# Subjects

The MIT Physics Department offers an outstanding course curriculum. We recommend that you acquaint yourself with the course offerings before choosing classes.

### Spring 2023 (updated 2/1/2023)

- 8.011 // Physics I – R. Milner [Site | Books]
- L01: MW12-2 in 36-144 – Milner
- R01: F10-11 in 32-124 – TBA

- 8.02 // Physics II – Staff [Site | Books]
- L01: MW9-1030, F9-10 in 26-152 – Abdelhafez
- L02: MW11-1230, F11-12 in 26-152 – Millholland
- L03: MW1-230, F1-2 in 26-152 – Gedik
- L04: MW 3-430, F3-4 in 26-152 – Katsavounidis
- L05: TR 9-1030, F10-11 in 26-152 – Shvonski
- L06: TR11-1230, F12-1 in 26-152 – Drury
- L07: TR1-230, F2-3 in 26-152 – Checkelsky
- L08: TR3-430, F4-5 in 26-152 – Dourmashkin

- 8.022 // Physics II – T. Slatyer [Site | Books]
- 8.03 // Physics III – M. Vogelsberger [Site | Books]
- L01: TR130-3 in 6-120 – Vogelsberger
- R01: MW10-11 in 26-314 – Ju
- R02: MW11-12 in 26-314 – Ju
- R03: MW1-2 in 26-314 – Hen
- R04: MW 2-3 in 26-314 – Hen

- 8.04 // Quantum Physics – A. Harrow [Site | Books]
- 8.044 // Statistical Physics – R. Fletcher [Site | Books]
- 8.051 // Quantum Physics II – B. Zwiebach [Site | Books]
- L01: MW10-11 in 2-105

- 8.06 // Quantum Physics II
**I**– M. Metlitski [Site | Books] - 8.13 // Experimental Physics I – Staff [Site | Books]
- B01: MW9-12 in 4-361 – G. Roland
- B02: MW2-5 in 4-361 – A. Levine

- 8.14 // Experimental Physics II – N. Fakri [Site | Books]
- B01: TR2-5 in 4-361

- (NEW) 8.16/316 // Data Science – P. Harris [Site | Books]
- L01: MW230-4 in 36-112

- 8.21 // Physics of Energy – M. Evans [Site | Books]
- L01: MW230-4 in 4-261
- R01: TR3-4 in 2-146

- 8.226 // Forty-three Orders of Magnitude – J. Gore [Site | Books]
- L01: TR1-230 in 35-308

- 8.282 // Intro to Astronomy – J. Hewitt [Site | Books]
- L01: TR1-230 in 4-231

- 8.292J // Fluid Physics – L. Bourouiba [Site | Books]
- L01: TR230-4 in 37-212

- 8.311 // Electromagnetic Theory – L. Fu [Site | Books]
- L01: MW1030-12 in 5-217

- (NEW) 8.16/316 // Data Science – P. Harris [Site | Books]
- L01: MW230-4 in 36-112

- 8.323 // QFT I – H. Liu [Site | Books]
- L01: MW430-6 in 4-163

- 8.325 // QFT III – W. Taylor [Site | Books]
- L01: TR9-1030 in 4-265

- 8.334 // Statistical Mechanics II – M. Kardar [Site | Books]
- L01: MW230-4 in 4-257

- 8.371 // Quantum Info Science – S. Choi [Site | Books]
- L01: MW930-11 in 2-190 – Shor

- 8.396 // LEAPS Part I (half-term) – A. Frebel [Site | Books]
- L01: TR930-11 in 32-082

- 8.397 // LEAPS Part II (half-term) – A. Frebel [Site | Books]
- L01: TR930-11 in 32-082

- 8.398 // Selected Topics in Graduate Physics – J. Thaler [Site | Books]
- L01: W12-1 in 26-414

- 8.422 // AMO II – M. Zwierlein [Site | Books]
- L01: MW1-230 in 56-154

- 8.512 // Theory of Solids II – L. Levitov [Site | Books]
- L01: TR1-230 in 4-159

- 8.514 // Strongly Correlated Systems – S. Todadri [Site | Books]
- L01: TR230-4 in 32-144

- 8.582J // Selected Topics in Condensed Matter – W. Oliver [Site | Books]
- L01: MW230-4 in 26-328

- 8.711 // Nuclear Physics – R. Garcia Ruiz [Site | Books]
- L01: TR1-230 in 26-328

- 8.751J // Quantum Technology and Devices – P. Cappellaro [Site | Books]
- L01: TR930-11 in 36-372

- 8.901 // Astrophysics I – A. Vanderburg [Site | Books]
- L01: MW1-230 in 4-261

- 8.962 // General Relativity – N. Engelhardt [Site | Books]
- L01: TR230-4 in 4-163

- 8.S998 // Special Subject: Undergraduate Mentoring – E. Bertschinger [Site | Books]
- L01 M11-12, B01 F1-2 in 26-168 – Bertschinger
- L02 T1-2, B02 F2-3 in 26-168 – Drury
- L03 W10-11, B03 R1-2 in 26-168 – Tomasik

### Fall 2023

Fall 2023 schedule will be posted in late Spring.

### IAP 2023

- 8.01L // Physics I – P. Jarillo-Herrero [Site | Books]
- L1: TR 930-11, F3-430 in 32-082 – TBA
- L2: TR 11-1230, F3-430 in 32-082 – TBA
- R1: F 3-430 in 32-082 – Drury

- 8.20 // Special Relativity – Y. Lee [Site | Books]
- L1: MTWRF 3-4:30 in 26-328
- R1: TR 430-5 in 26-328

- 8.223 // Classical Mechanics – M. Williams [Site | Books]
- L1: MTWRF 10-1130 in 4-270
- R1: MTWRF 1230-130 in 4-270

- 8.228 // Relativity II – T. Slatyer [Site | Books]
- L1: MTWRF 3-4 in 26-322
- R1: R 4 in 26-322
- R2: T 4 in 26-322

- 8.Mechanics Review (half-term) – D. Pritchard
- L1: MTWRF 10-12 in 36-153

- 8.298 // Special Topics – Staff [Site | Books]
- Tuesdays, Jan 10, 17, 24, 31 in 32-082

### All Subjects

Undergraduate Subjects

### 8.01 Physics I

U – Fall – GIR

Prereq: None

Units: 3-2-7

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.

### 8.011 Physics I

U – Spring – GIR

Prereq: Permission of instructor

Units: 5-0-7

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

U – Fall – GIR

Prereq: None

Units: 5-0-7

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. Freshmen admitted via AP or Math Diagnostic for Physics Placement results.

### 8.01L Physics I

U – Fall & IAP – GIR

Prereq: None

Units: 3-2-7

Credit cannot also be received for 8.01, 8.011, 8.012, ES.801, ES.8012

Ends late Jan. **+final**

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.

### 8.02 Physics II

U – Fall, Spring – GIR

Prereq: Calculus I (GIR) and Physics I (GIR)

Units: 3-2-7

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.

### 8.021 Physics II

U – Fall – GIR

Prereq: Calculus I (GIR), Physics I (GIR), and permission of instructor

Units: 5-0-7

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.

### 8.022 Physics II

U – Fall, Spring – GIR

Prereq: Physics I (GIR); *Coreq: Calculus II (GIR)*

Units: 5-0-7

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

U – Fall, Spring – REST substitution

Prereq: Calculus II (GIR) and Physics II (GIR)

Units: 5-0-7

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.

### 8.033 Relativity

U – Fall – REST substitution

Prereq: Calculus II (GIR) and Physics II (GIR)

Units: 5-0-7

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

U – Spring – REST substitution

Prereq: 8.03 and (18.03 or 18.032)

Units: 5-0-7

Credit cannot also be received for 8.S04

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

U – Fall – REST substitution

Prereq: 8.03 and (18.03 or 18.032)

Units: 2-0-10

Credit cannot also be received for 8.04

Blended version of 8.04 using a combination of online and in-person instruction. Covers 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.

### 8.044 Statistical Physics I

U – Spring

Prereq: 8.03 and 18.03

Units: 5-0-7

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

U – Fall

Prereq: 8.04

Units: 5-0-7

Credit cannot also be received for 8.051

Together 8.05 and 8.06 cover 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 wavefunctions. 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.

### 8.051 Quantum Physics II

U – Spring

Prereq: 8.04 and permission of instructor

Units: 2-0-10

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.

### 8.06 Quantum Physics III

U – Spring

Prereq: 8.05

Units: 5-0-7

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

U – Fall

Prereq: 8.03 and 18.03

Units: 4-0-8

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

U – Spring

Prereq: 8.044 and 8.05

Units: 4-0-8

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.

### 8.09 Classical Mechanics III

U – Fall

(Subject meets with 8.309)

Prereq: 8.223

Units: 4-0-8

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

U – Fall (*Not offered academic year 2021-2022*)

Prereq: None

Units: 2-0-0 [P/D/F]

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 rewriting. Subject can count toward the 9-unit discovery-focused credit limit for first year students.

### 8.13 Experimental Physics I

U – Fall, Spring – Institute Lab

Prereq: 8.04

Units: 0-6-12

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.

### 8.14 Experimental Physics II

U – Fall, Spring

Prereq: 8.05 and 8.13

Units: 0-6-12

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 (New)

U – Spring

(Subject meets with 8.316)

Prereq: 8.04 and (6.100A, 6.100B, or permission of instructor)

Units: 3-0-9

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

U – Fall, IAP, Spring, Summer (Can be repeated for credit)

Prereq: Permission of instructor

Units arranged [P/D/F]

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

### 8.19 Readings in Physics

U – Fall, IAP, Spring, Summer (Can be repeated for credit)

Prereq: None

Units arranged [P/D/F]

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

U – IAP – REST substitution

Prereq: Calculus I (GIR) and Physics I (GIR)

Units: 2-0-7

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

U – Spring – REST substitution

Prereq: Calculus II (GIR), Chemistry (GIR), and Physics II (GIR)

Units: 5-0-7

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

U – IAP

Prereq: Calculus II (GIR) and Physics I (GIR)

Units: 2-0-4

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

U – Fall

Prereq: 8.033 or 8.20

Units: 3-0-9

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 edbert@mit.edu. Limited to 40.

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

U – Fall – HASS Humanities

(Same subject as STS.042[J])

Prereq: None

Units: 3-0-9

Explores the changing roles of physics and physicists during the 20th century. Topics range from relativity theory and quantum mechanics to high-energy physics and cosmology. Examines the development of modern physics within shifting institutional, cultural, and political contexts, such as physics in Imperial Britain, Nazi Germany, US efforts during World War II, and physicists’ roles during the Cold War. Enrollment limited.

### 8.226 Forty-three Orders of Magnitude

U – Spring (Not offered regularly; consult department)

Prereq: (8.04 and 8.044) or permission of instructor

Units: 3-0-9

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 (New)

U – IAP

Prereq: 8.033 or permission of instructor

Units: 2-0-4

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

U – Fall

Prereq: 8.044; *Coreq: 8.05*

Units: 4-0-8

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

U – Spring

Prereq: Physics II (GIR) and (5.60 or 8.044)

Units: 4-0-8

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. 20.315 and 20.415 meet with 8.241 when offered concurrently.

### 8.245[J] Viruses, Pandemics, and Immunity

U – Spring (Not offered regularly; consult department)

(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

Units: 2-0-1

Covers the history of infectious diseases, basics of virology, immunology, and epidemiology, and ways in which diagnostic tests, vaccines, and antiviral therapies are currently designed and manufactured. Examines the origins of inequities in infection rates in society, and issues pertinent to vaccine safety. Final project explores how to create a more pandemic-resilient world. HST.438 intended for first-year students; all others should take HST.439.

### 8.251 String Theory for Undergraduates

U – Spring

Prereq: 8.033, 8.044, and 8.05

Units: 4-0-8

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

U – Spring (Not offered regularly; consult department)

Prereq: 8.033 and 8.04

Units: 4-0-8

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.

### 8.277 Introduction to Particle Accelerators

U – Fall, IAP, Spring, Summer – Can be repeated for credit

(Not offered regularly; consult department)

Prereq: (6.013 or 8.07) and permission of instructor

Units arranged

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.

### 8.282[J] Introduction to Astronomy

U – Spring – REST substitution

(Same subject as 12.402[J])

Prereq: Physics I (GIR)

Units: 3-0-6

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

U – Spring

Prereq: 8.04; *Coreq: 8.05*

Units: 3-0-9

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

U – Fall – REST substitution

Prereq: Physics II (GIR) and 18.03

Units: 3-0-9

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

U – Fall – Institute Lab

(Same subject as 12.410[J])

Prereq: 8.282, 12.409, or other introductory astronomy course

Units: 3-4-8

Fundamental physical and optical principles used for astronomical measurements at visible wavelengths and practical methods of astronomical observations. Topics: astronomical coordinates, time, optics, telescopes, photon counting, signal-to-noise ratios, data analysis (including least-squares model fitting), limitations imposed by the Earth’s atmosphere on optical observations, CCD detectors, photometry, spectroscopy, astrometry, and time variability. Project at Wallace Astrophysical Observatory. Written and oral project reports. Limited to 18; preference to Course 8 and Course 12 majors and minors.

### 8.290[J] Extrasolar Planets: Physics and Detection Techniques

U – Fall – REST substitution

(Same subject as 12.425[J])

(Subject meets with 12.625)

Prereq: 8.03 and 18.03

Units: 3-0-9

Presents basic principles of planet atmospheres and interiors applied to the study of extrasolar planets. Focuses on fundamental physical processes related to observable extrasolar planet properties. Provides a quantitative overview of detection techniques. Introduction to the feasibility of the search for Earth-like planets, biosignatures and habitable conditions on extrasolar planets. Students taking graduate version complete additional assignments.

### 8.292[J] Fluid Physics

U – Spring

(Same subject as 12.330[J])

Prereq: 5.60, 8.044, or permission of instructor

Units: 3-0-9

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.

### 8.295 Practical Experience in Physics

U – Fall, IAP, Spring, Summer – Can be repeated for credit

Prereq: None

Units: 0-1-0 [P/D/F]

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 supervisor. 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 supervisor. Subject to departmental approval. Consult departmental academic office.

### 8.298 Selected Topics in Physics

U – Fall, IAP, Spring, Summer – Can be repeated for credit

Prereq: Permission of instructor

Units arranged

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

### 8.299 Physics Teaching

U – Fall, Spring – Can be repeated for credit

Prereq: None

Units arranged [P/D/F]

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

U – Fall, Spring – Can be repeated for credit

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

Units: 0-0-1 [P/D/F]

Provides students with skills to prepare for and excel in the world of industry. Emphasizes practical application of career theory and professional development concepts. Introduces students to relevant and timely resources for career development, provides students with tools to embark on a successful internship search, and offers networking opportunities with employers and MIT alumni. Students work in groups, led by industry mentors, to improve their resumes and cover letters, interviewing skills, networking abilities, project management, and ability to give and receive feedback. Objective is for students to be able to adapt and contribute effectively to their future employment organizations. A total of two units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult UPOP website for more information.

### 8.S02 Special Subject: Physics

U – Spring

Prereq: None

Units: 1-0-2 [P/D/F]

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

### 8.S227 Special Subject: Physics

U – Spring

Prereq: None

Units: 3-0-9

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

### 8.S228 Special Subject: Physics

U – IAP (Not offered regularly; consult department)

Prereq: None

Units: 2-0-4

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

### 8.S271 Special Subject: Physics

U – Spring

Prereq: None

Units: 2-0-4

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

### 8.S30 Special Subject: Physics

U – Fall (Not offered regularly; consult department)

Prereq: None

Units arranged

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

### 8.S50 Special Subject: Physics

U – IAP – Can be repeated for credit (Not offered regularly; consult department)

Prereq: None

Units arranged [P/D/F]

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

### 8.S998 Special Subject: Undergraduate Mentoring

U – Fall, Spring

Prereq: None

Units: 2-0-1 [P/D/F]

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

### 8.UR Undergraduate Research

U – Fall, IAP, Spring, Summer – Can be repeated for credit

Prereq: None

Units arranged [P/D/F]

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

### 8.THU Undergraduate Physics Thesis

U – Fall, IAP, Spring, Summer – Can be repeated for credit

Prereq: None

Units arranged

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

Graduate Subjects

### 8.309 Classical Mechanics III

G – Fall

(Subject meets with 8.09)

Prereq: None

Units: 4-0-8

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.

### 8.311 Electromagnetic Theory I

G – Spring

Prereq: 8.07

Units: 4-0-8

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

G – Spring

(Same subject as 18.369[J])

Prereq: 8.07, 18.303, or permission of instructor

Units: 3-0-9

High-level approaches to understanding complex optical media, structured on the scale of the wavelength, that are not generally analytically soluable. The basis for understanding optical phenomena such as photonic crystals and band gaps, anomalous diffraction, mechanisms for optical confinement, optical fibers (new and old), nonlinearities, and integrated optical devices. Methods covered include linear algebra and eigensystems for Maxwell’s equations, symmetry groups and representation theory, Bloch’s theorem, numerical eigensolver methods, time and frequency-domain computation, perturbation theory, and coupled-mode theories.

### 8.316 Data Science in Physics (New)

G – Spring

(Same subject as 8.16)

Prereq: 8.04 and (6.100A, 6.100B, or permission of instructor)

Units: 3-0-9

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.

### 8.321 Quantum Theory I

G – Fall

Prereq: 8.05

Units: 4-0-8

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

G – Spring

Prereq: 8.07 and 8.321

Units: 4-0-8

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.

### 8.323 Relativistic Quantum Field Theory I

G – Spring

Prereq: 8.321

Units: 4-0-8

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

G – Fall

Prereq: 8.322 and 8.323

Units: 4-0-8

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

G – Spring

Prereq: 8.324

Units: 4-0-8

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

G – Fall

Prereq: 8.044 and 8.05

Units: 4-0-8

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

G – Spring

Prereq: 8.333

Units: 4-0-8

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

G – Fall

(Same subject as 6.946[J], 12.620[J])

Prereq: Physics I (GIR), 18.03, and permission of instructor

Units: 3-3-6

Classical mechanics in a computational framework, Lagrangian formulation, action, variational principles, and Hamilton’s principle. Conserved quantities, Hamiltonian formulation, surfaces of section, chaos, and Liouville’s theorem. Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems. Invariant curves and cantori. Nonlinear resonances, resonance overlap and transition to chaos. Symplectic integration. Adiabatic invariants. Applications to simple physical systems and solar system dynamics. Extensive use of computation to capture methods, for simulation, and for symbolic analysis. Programming experience required.

### 8.370[J] QIS I: Quantum Computation

G – Fall

(Same subject as 2.111[J], 6.6410[J], 18.435[J])

Prereq: 8.05, 18.06, 18.700, 18.701, or 18.C06

Units: 3-0-9

Provides an introduction to the theory and practice of quantum computation. Topics covered: physics of information processing; quantum algorithms including the factoring algorithm and Grover’s search algorithm; quantum error correction; quantum communication and cryptography. Knowledge of quantum mechanics helpful but not required.

### 8.371[J] QIS II: Quantum Information Science

G – Spring

(Same subject as 6.443[J], 18.436[J])

Prereq: 18.435

Units: 3-0-9

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.

### 8.372 QIS III: Quantum Information Science III

G – Fall

Prereq: 8.371

Units: 3-0-9

Third subject in the Quantum Information Science (QIS) sequence, building on 8.370 and 8.371. 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

G – Fall, Spring (Not offered regularly; consult department)

Prereq: Permission of instructor

Units: 3-0-9

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

G – Fall (Can be repeated for credit)

Prereq: Permission of instructor

Units arranged [P/D/F]

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

### 8.392 Pre-Thesis Research

G – Spring, Summer (Can be repeated for credit)

Prereq: Permission of instructor

Units arranged [P/D/F]

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

### 8.395[J] Teaching College-Level Science and Engineering

G – Fall

(Same subject as 1.95[J], 5.95[J], 7.59[J], 18.094[J])

(Subject meets with 2.978)

Prereq: None

Units: 2-0-2 [P/D/F]

Participatory seminar focuses on the knowledge and skills necessary for teaching science and engineering in higher education. Topics include theories of adult learning; course development; promoting active learning, problem solving, and critical thinking in students; communicating with a diverse student body; using educational technology to further learning; lecturing; creating effective tests and assignments; and assessment and evaluation. Students research and present a relevant topic of particular interest. Appropriate for both novices and those with teaching experience.

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

G – Spring (second half of term)

(Same subject as 5.961[J], 9.980[J], 12.396[J], 18.896[J])

Prereq: None

Units: 2-0-1 [P/D/F]

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. No required or recommended textbooks

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

G – Spring (first half of term)

(Same subject as 5.962[J], 9.981[J], 12.397[J], 18.897[J])

Prereq: None

Units: 2-0-1 [P/D/F]

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. No required or recommended textbooks

### 8.398 Selected Topics in Graduate Physics

G – Fall, Spring (Can be repeated for credit)

Prereq: None

Units arranged

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.

### 8.399 Physics Teaching

G – Fall, Spring (Can be repeated for credit)

Prereq: Permission of instructor

Units arranged [P/D/F]

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.

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

### 8.421 Atomic and Optical Physics I

G – Spring

Prereq: 8.05

Units: 3-0-9

The first of a two-term subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical physics. 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.

### 8.422 Atomic and Optical Physics II

G – Spring

Prereq: 8.05

Units: 3-0-9

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

G – Spring

(Same subject as 6.6340[J])

Prereq: 6.2300 or 8.07

Units: 3-0-9

Techniques of nonlinear optics with emphasis on fundamentals for research and engineering in optics, photonics, and spectroscopy. Electro optic modulators, harmonic generation, and frequency conversion devices. Nonlinear effects in optical fibers including self-phase modulation, nonlinear wave propagation, and solitons. Interaction of light with matter, laser operation, density matrix techniques, nonlinear spectroscopies, and femtosecond optics.

### 8.481, 8.482 Selected Topics in Physics of Atoms and Radiation

G – Fall, Spring (Not offered regularly; consult department)

Prereq: 8.321

Units: 3-0-9

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

G – Fall

Prereq: 8.231

Units: 3-0-9

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

G – Spring

Prereq: 8.511

Units: 3-0-9

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

G – Fall

Prereq: 8.033, 8.05, 8.08, and 8.231

Units: 3-0-9

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

G – Spring

Prereq: 8.322 and 8.333

Units: 3-0-9

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

G – Fall, Spring – Can be repeated for credit

Prereq: Permission of instructor

Units: 3-0-9

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 (New)

G – Fall

(Same subject as 7.74[J], 20.416[J])

Prereq: None

Units: 2-0-4 [P/D/F]

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.

### 8.591[J] Systems Biology

G – Fall

(Same subject as 7.81[J])

(Subject meets with 7.32)

Prereq: (18.03 and 18.05) or permission of instructor

Units: 3-0-9

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

G – Spring

(Same subject as HST.452[J])

Prereq: 8.333 or permission of instructor

Units: 3-0-9

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.

### 8.593[J] Biological Physics

G – Spring (Not offered regularly; consult department)

(Same subject as HST.450[J])

Prereq: 8.044 recommended but not necessary

Units: 4-0-8

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

G – Fall

(Same subject as 22.611[J])

Prereq: (6.013 or 8.07) and (18.04 or *Coreq: 18.075*)

Units: 3-0-9

Introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics. Elementary plasma concepts, plasma characterization. Motion of charged particles in magnetic fields. Coulomb collisions, relaxation times, transport processes. Two-fluid hydrodynamic and MHD descriptions. Plasma confinement by magnetic fields, simple equilibrium and stability analysis. Wave propagation in a magnetic field; application to RF plasma heating. Introduction to kinetic theory; Vlasov, Boltzmann and Fokker-Planck equations; relation of fluid and kinetic descriptions. Electron and ion acoustic plasma waves, Landau damping.

### 8.614[J] Introduction to Plasma Physics II

G – Spring

(Same subject as 22.612[J])

Prereq: 22.611

Units: 3-0-9

Follow-up to 22.611 provides in-depth coverage of several fundamental topics in plasma physics, selected for their wide relevance and applicability, from fusion to space- and astro-physics. Covers both kinetic and fluid instabilities: two-stream, Weibel, magnetorotational, parametric, ion-temperature-gradient, and pressure-anisotropy-driven instabilities (mirror, firehose). Also covers advanced fluid models, and drift-kinetic and gyrokinetic equations. Special attention to dynamo theory, magnetic reconnection, MHD turbulence, kinetic turbulence, and shocks.

### 8.624 Plasma Waves

G – Spring

Prereq: 22.611

Units: 3-0-9

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.

### 8.641 Physics of High-Energy Plasmas I

G – Fall (Not offered regularly; consult department)

Prereq: 22.611

Units: 3-0-9

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

G – Fall (Not offered regularly; consult department)

Prereq: 22.611

Units: 3-0-9

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.

### 8.670[J] Principles of Plasma Diagnostics

G – Fall (Not offered regularly; consult department)

(Same subject as 22.67[J])

Prereq: 22.611

Units: 4-4-4

Introduction to the physical processes used to measure the properties of plasmas, especially fusion plasmas. Measurements of magnetic and electric fields, particle flux, refractive index, emission and scattering of electromagnetic waves and heavy particles; their use to deduce plasma parameters such as particle density, pressure, temperature, and velocity, and hence the plasma confinement properties. Discussion of practical examples and assessments of the accuracy and reliability of different techniques.

### 8.681, 8.682 Selected Topics in Fluid and Plasma Physics

G – Fall, Spring – Can be repeated for credit (Not offered regularly; consult department)

Prereq: 22.611

Units: 3-0-9

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

### Nuclear and Particle Physics

### 8.701 Introduction to Nuclear and Particle Physics

G – Fall

Prereq: None. *Coreq: 8.321*

Units: 3-0-9

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

G – Spring

Prereq: 8.321 and 8.701

Units: 4-0-8

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

G – Fall, Spring – Can be repeated for credit (Not offered regularly; consult department)

Prereq: 8.711 or permission of instructor

Units: 3-0-9

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

G – Spring

(Same subject as 22.51[J])

(Subject meets with 22.022)

Prereq: 22.11

Units: 3-0-9

Examines the unique features of quantum theory to generate technologies with capabilities beyond any classical device. Introduces fundamental concepts in applied quantum mechanics, tools and applications of quantum technology, with a focus on quantum information processing beyond quantum computation. Includes discussion of quantum devices and experimental platforms drawn from active research in academia and industry. Students taking graduate version complete additional assignments.

### 8.781, 8.782 Selected Topics in Nuclear Theory

G – Fall, Spring (Not offered regularly; consult department)

Prereq: 8.323

Units: 3-0-9

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.

### 8.811 Particle Physics

G – Fall

Prereq: 8.701

Units: 3-0-9

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

G – IAP (Not offered regularly; consult department)

Prereq: 8.701

Units: 1-8-3

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

G – Fall

Prereq: 8.324

Units: 3-0-9

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

G – Fall – Can be repeated for credit

Prereq: Permission of instructor

Units: 3-0-9

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

G – Spring

Prereq: 8.324

Units: 3-0-9

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

G – Fall – Can be repeated for credit

Prereq: 8.323

Units: 3-0-9

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

G – Fall, Spring – Can be repeated for credit

Prereq: 8.323

Units: 3-0-9

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.

### 8.881, 8.882 Selected Topics in Experimental Particle Physics

G – Fall, Spring – Can be repeated for credit (Not offered regularly; consult department)

Prereq: 8.811

Units: 3-0-9

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

G – Spring

Prereq: Permission of instructor

Units: 3-0-9

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

G – Fall

Prereq: 8.901

Units: 3-0-9

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.

### 8.913 Plasma Astrophysics I

G – Fall (Not offered regularly; consult department)

Prereq: Permission of instructor

Units: 3-0-9

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

G – Spring (Not offered regularly; consult department)

Prereq: Permission of instructor

Units: 3-0-9

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.

### 8.921 Stellar Structure and Evolution

G – Spring (Not offered regularly; consult department)

Prereq: Permission of instructor

Units: 3-0-9

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

G – Fall

Prereq: Permission of instructor

Units: 3-0-9

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

G – Spring

Prereq: 8.323; *Coreq: 8.324*

Units: 3-0-9

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

### 8.971 Astrophysics Seminar

G – Fall, Spring – Can be repeated for credit (Not offered regularly; consult department)

Prereq: Permission of instructor

Units: 2-0-4 [P/D/F]

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.

### 8.972 Astrophysics Seminar

G – Fall, Spring – Can be repeated for credit (Not offered regularly; consult department)

Prereq: Permission of instructor

Units: 2-0-4 [P/D/F]

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

G – Spring – Can be repeated for credit (Not offered regularly; consult department)

Prereq: Permission of instructor

Units: 3-0-9 [P/D/F]

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

G – Fall, IAP, Spring, Summer – Can be repeated for credit

Prereq: None

Units arranged [P/D/F]

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 supervisor, 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 supervisor. Consult departmental academic office.

### 8.S301 Special Subject: Physics

G – Spring (Not offered regularly; consult department)

Prereq: Permission of instructor

Units arranged

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

### 8.S372 Special Subject: Physics

G – Fall

Prereq: None

Units: 3-0-9

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

### 8.S421 Special Subject: Physics

G – Fall – Can be repeated for credit (Not offered regularly; consult department)

Prereq: Permission of instructor

Units arranged

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

### 8.THG Graduate Physics Thesis

G – Fall, IAP, Spring, Summer – Can be repeated for credit

Prereq: Permission of instructor

Units arranged

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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