Subjects

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 or 8.041

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

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.

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.

U – Fall
Prereq: 8.04 or 8.041
Units: 5-0-7
Credit cannot also be received for 8.051

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

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.

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.

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.

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.

U – Fall, Spring
(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.

U – Fall (Not offered regularly; consult department)
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.

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.

U – 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.

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.

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.

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.

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.

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.

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.

U – Fall (Not offered regularly; consult department)
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.

U – Fall – HASS Humanities
(Same subject as STS.042[J])
Prereq: None
Units: 3-0-9

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

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.

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.

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.

U – Spring (Not offered regularly; consult department)
Prereq: Physics II (GIR) and (8.044 or (5.601 and 5.602))
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. Meets with 20.315 and 20.415 when offered concurrently.

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

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

U – Spring (Not offered regularly; consult department)
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.

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.

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.

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.

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.

U – Fall – REST substitution (Not offered regularly; consult department)
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.

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

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

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

See description under subject 12.425[J].

U – Spring (Not offered regularly; consult department)
(Same subject as 1.066[J], 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.

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.

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.

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.

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]

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

U – Spring (Not offered regularly; consult department)
Prereq: None
Units: 1-0-2 [P/D/F]

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

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

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

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.

U – Spring (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.

U – Fall, Spring (Not offered regularly; consult department)
Prereq: None
Units arranged

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

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.

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.

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.

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.

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.

G – Spring (Not offered regularly; consult department)
(Same subject as 18.369[J])
Prereq: 8.07, 18.303, or permission of instructor
Units: 3-0-9

See description under subject 18.369[J].

G – Spring (Not offered regularly; consult department)
(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.

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.

G – Spring (Not offered regularly; consult department)
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.

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.

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.

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.

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.

G – Spring (Not offered regularly; consult department)
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.

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

See description under subject 12.620[J].

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

See description under subject 18.435[J].

G – Spring
(Same subject as 6.6420[J], 18.436[J])
Prereq: 18.435[J]
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.

G – Fall (Not offered regularly; consult department)
Prereq: 8.371[J]
Units: 3-0-9

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

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.

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.

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.

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]

See description under subject 5.95[J].

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

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

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.

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.

G – Spring (Not offered regularly; consult department)
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.

G – Spring (Not offered regularly; consult department)
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.

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

See description under subject 6.6340[J].

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.

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.

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.

G – Fall (Not offered regularly; consult department)
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.

G – Spring (Not offered regularly; consult department)
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.

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

G – Fall (Not offered regularly; consult department)
(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.

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.

G – Spring (Not offered regularly; consult department)
(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.

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.

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

See description under subject 22.611[J].

G – Spring (Not offered regularly; consult department)
(Same subject as 22.612[J])
Prereq: 22.611
Units: 3-0-9

See description under subject 22.612[J].

G – Spring (Not offered regularly; consult department)
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.

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.

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.

G – Fall (Not offered regularly; consult department)
(Same subject as 22.67[J])
Prereq: 22.611
Units: 4-4-4

See description under subject 22.67[J].

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

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.

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.

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.

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

See description under subject 22.51[J].

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.

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.

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.

G – Fall (Not offered regularly; consult department)
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.

G – Fall (Not offered regularly; consult department) – 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.

G – Spring (Not offered regularly; consult department)
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.

G – Fall (Not offered regularly; consult department) – 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.

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

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

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.

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.

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.

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.

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.

G – Fall (Not offered regularly; consult department)
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.

G – Spring (Not offered regularly; consult department)
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.

G – Spring
Prereq: 8.07, 18.03, and 18.06
Units: 4-0-8

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

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

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

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

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.

U – Fall, Spring
Prereq: None
Units: 2-0-1 [P/D/F]

Designed for first-time physics mentors and others interested in improving their knowledge and skills in teaching one-on-one and in small groups, particularly TEAL TAs and graduate student TAs. Topics include: cognition, metacognition, and the role of affect; communication skills (practice listening, questioning, and eliciting student ideas); the roles of motivation and mindset in learning; fostering belonging and self-efficacy through peer mentorship; facilitating small-group interactions to enhance peer instruction and learning; physics-specific learning strategies, such as how to teach/learn problem solving; research-based techniques for effective mentorship in STEM. Includes a one-hour class on pedagogy topics, a one-hour weekly Physics Mentoring Community of Practice meeting, and weekly assignments to read or watch material in preparation for class discussions, and written reflections before class. No required or recommended textbooks

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.

G – Fall
Prereq: None
Units: 3-0-9

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

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.

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.