


Graduate Courses


16:750:501,502
Quantum Mechanics (3,3)
Historical introduction; waves and wave packets; onedimensional problems; representation theory; angular momentum and spin; timedependent and timeindependent perturbation theory; the WKB approximation; atomic and molecular systems; theory of scattering; semiclassical theory of radiation; Dirac equation.
Vanderbilt. Prerequisite: 01:750:417 or equivalent.

16:750:503
(F) Electricity and Magnetism I (3)
Advanced electromagnetic theory and related mathematical techniques. Boundaryvalue problems in electrostatics and magnetostatics; complex variables; Green's functions; multipole expansions; Maxwell's equations and plane electromagnetic waves; waveguides.
Haule. Prerequisite: 01:750:386 or equivalent.

16:750:504
(S) Electricity and Magnetism II (3)
Radiation; detailed discussion of special relativity, including spacetime diagrams, covariance and invariance, twin paradox, uniform acceleration, motion of a charged particle, and stressenergy tensors. Radiation by moving charges, bremsstrahlung, multipole fields, and radiation damping.
Yuzbashyan. Prerequisite: 16:750:503.

16:750:505
(S) Quantum Electronics (3)
Modern optics; atomic and solidstate phenomena; masers, lasers, theory of amplification, oscillation, and coherence; photon correlations; nonlinear optics. Electron and nuclear magnetic resonance. Tunneling phenomena.
Prerequisite: 01:750:417 or equivalent.

16:750:506
(S) Modern Experimental Techniques (4)
Modern instruments and techniques in experimental physics. Topics include passive network theory and transient and steadystate response analysis; transmission lines; operational amplifiers; digital circuits; a detailed study of noise; phasesensitive detection, including lockin amplifiers and signal averagers; lowlevel measurement techniques, including quantum interference devices; and particle detection techniques.
E. Andrei. Prerequisites: 01:750:326, 388 or equivalent.

16:750:507
(F) Classical Mechanics (3)
Advanced classical mechanics; Lagrangian mechanics and calculus of variations. Hamilton's equations, canonical transformations, HamiltonJacobi theory, and small oscillations. Rigid body motion.
Yuzbashyan. Prerequisite: 01:750:382 or equivalent.

16:750:509
(S) Physics Application of Computers (3)
Survey of applications. Survey of hardware and software of a computer installation; interactive computing. Advanced Fortran, program structures, style, documentation, and debugging. Machine language basics, data acquisition, and equipment control. Use of data tapes and data processing; Monte Carlo techniques; statistics and data fitting; and basic numerical methods. Laboratory: programming on several computers. Broadens knowledge of applications and facilitates development of techniques.
Haule. Lec. 2 hrs., lab. 3 hrs. Prerequisite: Programming experience.

16:750:511
(F) Mathematical Physics (3)
Physical applications of linear algebra, the exterior calculus, differential forms, complexes, and cohomology. Applications include Hamiltonian dynamics, normalmode analysis, Markov processes, thermodynamics, Schröedinger's equation, special relativity, electrostatics, magnetostatics, Maxwell's equations, and wave equations. Also offered as 01:750:464.
Prerequisites: 01:640:403, 423, or equivalent.

16:750:514
(S) Radiative Processes (3)
Electromagnetic phenomena in astrophysical systems. Radiative transfer. Radiation from moving charges. Emission mechanisms: Bremsstrahlung, synchrotron, Compton scattering. Plasma effects. Atomic and molecular structure and spectroscopy.
Jha. Prerequisite: 16:750:503.

16:750:523
(F) Techniques in Experimental Physics (3)
Electronics as it is used in experimental physics. Transistors and their equivalent circuits, amplifiers, networks, digital logic, light and particle detectors, and lowlevel measurements, including quantum interference devices.
Prerequisite: Elementary physics laboratory. Not intended for students in the Ph.D. program.

16:750:524
(S) Topics in Physics (3)
Selfpaced course in which the student studies independently and the faculty act as tutors, providing help as needed and administering examinations. Subject matter divided into units, covering a wide range of topics drawn from classical and modern physics. Units chosen in consultation with an adviser, taking into account the background and interests of each student.
Not intended for students in the Ph.D. program.

16:750:541
Stars and Star Formation (3)
Observed properties of stars. The internal structure of stars, energy generation and transport, neutrinos, and solar oscillations. The evolution of isolated and double stars, red giants, white dwarfs, variable stars, and supernovae. Challenges presented by the formation of stars and the importance of magnetic fields. Premain sequence stellar evolution. Also offered as 01:750:441.
Hughes

16:750:543
Galaxies and the Milky Way (3)
Properties of galaxies; photometry, kinematics, and masses. Disk galaxies; spiral patterns, bars, and warps; gas content; star formation rates; and chemical evolution. Elliptical galaxies; shapes. Structure of the Milky Way. The nature of dark matter. Also offered as 01:750:443.
Somerville

16:750:551
(F) Development of Ideas in Physical Science (3)
The epistemology of physics; the construction of knowledge; how physicists know what they know.
Etkina. Prerequisite: Permission of instructor.

16:750:552
(S) Teaching Physical Science (3)
Pedagogical content knowledge and skills; techniques for planning
and assessment.
Etkina. Prerequisite: Permission of instructor.

16:750:557
(S) Multiple Representations in Physical Science (3)
Multiple representation method used in constructing concepts and
problem solving.
Etkina. Prerequisite: Permission of instructor.

16:750:563
Molecular Simulations in Computational Biology (3)
Focuses on molecular modeling and simulations of biological macromolecules including proteins and nucleic acids, molecular dynamics and Monte Carlo methods, and solvation. Computer simulations and exercises are an integral part of the course. Also offered as 16:118:513.
Prerequisites: Advanced undergraduate courses in physical chemistry or physics.

16:750:567
Physics of Living Matter (3)
Review of physical phenomena that determine the properties of biological molecules, molecular assemblies, and fundamental biological processes. Also offered as 16:118:507.
Sengupta. Prerequisites: Linear algebra, differential equations, thermodynamics, and classical physics (at the junior level).

16:750:568
LargeScale Data Analysis in Physics and Astronomy (3)
Statistical analysis techniques including
probability distributions, maximum likelihood, significance tests, Bayesian
statistics, statistical/machine learning, kernel methods, and neural networks,
with example applications to current largescale analysis problems in physics
and astronomy.
Prerequisites: 01:750:501 and 16:750:507 or permission of the instructor.

16:750:601,602
(F,S) Solid State I,II (3,3)
Introduction to crystal lattices, scattering of radiation, lattice dynamics, electron bands, interaction among elementary excitations, disordered systems, transport properties, superconductivity and superfluidity, magnetism, crystalfield effects, phase transitions, and optical properties.
N. Andrei. Prerequisites: 01:750:351 and 16:750:502 or equivalent.

16:750:603
(S) SolidState Physics (3)
Advanced treatment of the areas surveyed in 16:750:601 and their extension to topics of current interest in solidstate physics.
Ioffe. Prerequisite: 16:750:601 or equivalent.

16:750:605
(S) Nuclear Physics (3)
Survey of essential topics: properties of ground states, shell model, collective model, electromagnetic properties, sample excitations, compoundnucleus and direct reactions, and beta decay. Additional topics may include alpha decay, fission, applications of nuclear physics, and topics of current interest.
Kloet. Prerequisite: 16:750:502 or equivalent.

16:750:606
(F) Stars and Planets (3)
Stellar properties, internal structure, energy generation and transport, neutrinos, atmospheres, solar oscillations. Stellar evolution, red giants, white dwarfs, variable stars, supernovae, neutron stars, black holes. Brown dwarfs, planets, extrasolar planets.
Pryor. Prerequisite: 16:750:514 or 504.

16:750:607
(S) Galaxies and Galaxy Dynamics (3)
Galaxy properties: photometry, structure, kinematics, gas content, chemical evolution; Milky Way. Stellar system equilibrium, stability, evolution. Disk and elliptical galaxy dynamics and evolution (spiral patterns, bars, warps). Astrophysical chaos.
Somerville. Prerequisite: 16:750:507.

16:750:608
(F) Cosmology (3)
Models of the universe, their fundamental parameters, and their estimation from observations. Evolution of the universe from soon after its formation to the present. Growth of structure and the formation of galaxies.
Somerville. Prerequisites: 01:750:341342 or equivalent.

16:750:609
(F) Fluid and Plasma Physics (3)
Fundamental physical properties of liquids, gases, and ionized systems. Includes selected topics from compressible and incompressible flow, electromagnetic interactions, instabilities, turbulence, nonequilibrium phenomena, kinetics, superfluid mechanics, related experimental techniques, and other topics of current interest in fluid and plasma research.
Sellwood. Prerequisite: 16:750:507 or equivalent.

16:750:610
(S) Interstellar Matter (3)
Structure of the interstellar medium: its molecular, neutral atomic, and plasma phases. Radiative transfer, dust, particle acceleration, magnetic fields, and cosmic rays. Effects of supernovae, shock fronts, and star formation.
Baker. Prerequisite: 16:750:541 or equivalent.

16:750:611
(S) Statistical Mechanics (3)
Statistical methods and probability; the statistical basis for irreversibility and equilibrium; ensemble theory; statistical thermodynamics; classical and quantum statistics; the density matrix; applications of statistical mechanics to nonideal gases, condensed matter, nuclei, and astrophysics; fluctuations, nonequilibrium statistical mechanics, and kinetic theory.
Rabe. Prerequisites: 16:750:501 and 507.

16:750:612
(S) HighEnergy Astrophysics (3)
Origin and detection of highenergy photons and particles in the universe. Radiation processes in lowdensity media. Sites of highenergy phenomena in astrophysics, such as supernovae, pulsars, active galactic nuclei and quasars, and processes, such as accretion and shocks.
Hughes. Prerequisites: 01:750:341342 or equivalent.

16:750:613
(S) Particles (3)
Introduction to the concepts and techniques underlying current research in elementary particles. Assumes knowledge of quantum mechanics, scattering theory, and nuclear spectroscopy. Properties of particles and their interactions based on the standard model of strong and electroweak interactions. Conservation laws. Discussion of specific experiments illustrating the standard model.
Kloet. Prerequisite: 16:750:502 or equivalent.

16:750:615
(F) Overview of Quantum Field Theory (3)
Lorentz group; relativistic waveequations; second quantization; global and local symmetries; QED and gauge invariance; spontaneous symmetry breaking; nonabelian gauge theories; Standard Model; Feynman diagrams; cross sections, decay rates; renormalization group.
Shapiro. Prerequisite: 16:750:502 or equivalent.

16:750:616
(S) Fields I (3)
Path integral quantization; perturbation theory; dimensional regularization and renormalization; the renormalization group; spontaneous symmetry breaking and effective potential; critical behavior of ferromagnets; f^{4} field theory; YangMills perturbation theory.
Shih. Prerequisite: 16:750:615.

16:750:617
(F) General Theory of Relativity (3)
Equivalence principle, tensor analysis with differential forms; review of special relativity and electromagnetism, affine connection and geodesic equation; curvature and geodesic deviation; Einstein field equations; Schwarzschild and Kerr solutions; homogeneous isotropic cosmologies; experimental and observational tests.
Zamolodchikov. Prerequisites: 16:750:504, 507, or equivalent.

16:750:618
(S) Applied Group Theory (3)
Abstract groups and their representations, finite groups, and Lie algebras; symmetries and currents; symmetric group; in homogeneous Lorentz group; SU(n); classification of Lie algebras and Dynkin diagrams. Spontaneous symmetry breaking mechanisms. Gauge theories.
Shapiro. Prerequisite: 16:750:502 or equivalent.

16:750:619
(F) Fields II (3)
Renormalization group applied to YangMills; asymptotic freedom; spontaneous symmetry breaking applied to YangMills; WeinbergSalam theory; lattice gauge theory; grand unified theories; supersymmetry; strings.
Lukyanov. Prerequisite: 16:750:616.

16:750:620
(F) Introduction to ManyBody Theory (3)
Second quantization; elementary excitations; theory of the Fermi
Liquid; density functional and HartreeFock methods. Zero and finite
temperature Green's functions. Relation of correlation functions to
experimental probes; perturbation theory; the electronphonon problem;
and collective excitations.
Coleman. Prerequisite: 16:750:502 or equivalent.

16:750:621
(S) Advanced ManyBody Physics (3)
Systems of interacting bosons and fermions. Theory of superconductivity and superfluidity. Application of the renormalization group to manybody problems. Onedimensional electron gas. Kondo problem and heavy fermions.
Ioffe. Prerequisite: 16:750:620 or equivalent.

16:750:623,624
Advanced Studies in Physics (3,3)
Individual studies supervised by a member of the faculty.
Prerequisite: Permission of graduate director.

16:750:627
(F) Surface Science I (3)
Introduction to structure and dynamics of clean surfaces, atoms and molecules on surfaces, and interfaces. Topics include atomistic description of geometrical structure, surface morphology, electronic structure, surface composition, and theoretical and experimental bases of modern experimental methods.

16:750:628
(S) Surface Science II (3)
Kinetics and dynamics of processes at surfaces; structure and reactivity of molecules at surfaces; thermal and nonthermal excitations; magnetic properties. Surfaces of metals, oxides, and semiconductors, as well as solidsolid and solidliquid interfaces.

16:750:629
(S) Observational Techniques (3)
Introduction to tools and techniques of modern observational astronomy. Survey of instruments and capabilities at current telescope sites around the world and in space. Data reduction methods. Practical experience with Serin Observatory.
Baker. Prerequisite: 16:750:541 or equivalent.

16:750:633,634
Seminar in Physics (0,0)
Seminars in fields of investigations of current interest.
Williams. Prerequisite: Permission of instructor.

16:750:636,637
Basics of Teaching Physics (1,1)
Intended for graduate students interested in improving their skills for teaching physics. Topics include teaching goals, results of recent research, lecturing, demonstrations, teaching problem solving, testing, active learning, course development, and teaching difficult concepts in selected areas of physics. Instructor observes the students teaching.
Prerequisite: Permission of instructor. Concurrent teaching assignment in physics or astronomy recommended.

The following courses may be taken in any order. Offered in alternate years.
16:750:677,678 Advanced
Topics in Statistical Mechanics and Biological Physics I,II (3,3)
16:750:681,682 Advanced Topics in SolidState Physics I,II (3,3)
16:750:685,686 Advanced Topics in Nuclear Physics I,II (3,3)
16:750:689,690 Advanced Topics in Astrophysics I,II (3,3)
16:750:693,694 Advanced Topics in HighEnergy Physics I,II (3,3)
16:750:695 Advanced Topics in Math Physics (3)
16:750:699 Nonthesis Study (1)
16:750:701,702 Research in Physics (BA,BA)






