Complex variables and contour integration. Asymptotic expansions. Fourier series, Fourier transforms, and Laplace transforms. Laplace and Helmholtz equations. Bessel functions and Legendre functions. Applications to antennas and quantum mechanics. Calculus of variations.

Infinite series: convergent series versus asymptotic series. Vector and tensor analysis. Lie groups and representations. Integral equations.

Physical optics. Radiation theory. Diffraction and interference. Polychromatic waves. Scattering, polarization, and double refraction. Lasers and quantum optics.

Variational principles and Lagrange’s equations. Rigid bodies, small oscillations and nonlinear oscillations. Transition from discrete to continuous systems. Classical field theories.

Hamilton’s equations of motion and canonical transformations. Hamilton-Jacobi theory. Canonical perturbation theory. Special relativity in classical mechanics and Lorentz tensors.

Charge and current distributions. Static multipole expansions. Slowly varying fields and induction. Energy and momentum density of fields. Poynting’s theorem. Boundary value problems for Laplace’s equation and Poisson’s equation. Greens functions. Static fields in matter: dielectricity, diamagnetism, paramagnetism, and ferromagnetism.

Time-dependent fields in matter. Reflection and refraction at interfaces; dispersion and dissipation in dielectrics and conductors. Propagation of guided waves. Radiation from antennas, from small sources, and from relativistic particles. Fraunhoffer and Fresnel diffraction. Special relativity and the covariant formulation of electromagnetism.

The Schrödinger equation. Wave packets and the uncertainty relation. One-dimensional quantum mechanics. Linear operators and Hilbert space. Three-dimensional problems. Orbital and spin angular momentum. One-electron atoms.

Interaction of charges with electromagnetic fields. Angular momentum coupling and Clebsch-Gordon coefficients. Time-dependent perturbation theory. Quantum theory of radiation. Emission and absorption of radiation by atoms. Scattering theory.

Specialized topics of current interest in physics.

Review of one-electron atoms leading to approximation schemes for many-electron atoms. Thomas-Fermi theory, Hartree-Fock theory, and central field approximation. LS, JJ, and intermediate coupling of angular momentum. Relativistic effects.

Treatment of symmetry in quantum mechanics. Group theory and applications for atoms and molecules. Spatial and time-reversal symmetry. Advanced quantum mechanics for atoms and molecules.

Ensemble theory. Applications to noninteracting systems, as well as perturbative and approximate treatment of interactions. Typical applications include equilibrium constants, polymers, white dwarfs, metals, superfluids, magnetic transitions.

Nuclear models and reaction theory. Hadrons and their quark constituents. Weak nuclear interactions and the electro-weak synthesis.

Lagrangian field theory. Abelian and nonabelian gauge theories. Spontaneous symmetry breaking. Standard model of the strong, weak, and electromagnetic interactrons. Quarks, leptons, and gauge bosons.

Crystal structure and reciprocal lattices. Waves in crystals. Band structure and metals.

Semiconductor band structure. Intrinsic and extrinsic semiconductors. Hall effect and magneto-transport effects. Fundamentals of nanostructures and quantum structures. Semiconductor device physics.

Paramagnetism. Magnetic phenomena in thin films and multilayers. Phase transitions: mean field theories and fluctuations. Superconductivity and BCS theory.

Absorption and dispersion in light propagation. Quantum wells and quantum dots. Solid state laser materials. Nonlinear optics and parametric amplification.

Naturally occurring plasmas in electrical discharges and in space. Artificially produced laboratory plasmas. Survey of plasma phenomena using both fluid and kinetic models.

Individual projects to teach mathematical and physical foundations of computer simulations and to develop and refine physical understanding and intuition of phenomena encountered in plasma research.

The Vlasov equation, quasilinear theory, nonlinear phenomena. Plasma waves and instabilities. Landau damping and finite-Larmor-radius effects.

The fluid approximation. Magnetohydrodynamic description of plasma equilibrium and stability. Confinement schemes and plasma waves. Emphasis on analytic theory.

Specialized topics in physics areas related to research in the Physics Department. Open only to students who have completed most of the basic graduate courses.

Directed research leading to a Ph.D. dissertation.

Observational techniques for radio astronomy and antenna theory. Synchrotron radiation, extragalctic sources, pulsars, cosmology.

Linux and programming in C. Numerical integration and interpolation. Model fitting and hypothesis testing. Fourier transform applications and Monte Carlo simulations.

Birth, life-cycle, and death of stars. Main sequence
evolution. Novae and supernovae. White dwarfs. Neutron stars and pulsars.

Dynamics of a galaxy. Rotation and spiral density waves. Stellar interaction and dynamics. The interstellar medium: neutral and ionized gas; interstellar dust. Shock wave theory and interstellar turbulence.

A basic course in physical optics covering wave mathematics, propagation, polarization, interference, and diffraction.

Relativistic mechanics, atomic structure, spectra.

( 2 semesters ) Scalar, vector, and tensor fields; curvilinear coordinate systems, kinematics and dynamics of particles, systems of particles, and rigid bodies. Langrangian and Hamiltonian formulation. Relativistic motion.

( 2 semesters ) Electrostatics, electrostatics in matter, magnetostatics, magnetostatics in matter, Maxwell’s equations, reflection and refraction, waveguides and cavities.

Experiments in physics designed to complement theory courses; gives experience in data taking and instrumentation, and methods of data evaluation and error analysis.

Fundamental principles of quantum mechanics; state functions in position and momentum space, operators, Schrodinger’s equation, one-dimensional problems, approximation methods, the hydrogen atom, angular momentum and spin.

Introduction to the statistical foundations of thermodynamics; applications of the fundamental laws of thermodynamics to physical and chemical systems.

Study of characteristic properties of nuclei and their structure as inferred from nuclear decays and reactions, leading to a knowledge of nuclear forces and models.

Properties of crystalline solids; includes crystal structure, interatomic bonding, lattice vibrations, electron theory of metals, and the band theory of solids.

Introductory course in the physics of ionized gases; particle and fluid treatments of plasmas, waves, equilibrium and stability, kinetic theory, and nonlinear effects.