PHYS G4003y. Advanced Mechanics. 3 pts.

Prerequisites: differential and integral calculus, differential equations, and PHYS W3003 or the equivalent. Lagrange's formulation of mechanics, calculus of variations and the Action Principle, Hamilton's formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics.

PHYS G4018y. Solid-State Physics. 3 pts.

Prerequisites: PHYS G4021 and G4023, or the equivalent. Introduction to solid-state physics: crystal structures, properties of periodic lattices, electrons in metals, band structure, transport properties, semiconductors, magnetism, and superconductivity.

PHYS G4019x. Mathematical Methods of Physics. 3 pts.

Prerequisites: differential and integral calculus. Highlights of complex analysis, differential equations, integral equations, Green's functions, special functions, Fourier and other transforms, approximation methods, group theory and representations, differential geometry and manifolds. Emphasis is placed on applications to physical problems.

PHYS G4021x-G4022y. Quantum Mechanics, I and II. 3 pts.

Prerequisite: PHYS C2601 or C2802, or the equivalent. Formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, and identical particles. Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models.

PHYS G4023x. Thermal and Statistical Physics. 3 pts.

Prerequisite: PHYS G4021 or the equivalent. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism.

PHYS G4040x. Introduction to General Relativity. 3 pts. Not offered in 2009-2010. Prerequisites:PHYS W3003, PHYS W3007 or the equivalent.

Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; test-particle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models.

PHYS G4051x-G4051y. Advanced Laboratory Work. 2 Pts. 2 pts. Prerequisites: Instructor's permission.

The laboratory has 13 available individual experiments, of which two are required per 2 points. Each experiment requires two (four-hour) laboratory sessions. Registration is limited by the laboratory capacity. May be repeated for credit with different experiment selection. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.

PHYS W4386x-W4387y. Geometrical Concepts In Physics. 3 pts. Not offered in 2009-2010. Prerequisites: Mathematics V1205 or the equivalent and V2010. Material from topology and differential geometry with illustrations of its use in electrodynamics, general relativity, and Yang-Mills theory. In particular, topological and differential manifolds, tensors, vector bundles, connections, and Lie groups will be covered.

PHYS G6010x. Physical Cosmology. 3 pts. Not offered in 2009-2010. Prerequisites: Physics G4021-G4022-G4023 or instructor's permission.

An introduction to the basic concepts of the Friedmann-Robertson-Walker universe: the thermal history from inflation through nucleosynthesis, recombination, reionization to today; constituents of the universe including dark matter and dark energy; distance scales; galaxy formation; large scale structure of the universe in its many manifestations: microwave background anisotropies, galaxy surveys, gravitational lensing, intergalactic medium, gravitational waves. Current topics of interest at the discretion of the instructor.

PHYS G6011y. Astrophysics I. 3 pts. Prerequisites: A strong undergraduate background in E-M and classical mechanics. Familiarity with tensors in flat space will be assumed. Qualified undergraduates may be admitted with the instructor's permission.

The basic physics of high energy astrophysical phenomena. General relativistic equations of motion; black hole orbits and light bending; theory of accretion and emission for black holes, white dwarfs and neutron stars; neutron star equation of state, magnetosphere and cooling theory; radiative transfer theory; nucleosynthesis and supernova explosions; shocks and fluids, gravitational radiation; supermassive stars; cosmic-rays; dark matter.

PHYS G6036x. Statistical Mechanics. 4.5 pts. Prerequisites: Physics G4021-G4022-G4023, or their equivalents.

Fundamentals of statistical mechanics; theory of ensembles; quantum statistics; imperfect gases; cooperative phenomena.

PHYS G6037x-G6038y. Quantum Mechanics, I and II. 4.5 pts.

Prerequisite: Physics G4021-G4022, or their equivalents. G6037: the fundamental principles of quantum mechanics; elementary examples; angular momentum and the rotation group; spin and identical particles; isospin; time-independent and time-dependent perturbation theory. G6038: applications to atoms and molecules, including Thomas-Fermi and Hartree-Fock atoms; interaction of radiation with matter; collision theory; second quantization.

PHYS G6040y. Nuclear Physics. 3 pts. Not offered in 2009-2010.

Prerequisite: Physics G6037 or the equivalent. Properties of nuclei, nuclear forces, models of nuclei, alpha decay, electromagnetic interactions, weak interactions, passage of nuclear radiations through matter and methods of detection, nuclear reactions, neutrons, fission, fusion, quarks in nuclei, heavy-ion reactions, high-energy accelerators.

PHYS G6042x. Experimental Methods for Nuclear and Particle Physics. 3 pts. Not offered in 2009-2010.

Prerequisite: Physics G4021 or instructor's permission. Introduction to current experimental methods and techniques in nuclear and particle physics. Radiation properties, passage of radiation through matter, and the statistical treatment of experimental data. General characteristics and the principles of operation of different detectors.

PHYS G6047y. Quantum Field Theory I. 4.5 pts.

Lagrangian density formalism of Lorentz scalar, Dirac and Weyl spinor, and vector gauge fields. Action variations, symmetries, conservation laws. Canonical quantization, Fock space. Interacting local fields, temporal evolution. Wicks theorem, propagators, and vertex functions, Feynman rules and diagrams. Scattering S matrix examples with tree level amplitudes. Path quantization. 1-loop intro to renormalization.

PHYS G6050x. Elementary Particle Physics: Particle Phenomenology. 3 pts.

Prerequisite: Physics G6037, or the equivalent. The elementary particles and their properties; interactions of charged particles and radiation with matter; accelerators, particle beams, detectors; conservation laws; symmetry principles; strong interactions, resonances, unitary symmetry; electromagnetic interactions; weak interactions; current topics.

PHYS G6060x. Atomic Physics. 3 pts.

Recent progress in control of atoms with lasers has led to creating the coldest matter in the universe, constructing ultra precise time and frequency standards, and capability to test high energy theories with tabletop experiments. This course will cover the essentials of atomic physics including the resonance phenomenon, atoms in magnetic and electric fields, and light-matter interactions. These naturally lead to line shapes and laser spectroscopy, as well as to a variety of topics relevant to modern research such as cooling and trapping of atoms. It is recommended for anyone interested in pursuing research in the vibrant field of atomic, molecular, and optical (AMO) physics, and is open to interested students with a one year background in quantum mechanics. Both graduate students and advanced undergraduates are welcome.

PHYS G6070y. Introduction To Biological Physics. 3 pts. Not offered in 2009-2010. Basic knowledge about the newly evolving fields of Biological Physics and Quantitative Biology. General concepts of soft matter physics, cell biology, and current research topics.

PHYS G6080x. Scientific Computing. 3 pts. Not offered in 2009-2010.

Prerequisites: basic programming, calculus and differential equations. Computational techniques for scientific problems with emphasis on practical applications and effective programming. Review of computers, programming, floating-point numbers, and numerical stability. Survey of basic numerical algorithms and numerical subroutine libraries and their application to scientific problems.

PHYS G6082y. Condensed Matter Physics, II. 3 pts.

Prerequisite: Physics E6081 or instructor's permission. Semiclassical and quantum mechanical electron dynamics and conduction; dielectric properties of insulators; semiconductors; defects; magnetism; superconductivity; low-dimensional structures; soft matter.

PHYS G6083x. Condensed Matter Physics III. 3 pts. Not offered in 2009-2010.

PHYS G6092x. Electromagnetic Theory, I. 4.5 pts.

Prerequisite: Physics W3008, or its equivalent. Fundamentals of electromagnetism from an advanced perspective with emphasis on electromagnetic fields in vaccum with no bounding surfaces present. A thorough understanding of Maxwells equations and their application to a wide variety of phenomena. Maxwells equations (in vacuum) and the Lorentz force law - noncovariant form. Scalar and vector potentials, gauge transformations. Generalized functions (delta functions and their derivatives), point changes. Fourier transforms, longitutdinal ad transverse vector fields. Solution of Maxwells equations in unbounded space for electrostatics and magnetostatics with given charge and current sources. Special relativity, Loretnz transformations, 4-momentum, relativistic reactions. Index mechanics of Cartesian tensor notation. Covariatn formulation of Maxwells equations and the Lorentz force law, Lorentz transformation properties of E and B. Lagrangian density for the electromagnetic field, Langrangian density for the Proca field. Symmetries and conservation laws, Noethers theorem. Field conservation laws (energy, linear momentum, angular momentum, stress tensor). Monochromatic plane wave solutions of the time-dependent source-free Maxwell equations, elliptical polarization, partially-polarized electromagnetgic waves, Stokes parameters. Solution of the time-dependent Maxwell equations in unbounded space with given chare and current sources (retarded and advanced solutions). Properties of electromagnetic fields in the radiaion zone, angular distribution of radiated power, frequency distribution of radiated energy, radiation form periodic and non-periodic motions. Radiation from antennas and antenna arrays. Lienard-Wiechert fields, the relativistic form of the Larmor radiation forumla, synchrotron radiation, bremsstrahlung, undulator and wiggler radiation. Electric dipole and magnetic dipole radiation. Scattering of electromagnetic radiation, the differential scattering cross-section, low-energy and high-energy approximations, scattering from a random or periodic array of scatterers. Radiation reaction force, Feynman-Wheeler theoryy. The macroscopic Maxwell equations (spatial averaging to get P, M, D, H). Convolutions, linear materials (permittivity, permeability, and conductivity), causality, analytics continuation, Kramers-Kronig relations. Propagation of monochromatic plane waves in isotropic and non-isotropic linear materials, ordinary ad extraordinary waves. Cherenkov radiation, transition radiation.

PHYS G6094y. Classical Fields and Waves. 4.5 pts. Prerequisites:PHYS G6092

This course will study the classical field theories used in electromagnetism, fluid dynamics, plasma physics, and elastic solid dynamics. General field theoretic concepts will be discussed, including the action, symmetries, conservation laws, and dissipation. In addition, classical field equations will be analyzed from the viewpoint of macroscopic averaging and small-parameter expansions of the fundamental microscopic dynamics. The course will also investigate the production and propagation of linear and nonlinear waves; with topics including linearized small-amplitude waves, ordinary and extraordinary waves, waves in a plasma, surface waves, nonlinear optics, wave-wave mixing, solitons, shock waves, and turbulence.

PHYS G6099x. Physical Phenomena. 3 pts. Not offered in 2009-2010.

Corequisite: Physics G6037 and G6092. Brief surveys of a wide variety of physical phenomena, with emphasis on fundamental principles, simple modeling, and order-of-magnitude estimates.

PHYS G6905x-G6905y. Graduate Student Seminar.

All first-year graduate students in the physics department must register for this course each term. Discussion of the experimental and theoretical research in the department.

PHYS G8012x. Astrophysics II. 3 pts.

Prerequisites: Physics G6011 or similar introductory astrophysics courses. A familiarity with basic general relativity is required. The selection of topics is likely to include accretion onto black holes and neutron stars, pulsars, supernovae, gamma-ray bursts, cosmic rays, radiative processes and magneto-hydrodynamics in astrophysics.

PHYS G8036y. Advanced Statistical Mechanics. 3 pts.

Advanced statistical mechanics.

PHYS G8040y. General Relativity. 4.5 pts. Not offered in 2009-2010.

Prerequisite: Physics G6037 or the equivalent, or instructor's permission. Tensor calculus and Riemannian geometry; Einstein's theory of gravitation; experimental tests of general relativity; gravitational waves; applications to cosmology and astronomy.

PHYS G8041x. Topics In General Relativity. 3 pts. Not offered in 2009-2010. Prerequisite: Physics G8040. Topics to be discussed include Hawking radiation and black hole thermodynamics, singularity theorems, and cosmology.

PHYS G8048x. Quantum Field Theory II. 4.5 pts.

Prerequisite: Physics G6037-G6038. Relativistic quantum mechanics and quantum field theory.

PHYS G8049y. Quantum Field Theory III. 3 pts.

Advanced topics at the discretion of the instructor, including string theory, supersymmetry and other aspects of beyond-standard-model physics.

PHYS G8050y. Advanced Mathematical Methods In Physics. 4.5 pts. Not offered in 2009-2010. Prerequisite: Physics G6037-G6038. Topics selected on the basis of current research problems.

PHYS G8066y. Condensed Matter - Special Topics. 3 pts. Not offered in 2009-2010.

Prerequisite: Physics G6037-G6038 or their equivalents. An intensive treatment of selected areas which vary from year to year.

PHYS G8069x. Particle Physics, I. 3 pts.

Prerequisite: Physics G6037-G6038. Basic aspects of particle physics, focusing on the Standard Model.

PHYS G8083x. Condensed Matter Physics II. 3 pts.

PHYS G8099x. Advanced Seminar In Current Research Problems. 3 pts. Not offered in 2009-2010. Prerequisites: Instructor's permission.

Discussions of current research activities in particle physics, astrophysics, and condensed-matter physics; with a detailed study of selected experiments in these fields.

PHYS G9301x-G9301y. Research for the Doctorate.

All Ph.D. candidates must register for this course each term while they are engaged in research in the department.