**2000-01 Handbook for Physics and Astronomy Graduate Students**

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**Course Descriptions**

501, 502 QUANTUM MECHANICS (3,3)

Prerequisite: 750:417 Introductory Quantum Mechanics, or equivalent. 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; semi-classical theory of radiation; Dirac equation.

503, 504 ELECTRICITY AND MAGNETISM (3,3)

Prerequisites: 750:386 or equivalent. Advanced Electromagnetic theory and related mathematical techniques. Boundary value problems in electrostatics and magnetostatics. Complex variables. Green's function, multipole expansions. Maxwell's equations and plane electromagnetic waves; waveguides. Radiation. Detailed discussion of special relativity, including, for example, 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.

506 MODERN EXPERIMENTAL TECHNIQUES (4)

Prerequisites: 750:326 Experimental Physics and 388 Modern Physics Lab, or equivalent. 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.

507 CLASSICAL MECHANICS (3)

Prerequisites: 750:382 Mechanics and 386 Electromagnetism, or equivalent. Advanced classical mechanics, calculus of variations, Hamilton's equations, canonical transformations, Hamilton-Jacobi theory, small oscillations, rigid body motion.

509 PHYSICS APPLICATIONS OF COMPUTERS (3)

Prerequisite: Programming experience. 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. The course is designed for the student who has some experience and wishes to broaden his/her knowledge of applications and develop techniques.

511 TOPICS IN MATHEMATICAL PHYSICS (3)

Prerequisites: 640:403 Complex Variables and 640:423 Partial Differential Equations, or equivalent. Functions of a complex variable, contour integration, calculus of residues, conformal mapping with applications to electrostatics, magnetostatics and fluid dynamics in two dimensions. Solution of boundary-value problems of physics by integral equation methods, construction of Green's functions. Fourier and Laplace transform theory with applications to harmonic motion, electrostatics, heat conduction, circuits and transients.

541 INTRODUCTORY ASTROPHYSICS (3)

Prerequisites: 750:382,386 or equivalent. Introduction to stellar astrophysics and modern astronomy. Stellar interiors, nucleosynthesis, energy transport, stellar evolution, white dwarfs, neutron stars, and black holes. Other topics of current interest from astrophysics.

601 SOLID-STATE PHYSICS I (3)

Prerequisites: 750:502 and 750:351 or equivalent. Introduction to: crystal lattices, scattering of radiation, lattice dynamics, electron bands, interaction among elementary excitations, disordered systems, transport properties, superconductivity and super-fluidity, magnetism, crystal-field effects, phase transitions, optical properties.

602, 603 SOLID STATE PHYSICS II, III (3,3)

Advanced treatment of topics surveyed in 750:601 and their extension to topics of current interest in solid-state physics.

605 NUCLEAR PHYSICS (3)

Prerequisite: 750:502, Quantum Mechanics, or equivalent. Survey of essential topics: properties of ground states, shell model, collective model, electromagnetic properties, simple excitations, compound-nucleus and direct reactions, beta decay. Additional topics may include alpha decay, fission, applications of nuclear physics, topics of current interest.

606 NUCLEAR PHYSICS II (3)

Advanced treatment of some topics discussed in 750:605, together with additional topics chosen in consultation with students.

607 GALACTIC DYNAMICS (3)

Prerequisites: 750:507, Classical Mechanics, and 750:341-342 Principles of Astrophysics or equivalent. Equilibrium and stability of stellar systems and the dynamical evolution of galaxies. Modern approach to dynamics with a few practical examples of chaotic systems.

608 COSMOLOGY (3)

Prerequisites: 750:341-342 Principles of Astrophysics or equivalent. 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.

609 FLUID AND PLASMA PHYSICS (3)

Prerequisites: 750:507 or equivalent. The 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.

610 INTERSTELLAR MATTER (3)

Prerequisite: 750:541 or equivalent. Structure of the inter-stellar 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.

611 STATISTICAL MECHANICS (3)

Prerequisites: 750:501, 502, Quantum Mechanics, 507 Classical Mechanics. 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 non-ideal gases, condensed matter, nuclei and astrophysics; fluctuations, non-equilibrium statistical mechanics; kinetic theory.

612 HIGH-ENERGY ASTROPHYSICS (3)

Prerequisite: 750:341-342 or equivalent. The 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.

613 PARTICLES (3)

Prerequisite: 750:502 Quantum Mechanics, or equivalent. 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.

615 OVERVIEW OF QUANTUM FIELD THEORY (3)

Prerequisite: 750:502 Quantum Mechanics, or equivalent. 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.

616 FIELDS I (3)

Prerequisite: 750:615 Advanced Quantum Mechanics. Path integral quantization; perturbation theory: dimensional regularization, renormalization; the renormalization group; spontaneous symmetry breaking and effective potential; critical behavior of ferromagnets; d field theory; Yang- Mills perturbation theory.

617 GENERAL THEORY OF RELATIVITY (3)

Prerequisites: 750:507, Classical Mechanics, or equivalent, 504 Electricity and Magnetism. 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.

618 APPLIED GROUP THEORY (3)

Prerequisite: 750:502 Quantum Mechanics, or equivalent. Abstract groups and their representations, finite groups and Lie algebras; symmetries and currents; symmetric group, inhomogeneous Lorentz group, SU(n); classification of Lie algebras, Dynkin diagrams. Spontaneous symmetry breaking mechanisms. Gauge theories.

619 FIELDS II (3)

Prerequisite: 16:750:616 Fields I. 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.

620 INTRODUCTION TO MANY-BODY THEORY (3)

Prerequisite: 750:502 Quantum Mechanics, or equivalent. Hartree-Fock and Thomas-Fermi methods, elementary excitations, theory of the Fermi liquid, properties of liquid helium; many-body perturbation theory at zero and finite temperature, statistical mechanics of many-particle systems, Green's function techniques, systems of interacting bosons and fermions, collective modes, theory of superconductivity and superfluidity, properties of nuclear matter. (A second semester of Many-Body Problems is available, temporarily listed as 682 Advanced Topics in Condensed Matter.)

621 ADVANCED MANY-BODY PHYSICS (3)

Prerequisite: 16:750:620 or equivalent. 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.

623,624 ADVANCED STUDIES IN PHYSICS (3,3)

Prerequisite: Consent of Graduate Director. Individual studies supervised by a member of the staff.

627 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.

628 SURFACE SCIENCE II (3)

Kinetics and dynamics of processes at surfaces; structure and reactivity of molecules at surfaces; thermal and non-thermal excitations; magnetic properties. Surfaces of metals, oxides and semiconductors, as well as solid-solid and solid-liquid interfaces.

629 OBSERVATIONAL TECHNIQUES (3)

Prerequisite: 750:541 Introductory Astrophysics or equivalent. 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.

633, 634 SEMINAR IN PHYSICS (1,1)

Prerequisite: Consent of instructor. Seminars in fields of investigation of current interest.

681, 682 ADVANCED TOPICS IN SOLID-STATE PHYSICS I AND II (3,3)

The courses may be taken in any order. Offered in alternate years.

685, 686 ADVANCED TOPICS IN NUCLEAR PHYSICS I AND II (3,3)

689, 690 ADVANCED TOPICS IN ASTROPHYSICS I AND II (3,3)

693, 694 ADVANCED TOPICS IN HIGH ENERGY PHYSICS I AND II (3,3)

695 ADVANCED TOPICS IN MATH PHYSICS (3)

699 PLAN B STUDY (1)

701, 702 RESEARCH IN PHYSICS (By Arrangement)

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