physics(On leave, fall)
David I. Kaiser, PhDGermeshausen Professor of the History of ScienceProfessor of Physics
Mehran Kardar, PhDFrancis L. Friedman Professor of Physics
Wolfgang Ketterle, PhDJohn D. MacArthur ProfessorProfessor of Physics
Patrick A. Lee, PhDWilliam and Emma Rogers ProfessorProfessor of Physics
Leonid Levitov, PhDProfessor of Physics
Hong Liu, PhDProfessor of Physics
Seth Lloyd, PhDNam Pyo Suh ProfessorProfessor of Mechanical EngineeringProfessor of Physics
Richard G. Milner, PhDProfessor of Physics
Leonid A. Mirny, PhDProfessor of PhysicsProfessor of Medical Engineering and ScienceCore Faculty, Institute for Medical Engineering and Science
Christoph M. E. Paus, PhDProfessor of Physics
Miklos Porkolab, PhDProfessor of Physics
David E. Pritchard, PhDCecil and Ida Green Professor of Physics
Krishna Rajagopal, PhDProfessor of Physics
Robert P. Redwine, PhDProfessor of Physics
Gunther M. Roland, PhDProfessor of Physics
Sara Seager, PhDClass of 1941 Professor of Planetary SciencesProfessor of PhysicsProfessor of Aeronautics and Astronautics
Robert A. Simcoe, PhDFrancis L. Friedman Professor of PhysicsProfessor of Physics
6 | Department of Physics
DEPARTMENT OF PHYSICS
Marin Soljačić, PhDProfessor of Physics
Iain Stewart, PhDProfessor of Physics
Washington Taylor IV, PhDProfessor of Physics
Max Erik Tegmark, PhDProfessor of Physics
Samuel C. C. Ting, PhDThomas D. Cabot Institute ProfessorProfessor of Physics
Senthil Todadri, PhDProfessor of Physics
Vladan Vuletić, PhDLester Wolfe ProfessorProfessor of Physics
Xiao-Gang Wen, PhDCecil and Ida Green Professor in Physics
Frank Wilczek, PhDHerman Feshbach (1942) Professor of Physics
Boleslaw Wyslouch, PhDProfessor of Physics
Barton Zwiebach, PhDProfessor of Physics
Martin Wolfram Zwierlein, PhDProfessor of Physics
Associate ProfessorsJoseph George Checkelsky, PhDAssociate Professor of Physics
Ibrahim I. Cisse, PhDAssociate Professor of Physics
William Detmold, PhDAssociate Professor of Physics
Matthew J. Evans, PhDAssociate Professor of Physics
Anna L. Frebel, PhDAssociate Professor of Physics
Liang Fu, PhDBiedenharn Career Development ProfessorAssociate Professor of Physics
Je Gore, PhDAssociate Professor of Physics
Aram W. Harrow, PhDAssociate Professor of Physics
Markus Klute, PhDAssociate Professor of Physics
Yen-Jie Lee, PhDAssociate Professor of Physics
Nuno F. Loureiro, PhDAssociate Professor of Nuclear Science and EngineeringAssociate Professor of Physics
Tracy Robyn Slatyer, PhDZacharias Career Development ProfessorAssociate Professor of Physics
Jesse Thaler, PhDAssociate Professor of Physics
Mark Vogelsberger, PhDAssociate Professor of Physics
Michael Williams, PhDAssociate Professor of Physics
Assistant ProfessorsRiccardo Comin, PhDAssistant Professor of Physics
Ian J. M. Crosseld, PhDAssistant Professor of Physics
Netta Engelhardt, PhDAssistant Professor of Physics
Nikta Fakhri, PhDThomas D. and Virginia W. Cabot ProfessorAssistant Professor of Physics
Daniel Harlow, PhDAssistant Professor of Physics
Philip Harris, PhDAssistant Professor of Physics
Or Hen, PhDAssistant Professor of Physics
Long Ju, PhDAssistant Professor of Physics
Erin Kara, PhDAssistant Professor of Physics
Department of Physics | 7
DEPARTMENT OF PHYSICS
Kiyoshi Masui, PhDAssistant Professor of Physics
Michael McDonald, PhDAssistant Professor of Physics
Max Metlitski, PhDAssistant Professor of Physics
Kerstin Perez, PhDAssistant Professor of Physics
Phiala E. Shanahan, PhDAssistant Professor of Physics
Salvatore Vitale, PhDAssistant Professor of Physics
Lindley Winslow, PhDZacharias Career Development ProfessorAssistant Professor of Physics
Professors of the PracticeWilliam D. Oliver, PhDProfessor of the Practice of Physics
Adjunct ProfessorsWilliam A. Barletta, PhDAdjunct Professor of Physics
Senior LecturersPeter Dourmashkin, PhDSenior Lecturer in Physics
LecturersSean P. Robinson, PhDLecturer in PhysicsTechnical Instructor of Physics
Michelle Tomasik, PhDLecturer in Physics
Technical InstructorsCaleb C. Bonyun, MSTechnical Instructor of Physics
Lauren Dana, BSTechnical Instructor of Physics
Kay Lowdon, BSTechnical Instructor of Physics
Aidan MacDonagh, BSETechnical Instructor of Digital Learning
Andy Neely, BSTechnical Instructor of Physics
Gladys Velez Caideco, BSTechnical Instructor of Physics
Joshua Wolfe, BSTechnical Instructor of Physics
Research Sta
Senior Research ScientistsEarl S. Marmar, PhDSenior Research Scientist of Physics
Jagadeesh Moodera, PhDSenior Research Scientist of Physics
Richard J. Temkin, PhDSenior Research Scientist of Physics
Professors Emeriti
Ulrich J. Becker, ScDProfessor Emeritus of Physics
George B. Benedek, PhDAlfred H. Caspary Professor Emeritus of PhysicsProfessor Emeritus of Biological Physics
Ahmet Nihat Berker, PhDProfessor Emeritus of Physics
Aron M. Bernstein, PhDProfessor Emeritus of Physics
William Bertozzi, PhDProfessor Emeritus of Physics
Robert J. Birgeneau, PhDProfessor Emeritus of Physics
Hale V. Bradt, PhDProfessor Emeritus of Physics
George W. Clark, PhDProfessor Emeritus of Physics
Thomas H. Dupree, PhDProfessor Emeritus of Nuclear Science and EngineeringProfessor Emeritus of Physics
Edward Farhi, PhDCecil and Ida Green Professor Emeritus of Physics
Daniel Z. Freedman, PhDProfessor Emeritus of MathematicsProfessor Emeritus of Physics
8 | Department of Physics
DEPARTMENT OF PHYSICS
Jerome I. Friedman, PhDInstitute Professor EmeritusProfessor Emeritus of Physics
Jerey Goldstone, PhDProfessor Emeritus of Physics
Thomas J. Greytak, PhDProfessor Emeritus of Physics
Lee Grodzins, PhDProfessor Emeritus of Physics
Erich P. Ippen, PhDElihu Thomson Professor EmeritusProfessor Emeritus of PhysicsProfessor Emeritus of Electrical Engineering
Roman Wladimir Jackiw, PhDJerrold Zacharias Professor Emeritus of PhysicsProfessor Emeritus of Physics
Paul Christopher Joss, PhDProfessor Emeritus of Physics
Marc A. Kastner, PhDDonner Professor of Science EmeritusProfessor Emeritus of Physics
Vera Kistiakowsky, PhDProfessor Emerita of Physics
Daniel Kleppner, PhDLester Wolfe Professor EmeritusProfessor Emeritus of Physics
Stanley B. Kowalski, PhDProfessor Emeritus of Physics
J. David Litster, PhDProfessor Emeritus of Physics
Earle L. Lomon, PhDProfessor Emeritus of Physics
June Lorraine Matthews, PhDProfessor Emerita of Physics
Ernest J. Moniz, PhDCecil and Ida Green Distinguished Professor EmeritusProfessor Emeritus of PhysicsProfessor Emeritus of Engineering Systems
John W. Negele, PhDWilliam A. Coolidge Professor EmeritusProfessor Emeritus of Physics
Irwin A. Pless, PhDProfessor Emeritus of Physics
Saul A. Rappaport, PhDProfessor Emeritus of Physics
Lawrence Rosenson, PhDProfessor Emeritus of Physics
Paul L. Schechter, PhDWilliam A. M. Burden Professor Emeritus in Astrophysics
Rainer Weiss, PhDProfessor Emeritus of Physics
James E. Young, PhDProfessor Emeritus of Physics
Undergraduate Subjects
8.01 Physics IPrereq: NoneU (Fall)3-2-7 units. PHYSICS ICredit cannot also be received for 8.011, 8.012, 8.01L, ES.801
Introduces classical mechanics. Space and time: straight-linekinematics; motion in a plane; forces and static equilibrium; particledynamics, with force and conservation of momentum; relativeinertial frames and non-inertial force; work, potential energy andconservation of energy; kinetic theory and the ideal gas; rigid bodiesand rotational dynamics; vibrational motion; conservation of angularmomentum; central force motions; fluid mechanics. Subject taughtusing the TEAL (Technology-Enabled Active Learning) format whichfeatures students working in groups of three, discussing concepts,solving problems, and doing table-top experiments with the aid ofcomputer data acquisition and analysis.J. Formaggio, P. Dourmashkin
8.011 Physics IPrereq: NoneU (Spring)5-0-7 units. PHYSICS ICredit cannot also be received for 8.01, 8.012, 8.01L, ES.801
Introduces classical mechanics. Space and time: straight-linekinematics; motion in a plane; forces and equilibrium; experimentalbasis 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 rotationaldynamics. Designed for students with previous experience in 8.01;the subject is designated as 8.01 on the transcript.D. Pritchard
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DEPARTMENT OF PHYSICS
8.012 Physics IPrereq: NoneU (Fall)5-0-7 units. PHYSICS ICredit cannot also be received for 8.01, 8.011, 8.01L, ES.801
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 elementarycalculus freely; concurrent registration in a math subject moreadvanced than 18.01 is recommended. In addition to covering thetheoretical subject matter, students complete a small experimentalproject of their own design. Freshmen admitted via AP or MathDiagnostic for Physics Placement results.M. Soljacic
8.01L Physics IPrereq: NoneU (Fall, IAP)3-2-7 units. PHYSICS ICredit cannot also be received for 8.01, 8.011, 8.012, ES.801
Introduction to classical mechanics (see description under 8.01).Includes components of the TEAL (Technology-Enabled ActiveLearning) format. Material covered over a longer interval so that thesubject is completed by the end of the IAP. Substantial emphasisgiven to reviewing and strengthening necessary mathematicstools, as well as basic physics concepts and problem-solving skills.Content, depth, and diculty is otherwise identical to that of 8.01.The subject is designated as 8.01 on the transcript.P. Jarillo-Herrero
8.02 Physics IIPrereq: Calculus I (GIR) and Physics I (GIR)U (Fall, Spring)3-2-7 units. PHYSICS IICredit cannot also be received for 8.021, 8.022, ES.802, ES.8022
Introduction to electromagnetism and electrostatics: electriccharge, Coulomb's law, electric structure of matter; conductorsand dielectrics. Concepts of electrostatic eld and potential,electrostatic energy. Electric currents, magnetic elds and Ampere'slaw. Magnetic materials. Time-varying elds and Faraday's lawof induction. Basic electric circuits. Electromagnetic waves andMaxwell's equations. Subject taught using the TEAL (TechnologyEnabled Active Learning) studio format which utilizes small groupinteraction and current technology to help students develop intuitionabout, and conceptual models of, physical phenomena.J. Belcher, I. Cisse
8.021 Physics IIPrereq: Calculus I (GIR), Physics I (GIR), and permission of instructorU (Fall)5-0-7 units. PHYSICS IICredit cannot also be received for 8.02, 8.022, ES.802, ES.8022
Introduction to electromagnetism and electrostatics: electriccharge, Coulomb's law, electric structure of matter; conductorsand dielectrics. Concepts of electrostatic eld and potential,electrostatic energy. Electric currents, magnetic elds and Ampere'slaw. Magnetic materials. Time-varying elds and Faraday'slaw of induction. Basic electric circuits. Electromagnetic wavesand Maxwell's equations. Designed for students with previousexperience in 8.02; the subject is designated as 8.02 on thetranscript. Enrollment limited.J. Checkelsky
8.022 Physics IIPrereq: Physics I (GIR); Coreq: Calculus II (GIR)U (Fall, Spring)5-0-7 units. PHYSICS IICredit cannot also be received for 8.02, 8.021, ES.802, ES.8022
Parallel to 8.02, but more advanced mathematically. Someknowledge of vector calculus assumed. Maxwell's equations, inboth dierential and integral form. Electrostatic and magneticvector potential. Properties of dielectrics and magnetic materials.In addition to the theoretical subject matter, several experimentsin electricity and magnetism are performed by the students in thelaboratory.D. Harlow
8.03 Physics IIIPrereq: 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, coupledoscillations, and normal modes; vibrations of continuous systems;reflection and refraction; phase and group velocity. Optics; wavesolutions to Maxwell's equations; polarization; Snell's Law,interference, Huygens's principle, Fraunhofer diraction, andgratings.Y-J. Lee, R. Comin
10 | Department of Physics
DEPARTMENT OF PHYSICS
8.033 RelativityPrereq: Calculus II (GIR) and Physics II (GIR)U (Fall)5-0-7 units. REST
Einstein's postulates; consequences for simultaneity, timedilation, length contraction, and clock synchronization; Lorentztransformation; relativistic eects and paradoxes; Minkowskidiagrams; invariants and four-vectors; momentum, energy, andmass; particle collisions. Relativity and electricity; Coulomb'slaw; magnetic elds. Brief introduction to Newtonian cosmology.Introduction to some concepts of general relativity; principle ofequivalence. The Schwarzchild metric; gravitational red shi;particle and light trajectories; geodesics; Shapiro delay.S. Vitale
8.04 Quantum Physics IPrereq: 8.03 and (18.03 or 18.032)U (Spring)5-0-7 units. RESTCredit cannot also be received for 8.S04
Experimental basis of quantum physics: photoelectric eect,Compton scattering, photons, Franck-Hertz experiment, the Bohratom, electron diraction, deBroglie waves, and wave-particleduality of matter and light. Introduction to wave mechanics:Schroedinger's equation, wave functions, wave packets, probabilityamplitudes, stationary states, the Heisenberg uncertainty principle,and zero-point energies. Solutions to Schroedinger's equation inone dimension: transmission and reflection at a barrier, barrierpenetration, potential wells, the simple harmonic oscillator.Schroedinger's equation in three dimensions: central potentials andintroduction to hydrogenic systems.V. Vuletic, M. Vogelsberger
8.S04 Special Subject: Quantum Physics IPrereq: 8.03 and (18.03 or 18.032)U (Fall)2-0-10 units. RESTCredit cannot also be received for 8.04
Experimental version of 8.04, which oers a combination of onlineand in-person instruction. See description of 8.04. Licensed by theCommittee on Curricula as an acceptable alternative to 8.04 for Fall2017.R. Ashoori
8.044 Statistical Physics IPrereq: 8.03 and 18.03U (Spring)5-0-7 units
Introduction to probability, statistical mechanics, andthermodynamics. Random variables, joint and conditionalprobability densities, and functions of a random variable. Conceptsof macroscopic variables and thermodynamic equilibrium,fundamental assumption of statistical mechanics, microcanonicaland canonical ensembles. First, second, and third laws ofthermodynamics. Numerous examples illustrating a wide variety ofphysical phenomena such as magnetism, polyatomic gases, thermalradiation, electrons in solids, and noise in electronic devices.Concurrent enrollment in 8.04 is recommended.N. Fakhri
8.05 Quantum Physics IIPrereq: 8.04U (Fall)5-0-7 unitsCredit cannot also be received for 8.051
Together 8.05 and 8.06 cover quantum physics with applicationsdrawn from modern physics. General formalism of quantummechanics: states, operators, Dirac notation, representations,measurement theory. Harmonic oscillator: operator algebra, states.Quantum mechanics in three dimensions: central potentials and theradial equation, bound and scattering states, qualitative analysis ofwavefunctions. 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-Gordanseries and coecients, spin systems, and allotropic forms ofhydrogen.W. Detmold
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DEPARTMENT OF PHYSICS
8.051 Quantum Physics IIPrereq: 8.04 and permission of instructorU (Spring)2-0-10 unitsCredit cannot also be received for 8.05
Blended version of 8.05 using a combination of online andin-person instruction. Together with 8.06 covers quantumphysics with applications drawn from modern physics. Generalformalism of quantum mechanics: states, operators, Diracnotation, representations, measurement theory. Harmonicoscillator: operator algebra, states. Quantum mechanics in threedimensions: central potentials and the radial equation, bound andscattering states, qualitative analysis of wave functions. Angularmomentum: operators, commutator algebra, eigenvalues andeigenstates, spherical harmonics. Spin: Stern-Gerlach devices andmeasurements, nuclear magnetic resonance, spin and statistics.Addition of angular momentum: Clebsch-Gordan series andcoecients, spin systems, and allotropic forms of hydrogen. Limitedto 20.Fall: StaSpring: W. Detmold
8.06 Quantum Physics IIIPrereq: 8.05U (Spring)5-0-7 units
Continuation of 8.05. Units: natural units, scales of microscopicphenomena, applications. Time-independent approximationmethods: degenerate and nondegenerate perturbation theory,variational method, Born-Oppenheimer approximation, applicationsto atomic and molecular systems. The structure of one- and two-electron atoms: overview, spin-orbit and relativistic corrections,ne structure, variational approximation, screening, Zeeman andStark eects. Charged particles in a magnetic eld: Landau levelsand integer quantum hall eect. Scattering: general principles,partial waves, review of one-dimension, low-energy approximations,resonance, Born approximation. Time-dependent perturbationtheory. Students research and write a paper on a topic related to thecontent of 8.05 and 8.06.B. Zwiebach
8.07 Electromagnetism IIPrereq: 8.03 and 18.03U (Fall)4-0-8 units
Survey of basic electromagnetic phenomena: electrostatics,magnetostatics; electromagnetic properties of matter. Time-dependent electromagnetic elds and Maxwell's equations.Electromagnetic waves, emission, absorption, and scattering ofradiation. Relativistic electrodynamics and mechanics.A. Guth
8.08 Statistical Physics IIPrereq: 8.044 and 8.05U (Spring)4-0-8 units
Probability distributions for classical and quantum systems.Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditionsof thermodynamic equilibrium for homogenous and heterogenoussystems. Applications: non-interacting Bose and Fermi gases;mean eld theories for real gases, binary mixtures, magneticsystems, polymer solutions; phase and reaction equilibria, criticalphenomena. Fluctuations, correlation functions and susceptibilities,and Kubo formulae. Evolution of distribution functions: Boltzmannand Smoluchowski equations.Fall: StaSpring: L. Fu
8.09 Classical Mechanics IIISubject meets with 8.309Prereq: 8.223U (Fall)4-0-8 units
Covers Lagrangian and Hamiltonian mechanics, systems withconstraints, rigid body dynamics, vibrations, central forces,Hamilton-Jacobi theory, action-angle variables, perturbationtheory, and continuous systems. Provides an introduction to idealand viscous fluid mechanics, including turbulence, as well as anintroduction to nonlinear dynamics, including chaos. Students takinggraduate version complete dierent assignments.I. Stewart
12 | Department of Physics
DEPARTMENT OF PHYSICS
Undergraduate Laboratory and Special Project Subjects
8.13 Experimental Physics IPrereq: 8.04U (Fall, Spring)0-6-12 units. Institute LAB
Four fundamental laboratory experiments are carried out each term,covering most aspects of modern physics relating to names suchas Rutherford, Franck-Hertz, Hall, Ramsauer, Doppler, Fraunhofer,Faraday, Mossbauer, Compton, and Stern-Gerlach. Stresses basicexperimental techniques and data analysis, and written and oralpresentation of experiment results.J. Conrad, J. Formaggio, A. Levine, K. Perez
8.14 Experimental Physics IIPrereq: 8.05 and 8.13U (Spring)0-6-12 units
Four fundamental laboratory experiments are carried out each term,covering most aspects of modern physics relating to names suchas Rutherford, Franck-Hertz, Hall, Ramsauer, Doppler, Fraunhofer,Faraday, Mossbauer, Compton, and Stern-Gerlach. Stresses basicexperimental techniques and data analysis, and written and oralpresentation of experiment results. 8.14 requires knowledge ofquantum mechanics at the 8.05 level.G. Roland
8.18 Research Problems in Undergraduate PhysicsPrereq: Permission of instructorU (Fall, IAP, Spring, Summer)Units arranged [P/D/F]Can be repeated for credit.
Opportunity for undergraduates to engage in experimental ortheoretical research under the supervision of a sta member.Specic approval required in each case.Consult N. Mavalvala
8.19 Readings in PhysicsPrereq: NoneU (Fall, IAP, Spring, Summer)Units arranged [P/D/F]Can be repeated for credit.
Supervised reading and library work. Choice of material andallotment of time according to individual needs. For students whowant to do work not provided for in the regular subjects. Specicapproval required in each case.Consult N. Mavalvala
Undergraduate Elective Subjects
8.20 Introduction to Special RelativityPrereq: Calculus I (GIR) and Physics I (GIR)U (IAP)2-0-7 units. REST
Introduces the basic ideas and equations of Einstein's specialtheory of relativity. Topics include Lorentz transformations, lengthcontraction and time dilation, four vectors, Lorentz invariants,relativistic energy and momentum, relativistic kinematics, Dopplershi, space-time diagrams, relativity paradoxes, and some conceptsof general relativity. Intended for freshmen and sophomores. Notusable as a restricted elective by Physics majors. Credit cannot bereceived for 8.20 if credit for 8.033 is or has been received in thesame or prior terms.S. Vitale
8.21 Physics of EnergyPrereq: Calculus II (GIR), Chemistry (GIR), and Physics II (GIR)U (Spring)5-0-7 units. REST
A comprehensive introduction to the fundamental physics of energysystems that emphasizes quantitative analysis. Focuses on thefundamental physical principles underlying energy processes and onthe application of these principles to practical calculations. Appliesmechanics and electromagnetism to energy systems; introduces andapplies basic ideas from thermodynamics, quantum mechanics, andnuclear physics. Examines energy sources, conversion, transport,losses, storage, conservation, and end uses. Analyzes the physics ofside eects, such as global warming and radiation hazards. Providesstudents with technical tools and perspective to evaluate energychoices quantitatively at both national policy and personal levels.R. Jae
8.223 Classical Mechanics IIPrereq: Calculus II (GIR) and Physics I (GIR)U (IAP)2-0-4 units
A broad, theoretical treatment of classical mechanics, useful in itsown right for treating complex dynamical problems, but essential tounderstanding the foundations of quantum mechanics and statisticalphysics. Generalized coordinates, Lagrangian and Hamiltonianformulations, canonical transformations, and Poisson brackets.Applications to continuous media. The relativistic Lagrangian andMaxwell's equations.Sta, M. Evans
Department of Physics | 13
DEPARTMENT OF PHYSICS
8.224 Exploring Black Holes: General Relativity andAstrophysicsPrereq: 8.033 or 8.20U (Spring)Not oered regularly; consult department3-0-9 units
Study of physical eects in the vicinity of a black hole as a basisfor understanding general relativity, astrophysics, and elementsof cosmology. Extension to current developments in theory andobservation. Energy and momentum in flat space-time; the metric;curvature of space-time near rotating and nonrotating centers ofattraction; trajectories and orbits of particles and light; elementarymodels of the Cosmos. Weekly meetings include an evening seminarand recitation. The last third of the term is reserved for collaborativeresearch 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 moreadvanced models of the cosmos. Subject has online componentsthat are open to selected MIT alumni. Alumni wishing to participateshould contact Professor Bertschinger at [email protected]. Limited to40.E. Bertschinger
8.225[J] Einstein, Oppenheimer, Feynman: Physics in the 20thCenturySame subject as STS.042[J]Prereq: NoneAcad Year 2019-2020: Not oeredAcad Year 2020-2021: U (Fall)3-0-9 units. HASS-H
See description under subject STS.042[J]. Enrollment limited.D. I. Kaiser
8.226 Forty-three Orders of MagnitudePrereq: (8.04 and 8.044) or permission of instructorAcad Year 2019-2020: Not oeredAcad Year 2020-2021: U (Spring)3-0-9 units
Examines the widespread societal implications of current scienticdiscoveries in physics across forty-three orders of magnitude inlength scale. Addresses topics ranging from climate change tonuclear nonproliferation. Students develop their ability to expressconcepts 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.J. Conrad
8.231 Physics of Solids IPrereq: 8.044; Coreq: 8.05U (Fall)4-0-8 units
Introduction to the basic concepts of the quantum theory of solids.Topics: periodic structure and symmetry of crystals; diraction;reciprocal lattice; chemical bonding; lattice dynamics, phonons,thermal properties; free electron gas; model of metals; Blochtheorem and band structure, nearly free electron approximation;tight binding method; Fermi surface; semiconductors, electrons,holes, impurities; optical properties, excitons; and magnetism.S. Todadri
8.241 Introduction to Biological PhysicsSubject meets with 20.315, 20.415Prereq: Physics II (GIR) and (5.60 or 8.044)U (Spring)4-0-8 units
Introduces the main concepts of biological physics, with a focuson biophysical phenomena at the molecular and cellular scales.Presents the role of entropy and diusive transport in living matter;challenges to life resulting from the highly viscous environmentpresent at microscopic scales, including constraints on force,motion and transport within cells, tissues, and fluids; principlesof how cellular machinery (e.g., molecular motors) can convertelectro-chemical energy sources to mechanical forces and motion.Also covers polymer physics relevant to DNA and other biologicalpolymers, including the study of congurations, fluctuations,rigidity, and entropic elasticity.I. Cisse
8.251 String Theory for UndergraduatesPrereq: 8.033, 8.044, and 8.05Acad Year 2019-2020: Not oeredAcad Year 2020-2021: U (Spring)4-0-8 unitsCredit cannot also be received for 8.821
Introduction to the main concepts of string theory, i.e., quantummechanics of a relativistic string. Develops aspects of stringtheory and makes it accessible to students familiar with basicelectromagnetism and statistical mechanics, including the study ofD-branes and string thermodynamics. Meets with 8.821 when oeredconcurrently.H. Liu
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DEPARTMENT OF PHYSICS
8.276 Nuclear and Particle PhysicsPrereq: 8.033 and 8.04U (Spring)Not oered regularly; consult department4-0-8 units
Presents a modern view of the fundamental structure of matter.Starting from the Standard Model, which views leptons and quarksas basic building blocks of matter, establishes the propertiesand interactions of these particles. Explores applications of thisphenomenology to both particle and nuclear physics. Emphasizescurrent topics in nuclear and particle physics research at MIT.Intended for students with a basic knowledge of relativity andquantum physics concepts.M. Williams
8.277 Introduction to Particle AcceleratorsPrereq: (6.013 or 8.07) and permission of instructorAcad Year 2019-2020: Not oeredAcad Year 2020-2021: U (Fall, IAP, Spring)Units arrangedCan be repeated for credit.
Principles of acceleration: beam properties; linear accelerators,synchrotrons, and storage rings. Accelerator technologies:radio frequency cavities, bending and focusing magnets, beamdiagnostics. Particle beam optics and dynamics. Special topics:measures of accelerators performance in science, medicine andindustry; synchrotron radiation sources; free electron lasers; high-energy colliders; and accelerators for radiation therapy. May berepeated for credit for a maximum of 12 units.W. Barletta
8.282[J] Introduction to AstronomySame subject as 12.402[J]Prereq: Physics I (GIR)U (Spring)3-0-6 units. REST
Quantitative introduction to physics of the solar system, stars,interstellar medium, the galaxy, and universe, as determined froma variety of astronomical observations and models. Topics: planets,planet formation; stars, the Sun, "normal" stars, star formation;stellar evolution, supernovae, compact objects (white dwarfs,neutron stars, and black holes), plusars, binary x-ray sources; starclusters, globular and open clusters; interstellar medium, gas, dust,magnetic elds, cosmic rays; distance ladder; galaxies, normal andactive galaxies, jets; gravitational lensing; large scaling structure;Newtonian cosmology, dynamical expansion and thermal historyof the universe; cosmic microwave background radiation; big bangnucleosynthesis. No prior knowledge of astronomy necessary. Notusable as a restricted elective by Physics majors.A. Frebel
8.284 Modern AstrophysicsPrereq: 8.04; Coreq: 8.05U (Spring)3-0-9 units
Applications of physics (Newtonian, statistical, and quantummechanics) to fundamental processes that occur in celestial objects.Includes main-sequence stars, collapsed stars (white dwarfs,neutron stars, and black holes), pulsars, supernovae, the interstellarmedium, galaxies, and as time permits, active galaxies, quasars, andcosmology. Observational data discussed. No prior knowledge ofastronomy is required.N. Weinberg
8.286 The Early UniversePrereq: Physics II (GIR) and 18.03Acad Year 2019-2020: Not oeredAcad Year 2020-2021: U (Fall)3-0-9 units. REST
Introduction to modern cosmology. First half deals with thedevelopment of the big bang theory from 1915 to 1980, and latter halfwith recent impact of particle theory. Topics: special relativity andthe Doppler eect, Newtonian cosmological models, introductionto non-Euclidean spaces, thermal radiation and early history ofthe universe, big bang nucleosynthesis, introduction to grandunied theories and other recent developments in particle theory,baryogenesis, the inflationary universe model, and the evolution ofgalactic structure.A. Guth
8.287[J] Observational Techniques of Optical AstronomySame subject as 12.410[J]Prereq: 8.282[J], 12.409, or other introductory astronomy courseU (Fall)3-4-8 units. Institute LAB
See description under subject 12.410[J]. Limited to 18; preference toCourse 8 and Course 12 majors and minors.R. Binzel, A. Bosh
8.290[J] Extrasolar Planets: Physics and Detection TechniquesSame subject as 12.425[J]Subject meets with 12.625Prereq: 8.03 and 18.03Acad Year 2019-2020: Not oeredAcad Year 2020-2021: U (Fall)2-1-9 units. REST
See description under subject 12.425[J].S. Seager
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DEPARTMENT OF PHYSICS
8.292[J] Fluid PhysicsSame subject as 12.330[J]Prereq: 5.60, 8.044, or permission of instructorU (Spring)Not oered regularly; consult department3-0-9 units
A physics-based introduction to the properties of fluids and fluidsystems, with examples drawn from a broad range of sciences,including atmospheric physics and astrophysics. Denitionsof fluids and the notion of continuum. Equations of state andcontinuity, hydrostatics and conservation of momentum; ideal fluidsand Euler's equation; viscosity and the Navier-Stokes equation.Energy considerations, fluid thermodynamics, and isentropicflow. Compressible versus incompressible and rotational versusirrotational flow; Bernoulli's theorem; steady flow, streamlines andpotential flow. Circulation and vorticity. Kelvin's theorem. Boundarylayers. Fluid waves and instabilities. Quantum fluids.Sta
8.295 Practical Work ExperiencePrereq: NoneU (Fall, IAP, Spring, Summer)0-1-0 unitsCan be repeated for credit.
For Course 8 students participating in o-campus work experiencesin physics. Before registering for this subject, students must have anemployment oer from a company or organization and must identifya Physics supervisor. Upon completion of the work, student mustsubmit a letter from the employer describing the work accomplished,along with a substantive nal report from the student approvedby the MIT supervisor. Subject to departmental approval. Consultdepartmental academic oce.Consult N. Mavalvala
8.298 Selected Topics in PhysicsPrereq: Permission of instructorU (Fall, IAP, Spring, Summer)Units arrangedCan be repeated for credit.
Presentation of topics of current interest, with content varying fromyear to year.Consult I. Stewart
8.299 Physics TeachingPrereq: NoneU (Fall, Spring)Units arranged [P/D/F]Can be repeated for credit.
For qualied undergraduate students interested in gaining someexperience in teaching. Laboratory, tutorial, or classroom teachingunder the supervision of a faculty member. Students selected byinterview.Consult N. Mavalvala
8.EPE UPOP Engineering Practice ExperienceEngineering School-Wide Elective Subject.Oered under: 1.EPE, 2.EPE, 3.EPE, 6.EPE, 8.EPE, 10.EPE, 15.EPE,16.EPE, 20.EPE, 22.EPEPrereq: 2.EPW or permission of instructorU (Fall, Spring)0-0-1 units
See description under subject 2.EPE.Sta
8.S04 Special Subject: Quantum Physics IPrereq: 8.03 and (18.03 or 18.032)U (Fall)2-0-10 units. RESTCredit cannot also be received for 8.04
Experimental version of 8.04, which oers a combination of onlineand in-person instruction. See description of 8.04. Licensed by theCommittee on Curricula as an acceptable alternative to 8.04 for Fall2017.R. Ashoori
8.S10 Special Subject: PhysicsPrereq: NoneU (Spring)Units arrangedCan be repeated for credit.
Opportunity for group study of subjects in physics not otherwiseincluded in the curriculum.A. Adams, K. Ellenbogen
8.S30 Special Subject: PhysicsPrereq: NoneAcad Year 2019-2020: Not oeredAcad Year 2020-2021: U (IAP)Units arranged
Opportunity for group study of subjects in physics not otherwiseincluded in the curriculum.A. Bernstein, J. Walsh
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DEPARTMENT OF PHYSICS
8.S50 Special Subject: PhysicsPrereq: NoneU (IAP)Units arranged [P/D/F]Can be repeated for credit.
Opportunity for group study of subjects in physics not otherwiseincluded in the curriculum.E. Bertschinger
8.UR Undergraduate ResearchPrereq: NoneU (Fall, IAP, Spring, Summer)Units arranged [P/D/F]Can be repeated for credit.
Research opportunities in physics. For further information, contactthe departmental UROP coordinator.N. Mavalvala
8.THU Undergraduate Physics ThesisPrereq: NoneU (Fall, IAP, Spring, Summer)Units arrangedCan be repeated for credit.
Program of research leading to the writing of an S.B. thesis; to bearranged by the student under approved supervision.Information: N. Mavalvala
Graduate Subjects
8.309 Classical Mechanics IIISubject meets with 8.09Prereq: NoneG (Fall)4-0-8 units
Covers Lagrangian and Hamiltonian mechanics, systems withconstraints, rigid body dynamics, vibrations, central forces,Hamilton-Jacobi theory, action-angle variables, perturbationtheory, and continuous systems. Provides an introduction to idealand viscous fluid mechanics, including turbulence, as well as anintroduction to nonlinear dynamics, including chaos. Students takinggraduate version complete dierent assignments.I. Stewart
8.311 Electromagnetic Theory IPrereq: 8.07G (Spring)4-0-8 units
Basic principles of electromagnetism: experimental basis,electrostatics, magnetic elds of steady currents, motional emf andelectromagnetic induction, Maxwell's equations, propagation andradiation of electromagnetic waves, electric and magnetic propertiesof matter, and conservation laws. Subject uses appropriatemathematics but emphasizes physical phenomena and principles.J. Belcher
8.315[J] Mathematical Methods in NanophotonicsSame subject as 18.369[J]Prereq: 8.07, 18.303, or permission of instructorAcad Year 2019-2020: G (Spring)Acad Year 2020-2021: Not oered3-0-9 units
See description under subject 18.369[J].S. G. Johnson
8.321 Quantum Theory IPrereq: 8.05G (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 quantummechanics, representations of symmetry groups. Variational andperturbation approximations. Systems of identical particles andapplications. Time-dependent perturbation theory. Scatteringtheory: phase shis, Born approximation. The quantum theory ofradiation. Second quantization and many-body theory. Relativisticquantum mechanics of one electron.H. Liu
Department of Physics | 17
DEPARTMENT OF PHYSICS
8.322 Quantum Theory IIPrereq: 8.07 and 8.321Acad Year 2019-2020: G (Spring)Acad Year 2020-2021: Not oered4-0-8 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 quantummechanics, representations of symmetry groups. Variational andperturbation approximations. Systems of identical particles andapplications. Time-dependent perturbation theory. Scatteringtheory: phase shis, Born approximation. The quantum theory ofradiation. Second quantization and many-body theory. Relativisticquantum mechanics of one electron.S. Todadri
8.323 Relativistic Quantum Field Theory IPrereq: 8.321G (Spring)4-0-8 units
A one-term self-contained subject in quantum eld theory. Conceptsand basic techniques are developed through applications inelementary particle physics, and condensed matter physics.Topics: classical eld theory, symmetries, and Noether's theorem.Quantization of scalar elds, spin elds, and Gauge bosons.Feynman graphs, analytic properties of amplitudes and unitarityof the S-matrix. Calculations in quantum electrodynamics (QED).Introduction to renormalization.T. Slatyer
8.324 Relativistic Quantum Field Theory IIPrereq: 8.322 and 8.323G (Fall)4-0-8 units
The second term of the quantum eld theory sequence. Developsin depth some of the topics discussed in 8.323 and introducessome advanced material. Topics: perturbation theory and Feynmandiagrams, scattering theory, Quantum Electrodynamics, one looprenormalization, quantization of non-abelian gauge theories, theStandard Model of particle physics, other topics.T. Slatyer
8.325 Relativistic Quantum Field Theory IIIPrereq: 8.324G (Spring)4-0-8 units
The third and last term of the quantum eld theory sequence. Its aimis the proper theoretical discussion of the physics of the standardmodel. Topics: quantum chromodynamics; Higgs phenomenonand a description of the standard model; deep-inelastic scatteringand structure functions; basics of lattice gauge theory; operatorproducts and eective theories; detailed structure of the standardmodel; spontaneously broken gauge theory and its quantization;instantons and theta-vacua; topological defects; introduction tosupersymmetry.W. Taylor
8.333 Statistical Mechanics IPrereq: 8.044 and 8.05G (Fall)4-0-8 units
First part of a two-subject sequence on statistical mechanics.Examines the laws of thermodynamics and the concepts oftemperature, work, heat, and entropy. Postulates of classicalstatistical mechanics, microcanonical, canonical, and grandcanonical distributions; applications to lattice vibrations, idealgas, photon gas. Quantum statistical mechanics; Fermi and Bosesystems. Interacting systems: cluster expansions, van der Waal'sgas, and mean-eld theory.M. Kardar
8.334 Statistical Mechanics IIPrereq: 8.333Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Spring)4-0-8 units
Second part of a two-subject sequence on statistical mechanics.Explores topics from modern statistical mechanics: thehydrodynamic limit and classical eld theories. Phase transitionsand broken symmetries: universality, correlation functions,and scaling theory. The renormalization approach to collectivephenomena. Dynamic critical behavior. Random systems.Sta
8.351[J] Classical Mechanics: A Computational ApproachSame subject as 6.946[J], 12.620[J]Prereq: Physics I (GIR), 18.03, and permission of instructorG (Fall)3-3-6 units
See description under subject 12.620[J].J. Wisdom, G. J. Sussman
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DEPARTMENT OF PHYSICS
8.361 Quantum Theory of Many-Particle SystemsPrereq: 8.322 and 8.333G (Fall)Not oered regularly; consult department3-0-9 units
Introduces general many-body theory applicable to low temperature,nuclear, and solid-state physics. Reviews occupation numberrepresentation and classical Mayer expansion. Perturbation theory:diagrammatic expansions and linked-cluster theorem for zero ornite temperature systems of fermions or bosons. Green's functions:analytic properties, equations of motion, relation to observables,approximations, linear response theory, and random phaseapproximation. Superconductivity: electron-phonon interaction,instability of normal state, BCS ground state, perturbation theory.Sta
8.370[J] Quantum ComputationSame subject as 2.111[J], 18.435[J]Prereq: Permission of instructorG (Fall)3-0-9 units
See description under subject 18.435[J].I. Chuang, A. Harrow, S. Lloyd, P. Shor
8.371[J] Quantum Information ScienceSame subject as 6.443[J], 18.436[J]Prereq: 18.435[J]G (Spring)3-0-9 units
Examines quantum computation and quantum information. Topicsinclude quantum circuits, the quantum Fourier transform andsearch algorithms, the quantum operations formalism, quantumerror correction, Calderbank-Shor-Steane and stabilizer codes,fault tolerant quantum computation, quantum data compression,quantum entanglement, capacity of quantum channels, and quantumcryptography and the proof of its security. Prior knowledge ofquantum mechanics required.I. Chuang, A. Harrow
8.381, 8.382 Selected Topics in Theoretical PhysicsPrereq: Permission of instructorG (Fall, Spring)Not oered regularly; consult department3-0-9 units
Topics of current interest in theoretical physics, varying from year toyear. Subject not routinely oered; given when sucient interest isindicated.Sta
8.391 Pre-Thesis ResearchPrereq: Permission of instructorG (Fall)Units arranged [P/D/F]Can be repeated for credit.
Advanced problems in any area of experimental or theoreticalphysics, with assigned reading and consultations.Sta
8.392 Pre-Thesis ResearchPrereq: Permission of instructorG (Spring, Summer)Units arranged [P/D/F]Can be repeated for credit.
Advanced problems in any area of experimental or theoreticalphysics, with assigned reading and consultations.Sta
8.395[J] Teaching College-Level Science and EngineeringSame subject as 1.95[J], 5.95[J], 7.59[J], 18.094[J]Subject meets with 2.978Prereq: NoneAcad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Fall)2-0-2 units
See description under subject 5.95[J].J. Rankin
8.398 Selected Topics in Graduate PhysicsPrereq: Permission of instructorG (Fall, IAP, Spring)Units arrangedCan be repeated for credit.
Presentation of topics of current interest with content varying fromyear to year.Consult N. Mavalvala
8.399 Physics TeachingPrereq: Permission of instructorG (Fall, Spring)Units arranged [P/D/F]Can be repeated for credit.
For qualied graduate students interested in gaining someexperience in teaching. Laboratory, tutorial, or classroom teachingunder the supervision of a faculty member. Students selected byinterview.Consult C. Paus
Department of Physics | 19
DEPARTMENT OF PHYSICS
Physics of Atoms, Radiation, Solids, Fluids, and Plasmas
8.421 Atomic and Optical Physics IPrereq: 8.05Acad Year 2019-2020: G (Spring)Acad Year 2020-2021: Not oered3-0-9 units
The rst of a two-term subject sequence that provides thefoundations for contemporary research in selected areas of atomicand 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, behaviorin very strong elds; fundamental tests: time reversal, parityviolations, Bell's inequalities; and experimental methods.M. Zwierlein
8.422 Atomic and Optical Physics IIPrereq: 8.05Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Spring)3-0-9 units
The second of a two-term subject sequence that provides thefoundations for contemporary research in selected areas of atomicand optical physics. Non-classical states of light- squeezed states;multi-photon processes, Raman scattering; coherence- levelcrossings, 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.Sta
8.431[J] Nonlinear OpticsSame subject as 6.634[J]Prereq: 6.013 or 8.07G (Spring)3-0-9 units
See description under subject 6.634[J].J. G. Fujimoto
8.481, 8.482 Selected Topics in Physics of Atoms and RadiationPrereq: 8.321G (Fall, Spring)Not oered regularly; consult department3-0-9 units
Presentation of topics of current interest, with content varying fromyear to year. Subject not routinely oered; given when sucientinterest is indicated.Sta
8.511 Theory of Solids IPrereq: 8.231G (Fall)3-0-9 units
First term of a theoretical treatment of the physics of solids. Conceptof elementary excitations. Symmetry- translational, rotational, andtime-reversal invariances- theory of representations. Energy bands-electrons and phonons. Topological band theory. Survey of electronicstructure of metals, semimetals, semiconductors, and insulators,excitons, critical points, response functions, and interactions in theelectron gas. Theory of superconductivity.L. Levitov
8.512 Theory of Solids IIPrereq: 8.511G (Spring)3-0-9 units
Second term of a theoretical treatment of the physics of solids.Interacting electron gas: many-body formulation, Feynmandiagrams, random phase approximation and beyond. Generaltheory of linear response: dielectric function; sum rules; plasmons;optical properties; applications to semiconductors, metals, andinsulators. Transport properties: non-interacting electron gaswith impurities, diusons. Quantum Hall eect: integral andfractional. Electron-phonon interaction: general theory, applicationsto metals, semiconductors and insulators, polarons, and eld-theory description. Superconductivity: experimental observations,phenomenological theories, and BCS theory.L. Levitov
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DEPARTMENT OF PHYSICS
8.513 Many-Body Theory for Condensed Matter SystemsPrereq: 8.033, 8.05, 8.08, and 8.231Acad Year 2019-2020: G (Fall)Acad Year 2020-2021: Not oered3-0-9 units
Concepts and physical pictures behind various phenomena thatappear in interacting many-body systems. Visualization occursthrough concentration on path integral, mean-eld theories andsemiclassical picture of fluctuations around mean-eld state. Topicscovered: interacting boson/fermion systems, Fermi liquid theoryand bosonization, symmetry breaking and nonlinear sigma-model,quantum gauge theory, quantum Hall theory, mean-eld theoryof spin liquids and quantum order, string-net condensation andemergence of light and fermions.X-G. Wen
8.514 Strongly Correlated Systems in Condensed Matter PhysicsPrereq: 8.322 and 8.333Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Spring)3-0-9 units
Study of condensed matter systems where interactions betweenelectrons play an important role. Topics vary depending on lecturerbut may include low-dimension magnetic and electronic systems,disorder and quantum transport, magnetic impurities (the Kondoproblem), quantum spin systems, the Hubbard model and high-temperature superconductors. Topics are chosen to illustrate theapplication of diagrammatic techniques, eld-theory approaches,and renormalization group methods in condensed matter physics.S. Todadri
8.581, 8.582 Selected Topics in Condensed Matter PhysicsPrereq: Permission of instructorG (Fall, Spring)Not oered regularly; consult department3-0-9 unitsCan be repeated for credit.
Presentation of topics of current interest, with contents varying fromyear to year. Subject not routinely oered; given when sucientinterest is indicated.Sta
8.590[J] Topics in Biophysics and Physical BiologySame subject as 7.74[J], 20.416[J]Prereq: NoneG (Fall)2-0-4 units
See description under subject 20.416[J].I. Cisse, N. Fakhri, M. Guo
8.591[J] Systems BiologySame subject as 7.81[J]Subject meets with 7.32Prereq: (18.03 and 18.05) or permission of instructorG (Fall)3-0-9 units
Introduction to cellular and population-level systems biology withan emphasis on synthetic biology, modeling of genetic networks,cell-cell interactions, and evolutionary dynamics. Cellular systemsinclude genetic switches and oscillators, network motifs, geneticnetwork evolution, and cellular decision-making. Population-level systems include models of pattern formation, cell-cellcommunication, and evolutionary systems biology. Students takinggraduate version explore the subject in more depth.J. Gore
8.592[J] Statistical Physics in BiologySame subject as HST.452[J]Prereq: 8.333 or permission of instructorAcad Year 2019-2020: G (Spring)Acad Year 2020-2021: Not oered3-0-9 units
A survey of problems at the interface of statistical physics andmodern biology: bioinformatic methods for extracting informationcontent of DNA; gene nding, sequence comparison, phylogenetictrees. Physical interactions responsible for structure of biopolymers;DNA double helix, secondary structure of RNA, elements of proteinfolding. Considerations of force, motion, and packaging; proteinmotors, membranes. Collective behavior of biological elements;cellular networks, neural networks, and evolution.M. Kardar, L. Mirny
Department of Physics | 21
DEPARTMENT OF PHYSICS
8.593[J] Biological PhysicsSame subject as HST.450[J]Prereq: 8.044 recommended but not necessaryG (Spring)Not oered regularly; consult department4-0-8 units
Designed to provide seniors and rst-year graduate students witha quantitative, analytical understanding of selected biologicalphenomena. Topics include experimental and theoretical basisfor the phase boundaries and equation of state of concentratedprotein solutions, with application to diseases such as sicklecell anemia and cataract. Protein-ligand binding and linkageand the theory of allosteric regulation of protein function, withapplication to proteins as stores as transporters in respiration,enzymes in metabolic pathways, membrane receptors, regulatorsof gene expression, and self-assembling scaolds. The physics oflocomotion and chemoreception in bacteria and the biophysics ofvision, including the theory of transparency of the eye, molecularbasis of photo reception, and the detection of light as a signal-to-noise discrimination.G. Benedek
8.613[J] Introduction to Plasma Physics ISame subject as 22.611[J]Prereq: (6.013 or 8.07) and (18.04 or Coreq: 18.075)G (Fall)3-0-9 units
See description under subject 22.611[J].I. Hutchinson
8.614[J] Introduction to Plasma Physics II (New)Same subject as 22.612[J]Prereq: 22.611[J]Acad Year 2019-2020: G (Spring)Acad Year 2020-2021: Not oered3-0-9 units
See description under subject 22.612[J].Sta
8.624 Plasma WavesPrereq: 22.611[J]Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Spring)3-0-9 units
Comprehensive theory of electromagnetic waves in a magnetizedplasma. Wave propagation in cold and hot plasmas. Energy flow.Absorption by Landau and cyclotron damping and by transit timemagnetic pumping (TTMP). Wave propagation in inhomogeneousplasma: accessibility, WKB theory, mode conversion, connectionformulae, 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 ioncyclotron (ICRF), electron cyclotron (ECRH), and lower hybrid (LHH)wave heating. Quasi-linear theory and applications to RF currentdrive in tokamaks. Extensive discussion of relevant experimentalobservations.M. Porkolab
8.641 Physics of High-Energy Plasmas IPrereq: 22.611[J]G (Fall)Not oered regularly; consult department3-0-9 units
Physics of High-Energy Plasmas I and II address basic concepts ofplasmas, with temperatures of thermonuclear interest, relevantto fusion research and astrophysics. Microscopic transportprocesses due to interparticle collisions and collective modes (e.g.,microinstabilities). Relevant macroscopic transport coecients(electrical resistivity, thermal conductivities, particle "diusion").Runaway and slide-away regimes. Magnetic reconnectionprocesses and their relevance to experimental observations.Radiation emission from inhomogeneous plasmas. Conditions forthermonuclear burning and ignition (D-T and "advanced" fusionreactions, plasmas with polarized nuclei). Role of "impurity" nuclei."Finite-β" (pressure) regimes and ballooning modes. Convectivemodes in conguration and velocity space. Trapped particle regimes.Nonlinear and explosive instabilities. Interaction of positive andnegative energy modes. Each subject can be taken independently.Sta
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DEPARTMENT OF PHYSICS
8.642 Physics of High-Energy Plasmas IIPrereq: 22.611[J]G (Fall)Not oered regularly; consult department3-0-9 units
Physics of High-Energy Plasmas I and II address basic concepts ofplasmas, with temperatures of thermonuclear interest, relevantto fusion research and astrophysics. Microscopic transportprocesses due to interparticle collisions and collective modes (e.g.,microinstabilities). Relevant macroscopic transport coecients(electrical resistivity, thermal conductivities, particle "diusion").Runaway and slide-away regimes. Magnetic reconnectionprocesses and their relevance to experimental observations.Radiation emission from inhomogeneous plasmas. Conditions forthermonuclear burning and ignition (D-T and "advanced" fusionreactions, plasmas with polarized nuclei). Role of "impurity" nuclei."Finite-β" (pressure) regimes and ballooning modes. Convectivemodes in conguration and velocity space. Trapped particle regimes.Nonlinear and explosive instabilities. Interaction of positive andnegative energy modes. Each subject can be taken independently.Sta
8.670[J] Principles of Plasma DiagnosticsSame subject as 22.67[J]Prereq: 22.611[J]G (Fall)Not oered regularly; consult department4-4-4 units
See description under subject 22.67[J].A. White
8.681, 8.682 Selected Topics in Fluid and Plasma PhysicsPrereq: 22.611[J]G (Fall, Spring)Not oered regularly; consult department3-0-9 unitsCan be repeated for credit.
Presentation of topics of current interest, with content varying fromyear to year. Subject not routinely oered; given when interest isindicated.Consult M. Porkolab
Nuclear and Particle Physics
8.701 Introduction to Nuclear and Particle PhysicsPrereq: None. Coreq: 8.321G (Fall)3-0-9 units
The phenomenology and experimental foundations of particle andnuclear 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, parityviolation, lepton-nucleon scattering, and structure functions. QCD,gluon eld and color. W and Z elds, electro-weak unication,the CKM matrix. Nucleon-nucleon interactions, properties ofnuclei, single- and collective- particle models. Electron and hadroninteractions with nuclei. Relativistic heavy ion collisions, andtransition to quark-gluon plasma.M. Williams
8.711 Nuclear PhysicsPrereq: 8.321 and 8.701G (Spring)4-0-8 units
Modern, advanced study in the experimental foundations andtheoretical understanding of the structure of nuclei, beginning withthe two- and three-nucleon problems. Basic nuclear properties,collective and single-particle motion, giant resonances, meaneld models, interacting boson model. Nuclei far from stability,nuclear astrophysics, big-bang and stellar nucleosynthesis. Electronscattering: nucleon momentum distributions, scaling, olarizationobservables. Parity-violating electron scattering. Neutrino physics.Current results in relativistic heavy ion physics and hadronic physics.Frontiers and future facilities.O. Hen
8.712 Advanced Topics in Nuclear PhysicsPrereq: 8.711 or permission of instructorG (Fall, Spring)Not oered regularly; consult department3-0-9 unitsCan be repeated for credit.
Subject for experimentalists and theorists with rotation of thefollowing topics: (1) Nuclear chromodynamics-- introduction to QCD,structure of nucleons, lattice QCD, phases of hadronic matter; andrelativistic heavy ion collisions. (2) Medium-energy physics-- nuclearand nucleon structure and dynamics studied with medium- and high-energy probes (neutrinos, photons, electrons, nucleons, pions, andkaons). Studies of weak and strong interactions.Sta
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DEPARTMENT OF PHYSICS
8.781, 8.782 Selected Topics in Nuclear TheoryPrereq: 8.323G (Fall, Spring)Not oered regularly; consult department3-0-9 units
Presents topics of current interest in nuclear structure and reactiontheory, with content varying from year to year. Subject not routinelyoered; given when sucient interest is indicated.Consult E. Farhi
8.811 Particle PhysicsPrereq: 8.701G (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 eeand pp colliders. Mass generation, W, Z, and Higgs physics. Weakdecays of mesons, including heavy flavors with QCD corrections.Mixing phenomena for K, D, B mesons and neutrinos. CP violationwith results from B-factories. Future physics expectations: Higgs,SUSY, sub-structure as addressed by new experiments at the LHCcollider.L. Winslow
8.812 Graduate Experimental PhysicsPrereq: 8.701G (IAP)Not oered regularly; consult department1-8-3 units
Provides practical experience in particle detection with vericationby (Feynman) calculations. Students perform three experiments;at least one requires actual construction following design. Topicsinclude Compton eect, Fermi constant in muon decay, particleidentication by time-of-flight, Cerenkov light, calorimeter response,tunnel eect in radioactive decays, angular distribution of cosmicrays, scattering, gamma-gamma nuclear correlations, and modernparticle localization.U. Becker
8.821 String TheoryPrereq: 8.324Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Fall)3-0-9 unitsCredit cannot also be received for 8.251
An introduction to string theory. Basics of conformal eld theory;light-cone and covariant quantization of the relativistic bosonicstring; quantization and spectrum of supersymmetric 10-dimensionalstring theories; T-duality and D-branes; toroidal compacticationand orbifolds; 11-dimensional supergravity and M-theory. Meets with8.251 when oered concurrently.H. Liu
8.831 Supersymmetric Quantum Field TheoriesPrereq: Permission of instructorAcad Year 2019-2020: G (Fall)Acad Year 2020-2021: Not oered3-0-9 unitsCan be repeated for credit.
Topics selected from the following: SUSY algebras and their particlerepresentations; Weyl and Majorana spinors; Lagrangians of basicfour-dimensional SUSY theories, both rigid SUSY and supergravity;supermultiplets of elds and superspace methods; renormalizationproperties, and the non-renormalization theorem; spontaneousbreakdown of SUSY; and phenomenological SUSY theories. Someprior knowledge of Noether's theorem, derivation and use ofFeynman rules, l-loop renormalization, and gauge theories isessential.J. Thaler
8.841 Electroweak InteractionsPrereq: 8.324Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Spring)3-0-9 units
An introduction to the standard model of electroweak interactionsand beyond; neutrino interactions and masses; the CKM matrix;lepton scattering o of necleons and nuclei; the search for the Higgsboson; supersymmetric extension of the standard model. Topics varywith instructor.Sta
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DEPARTMENT OF PHYSICS
8.851 Eective Field TheoryPrereq: 8.324Acad Year 2019-2020: G (Spring)Acad Year 2020-2021: Not oered3-0-9 unitsCredit cannot also be received for 8.S851
Covers the framework and tools of eective eld theory, including:identifying degrees of freedom and symmetries; power countingexpansions (dimensional and otherwise); eld redenitions, bottom-up and top-down eective theories; ne-tuned eective theories;matching and Wilson coecients; reparameterization invariance;and advanced renormalization group techniques. Main examples aretaken from particle and nuclear physics, including the So-CollinearEective Theory.I. Stewart
8.S851 Special Subject: Eective Field TheoryPrereq: 8.324 and permission of instructorAcad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Spring)2-0-10 unitsCredit cannot also be received for 8.851
Experimental version of 8.851, which oers a combination of onlineand in-person instruction. See description of 8.851. Licensedfor Spring 2019 by the Committee on Graduate Programs as anacceptable alternative to 8.851. Limited to 15.I. Stewart
8.861 Advanced Topics in SuperfluidityPrereq: 8.324G (Fall)Not oered regularly; consult department3-0-9 units
Basic pairing theory, eective eld theory and spontaneoussymmetry breaking; well-established applications to liquid helium3 as a warm-up; research will be explored including anisotropicsuperconductivity in heavy fermion systems and cuprates; colorsuperconductivity in high-density QCD; and pairing in fermionsystems with mismatched Fermi surfaces, including ultracoldatom systems. Additional ideas needed to discuss the fractionalquantum Hall eect will be reviewed, emphasizing its connection toconventional superfluidity, and pointing toward aspects of anyonbehavior potentially relevant for quantum information processing.Sta
8.871 Selected Topics in Theoretical Particle PhysicsPrereq: 8.323Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Fall)3-0-9 unitsCan be repeated for credit.
Presents topics of current interest in theoretical particle physics,with content varying from year to year. Subject not routinely oered;given when sucient interest is indicated.F. Wilczek
8.872 Selected Topics in Theoretical Particle PhysicsPrereq: 8.323Acad Year 2019-2020: Not oeredAcad Year 2020-2021: G (Fall, Spring)3-0-9 unitsCan be repeated for credit.
Presents topics of current interest in theoretical particle physics,with content varying from year to year. Subject not routinely oered;given when sucient interest is indicated.W. Taylor
8.881, 8.882 Selected Topics in Experimental Particle PhysicsPrereq: 8.811G (Fall, Spring)Not oered regularly; consult department3-0-9 unitsCan be repeated for credit.
Presents topics of current interest in experimental particle physics,with content varying from year to year. Subject not routinely oered;given when sucient interest is indicated.Sta
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DEPARTMENT OF PHYSICS
Space Physics and Astrophysics
8.901 Astrophysics IPrereq: Permission of instructorG (Spring)3-0-9 units
Size and time scales. Historical astronomy. Astronomicalinstrumentation. Stars: spectra and classication. Stellar structureequations and survey of stellar evolution. Stellar oscillations.Degenerate and collapsed stars; radio pulsars. Interactingbinary systems; accretion disks, x-ray sources. Gravitationallenses; dark matter. Interstellar medium: HII regions, supernovaremnants, molecular clouds, dust; radiative transfer; Jeans' mass;star formation. High-energy astrophysics: Compton scattering,bremsstrahlung, synchrotron radiation, cosmic rays. Galactic stellardistributions and populations; Oort constants; Oort limit; andglobular clusters.S. Hughes
8.902 Astrophysics IIPrereq: 8.901G (Fall)3-0-9 units
Galactic dynamics: potential theory, orbits, collisionless Boltzmannequation, etc. Galaxy interactions. Groups and clusters; darkmatter. Intergalactic medium; x-ray clusters. Active galactic nuclei:unied models, black hole accretion, radio and optical jets, etc.Homogeneity and isotropy, redshi, galaxy distance ladder.Newtonian cosmology. Roberston-Walker models and cosmography.Early universe, primordial nucleosynthesis, recombination. Cosmicmicrowave background radiation. Large-scale structure, galaxyformation.M. McDonald
8.913 Plasma Astrophysics IPrereq: Permission of instructorG (Fall)Not oered regularly; consult department3-0-9 units
For students interested in space physics, astrophysics, and plasmaphysics in general. Magnetospheres of rotating magnetizedplanets, ordinary stars, neutron stars, and black holes. Pulsarmodels: processes for slowing down, particle acceleration, andradiation emission; accreting plasmas and x-ray stars; stellar winds;heliosphere and solar wind- relevant magnetic eld conguration,measured particle distribution in velocity space and inducedcollective modes; stability of the current sheet and collisionlessprocesses for magnetic reconnection; theory of collisionless shocks;solitons; Ferroaro-Rosenbluth sheet; solar flare models; heatingprocesses of the solar corona; Earth's magnetosphere (auroralphenomena and their interpretation, bowshock, magnetotail,trapped particle eects); relationship between gravitational(galactic) plasmas and electromagnetic plasmas. 8.913 deals withheliospheric, 8.914 with extra-heliospheric plasmas.Sta
8.914 Plasma Astrophysics IIPrereq: Permission of instructorG (Spring)Not oered regularly; consult department3-0-9 units
For students interested in space physics, astrophysics, and plasmaphysics in general. Magnetospheres of rotating magnetizedplanets, ordinary stars, neutron stars, and black holes. Pulsarmodels: processes for slowing down, particle acceleration, andradiation emission; accreting plasmas and x-ray stars; stellar winds;heliosphere and solar wind- relevant magnetic eld conguration,measured particle distribution in velocity space and inducedcollective modes; stability of the current sheet and collisionlessprocesses for magnetic reconnection; theory of collisionless shocks;solitons; Ferroaro-Rosenbluth sheet; solar flare models; heatingprocesses of the solar corona; Earth's magnetosphere (auroralphenomena and their interpretation, bowshock, magnetotail,trapped particle eects); relationship between gravitational(galactic) plasmas and electromagnetic plasmas. 8.913 deals withheliospheric, 8.914 with extra-heliospheric plasmas.B. Coppi
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DEPARTMENT OF PHYSICS
8.921 Stellar Structure and EvolutionPrereq: Permission of instructorG (Spring)Not oered regularly; consult department3-0-9 units
Observable stellar characteristics; overview of observationalinformation. Principles underlying calculations of stellar structure.Physical processes in stellar interiors; properties of matter andradiation; radiative, conductive, and convective heat transport;nuclear energy generation; nucleosynthesis; and neutrino emission.Protostars; the main sequence, and the solar neutrino flux; advancedevolutionary stages; variable stars; planetary nebulae, supernovae,white dwarfs, and neutron stars; close binary systems; andabundance of chemical elements.Sta
8.942 CosmologyPrereq: Permission of instructorAcad Year 2019-2020: G (Fall)Acad Year 2020-2021: Not oered3-0-9 units
Thermal backgrounds in space. Cosmological principle and itsconsequences: Newtonian cosmology and types of "universes";survey of relativistic cosmology; horizons. Overview of evolution incosmology; radiation and element synthesis; physical models ofthe "early stages." Formation of large-scale structure to variabilityof physical laws. First and last states. Some knowledge of relativityexpected. 8.962 recommended though not required.K. Masui
8.952 Particle Physics of the Early UniversePrereq: 8.323; Coreq: 8.324Acad Year 2019-2020: G (Spring)Acad Year 2020-2021: Not oered3-0-9 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 particlephysics, electroweak and QCD phase transition, basics of grouptheory, grand unied theories, baryon asymmetry, monopoles,cosmic strings, domain walls, axions, inflationary universe, andstructure formation.A. Guth
8.962 General RelativityPrereq: 8.07, 18.03, and 18.06G (Spring)4-0-8 units
The basic principles of Einstein's general theory of relativity,dierential geometry, experimental tests of general relativity, blackholes, and cosmology.A. Guth
8.971 Astrophysics SeminarPrereq: Permission of instructorG (Fall, Spring)Not oered regularly; consult department2-0-4 unitsCan be repeated for credit.
Advanced seminar on current topics, with a dierent focus eachterm. Typical topics: astronomical instrumentation, numerical andstatistical methods in astrophysics, gravitational lenses, neutronstars and pulsars.Consult D. Chakrabarty
8.972 Astrophysics SeminarPrereq: Permission of instructorG (Fall, Spring)Not oered regularly; consult department2-0-4 unitsCan be repeated for credit.
Advanced seminar on current topics, with a dierent focus each term.Typical topics: gravitational lenses, active galactic nuclei, neutronstars and pulsars, galaxy formation, supernovae and supernovaremnants, brown dwarfs, and extrasolar planetary systems. Thepresenter at each session is selected by drawing names from a hatcontaining those of all attendees. Oered if sucient interest isindicated.Consult D. Chakrabarty
8.981, 8.982 Selected Topics in AstrophysicsPrereq: Permission of instructorG (Spring)Not oered regularly; consult department3-0-9 unitsCan be repeated for credit.
Topics of current interest, varying from year to year. Subject notroutinely oered; given when sucient interest is indicated.Consult D. Chakrabarty
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DEPARTMENT OF PHYSICS
8.995 Practical Work ExperiencePrereq: NoneG (Fall, IAP, Spring, Summer)Units arranged [P/D/F]Can be repeated for credit.
For Course 8 students participating in o-campus work experiencesin physics. Before registering for this subject, students must have anemployment oer from a company or organization, must identify aPhysics supervisor, and must receive prior approval from the PhysicsDepartment. Upon completion of the work, student must submit aletter from the employer describing the work accomplished, alongwith a substantive nal report from the student approved by the MITsupervisor. Consult departmental academic oce.Consult N. Mavalvala
8.S301 Special Subject: PhysicsPrereq: Permission of instructorG (Spring)Not oered regularly; consult departmentUnits arranged
Covers topics in Physics that are not oered in the regularcurriculum. Limited enrollment; preference to Physics graduatestudents.A. Lightman
8.S421 Special Subject: PhysicsPrereq: Permission of instructorG (Fall)Not oered regularly; consult departmentUnits arrangedCan be repeated for credit.
Opportunity for group study of subjects in physics not otherwiseincluded in the curriculum.W. Ketterle
8.THG Graduate Physics ThesisPrereq: Permission of instructorG (Fall, IAP, Spring, Summer)Units arrangedCan be repeated for credit.
Program of research leading to the writing of an SM, PhD, or ScDthesis; to be arranged by the student and an appropriate MIT facultymember.Consult I. Stewart
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