16:750:501,502Quantum Mechanics (3,3) Historical introduction; waves and wave packets; one-dimensional problems; representation theory; angular momentum and spin; time-dependent and time-independent perturbation theory, the WKB approximation; atomic and molecular systems; theory of scattering; semiclassical theory of radiation; Dirac equation. Coleman. Prerequisite: 01:750:417 or equivalent. |

16:750:503(F) Electricity and Magnetism I (3) Advanced electromagnetic theory and related mathematical techniques. Boundary-value problems in electrostatics and magnetostatics. Complex variables. Green`s functions, multipole expansions. Maxwell`s equations and plane electromagnetic waves; waveguides. Sak. Prerequisite: 01:750:386 or equivalent. |

16:750:504(S) Electricity and Magnetism II (3) Radiation. Detailed discussion of special relativity, including space-time diagrams, covariance and invariance, twin paradox, uniform acceleration, motion of a charged particle, stress-energy tensors. Radiation by moving charges, bremsstrahlung, multipole fields, radiation damping. Sak. Prerequisite: 16:750:503. |

16:750:505(S) Quantum Electronics (3) Modern optics; atomic and solid-state phenomena; masers, lasers, theory of amplification, oscillation, 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 steady- state response analysis; transmission lines; operational amplifiers; digital circuits; a detailed study of noise; phase sensitive detection, including lock-in amplifiers and signal averagers; low-level measurement techniques, including quantum interference devices; particle detection techniques. Prerequisites: 01:750:326, 388, or equivalent. |

16:750:507(F) Classical Mechanics (3) Advanced classical mechanics: Lagrangian mechanics, calculus of variations. Hamilton`s equations, canonical transformations, Hamilton-Jacobi theory, small oscillations. Rigid body motion. Lukyanov. 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, debugging. Machine language basics, data acquisition, equipment control. Use of data tapes, data processing. Monte Carlo techniques. Statistics and data fitting. Basic numerical methods. Laboratory: programming on several computers. Broadens knowledge of applications and facilitates development of techniques. Kotliar. 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, normal-mode analysis, Markov processes, thermodynamics, Schröedinger`s equation, special relativity, electrostatics, magnetostatics, Maxwell`s equations, and wave equations. Zapolsky. Prerequisites: 01:640:403, 423, or equivalent. |

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, low-level 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) Self-paced 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 subjects 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. |

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

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

16:750:601,602(F) Solid-State Physics (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, crystal-field effects, phase transitions, optical properties. N. Andrei. Prerequisites: 01:750:351 and 16:750:502, or equivalent. |

16:750:603(S) Solid-State Physics (3) Advanced treatment of the areas surveyed in 16:750:601 and their extension to topics of current interest in solid-state physics. 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, compound-nucleus and direct reactions, beta decay. Additional topics may include alpha decay, fission, applications of nuclear physics, topics of current interest. Kloet. Prerequisite: 16:750:502 or equivalent. |

16:750:606(S) Nuclear Physics (3) Advanced treatment of some topics discussed in 16:750: 605, together with additional topics chosen in consultation with students. |

16:750:607(F) Galactic Dynamics (3) Equilibrium and stability of stellar systems and the dynamical evolution of galaxies. Modern approach to dynamics with a few practical examples of chaotic systems. Merritt. Prerequisites: 01:750:341-342, 16:750:507, or equivalents. |

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. Kosowsky. Prerequisites: 01:750:341-342 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. 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. Sellwood. Prerequisite: 16:750:541 or equivalent. |

16:750:611(S) Statistical Mechanics (3) Statistical methods and probability; the statistical basis for irrevers-ibility 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; kinetic theory. Ioffe. Prerequisites: 16:750:501 and 507. |

16:750:612(S) High-Energy Astrophysics (3) Origin and detection of high-energy photons and particles in the universe. Radiation processes in low-density media. Sites of high-energy phenomena in astrophysics, such as supernovae, pulsars, active galactic nuclei and quasars, and processes, such as accretion and shocks. Hughes. Prerequisites: 01:750:341-342 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. Neuberger. Prerequisite: 16:750:502 or equivalent. |

16:750:615(F) Overview of Quantum Field Theory (3) Lorentz group; relativistic wave-equations; 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. Prerequisite: 16:750:502 or equivalent. |

16:750:616(S) Fields I (3) Path integral quantization; perturbation theory: dimensional regularization, renormalization; the renormalization group; spontaneous symmetry breaking and effective potential; critical behavior of ferromagnets; f^{4} field theory; Yang-Mills perturbation theory. Zamolodchikov. 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. Zapolsky. 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, Dynkin diagrams. Spontaneous symmetry breaking mechanisms. Gauge theories. Prerequisite: 16:750:502 or equivalent. |

16:750:619(F) Fields II (3) Renormalization group applied to Yang-Mills; asymptotic freedom; spontaneous symmetry breaking applied to Yang-Mills; Weinberg-Salam theory; lattice gauge theory; grand unified theories; supersymmetry; strings. Zamolodchikov. Prerequisite: 16:750:616. |

16:750:620(F) Introduction to Many-Body Theory (3) Second quantization. Elementary excitations. Theory of the Fermi Liquid. Density functional and Hartree-Fock methods. Zero and finite temperature Green`s functions. Relation of correlation functions to experimental probes. Perturbation theory. The electron-phonon problem. Collective excitations. Kotliar. Prerequisite: 16:750:502 or equivalent. |

16:750:621(S) Advanced Many-Body Physics (3) Systems of interacting bosons and fermions. Theory of superconductivity and superfluidity. Application of the renormalization group to many-body problems. One-dimensional electron gas. Kondo problem and heavy fermions. Kotliar. Prerequisite: 16:750:620 or equivalent. |

16:750:623,624Advanced 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. Madey |

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 solid-solid and solid-liquid interfaces. Madey |

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. Coté. Prerequisite: 16:750:541 or equivalent. |

16:750:633,634Seminar in Physics (1,1) Seminars in fields of investigations of current interest. Williams. Prerequisite: Permission of instructor. |

16:750:636,637Basics 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. |