Computer modeling and instrument design and development of detectors for the in-situ measurement of physical and dynamic characteristics of dust in interplanetary space and planetary ring systems.
Students are required to register for the weekly colloquium and to present papers. No more than three semester hours may be counted on a master's degree and no more than six may be counted on the Ph.D. degree.
To fulfill requirements for non-thesis master's students who need to complete final degree requirements other than coursework during their last semester. This may include such things as a comprehensive examination, oral examination, or foreign language requirement. Students are required to be registered during the semester they graduate.
Elementary mechanics, variational principles, Lagrange's equations, two-body central forces, scattering, kinematics, rotations, rigid body motion, and Hamilton's equations of motion; special relativity, including covariant Lagrangian formulation.
Small oscillations; canonical transformations; Hamilton-Jacobi theory; canonical perturbation theory; Lagrangian and Hamiltonian densities, critical points, Lyapunov exponents, bifurcation, chaos, noise, and other topics in non-linear dynamics.
Advanced electrostatics and magnetostatics, boundary-value problems, time-varying fields, conservation laws, plane electromagnetic waves, wave guides and resonant cavities, and simple radiating systems and diffraction.
Magnetohydrodynamics and plasma physics, advanced relativistic electrodynamics, collisions of charged particles, scattering, Lienard-Wiechert potentials and radiation by moving charges, Bremsstrahlung, the method of virtual quanta, dynamic multipole fields, radiation damping, self-fields of a particle, and scattering and absorption by a bound system.
Probability, statistical methods, classical and quantum statistical mechanics, postulates, ensembles, ideal systems, real gases, cluster expansions, liquid helium, and phase transitions.
Theory of solids: crystal symmetry, lattice dynamics, band theory, lattice defects, impurity states. Applications to the thermal, magnetic, and electrical properties of solids.
Stellar structure, hydrostatic equilibrium, radiative transfer, stellar surface phenomena, and corona interactions. Cosmical electrodynamics and nuclear reactions in astrophysics, basic stellar evolution, variable stars, degenerate cores, white dwarfs, and neutron stars.
A systematic exposition of Einstein's general theory of relativity, with emphasis on applications to astrophysical and cosmological problems.
Space plasma and electromagnetic field phenomena; the guiding center drift equation (with applications); adiabatic invariant theory; the basic equations of magnetohydrodynamics; plasma convection, currents (including Chapman-Ferraro currents and ring currents), oscillations; magnetohydrodynamic boundaries, diffusion, waves, shocks, and instabilities.
Theory of analytical functions, Laplace and Fourier transforms, Fourier series, theory of distributions, ordinary differential equations, eigenvalue problems, special functions defined by eigenvalue problems, Green's functions, partial differential equations, radiation problems and scattering problems.
Conformal mapping, electrostatic problems, dispersion relations, asymptotic expansions, method of steepest descent, calculus of variations, Rayleigh-Ritz principle, finite-dimensional vector spaces, matrix theory, orthogonal transformations, normal coordinates, Hilbert vector spaces, unitary transformations, resolvent operators, operator calculus, integral equations, and approximate methods for solution of boundary value problems.
Schrodinger equation, eigenfunctions and eigenvalues, harmonic oscillator, and hydrogen atom. WKB approximation, collision theory, matrix formulation of quantum mechanics, transformation theory, and representation theory, including Schrdinger and Heisenberg picture.
Angular momentum algebra, Pauli Principle, many-particle systems, conservation laws, symmetry principles, time-dependent approximation methods, time-independent approximation methods, atoms, molecules, and relativistic wave equations.
Selected topics in physics. May be repeated once with change of content.
The research is intended for those students who have not yet passed the Ph.D. qualifying examination and who have not yet selected a Ph.D. dissertation topic. May be repeated for no more than twelve semester hours of credit. (Not to be counted on master's degree). (0-9) or
Relativistic astrophysics, and the final stages of stellar evolution; supernovae, binary stars, accretion disks, pulsars; extragalactic radio sources; active galactic nuclei; compact objects.
Cosmology: extragalactic distance determinations; relativist relativistic cosmological models; galaxy formation and clustering; thermal history of the universe, microwave background; cosmological tests, advanced topics in general relativity.
Radiative transfer, scattering, the interaction of matter and radiation, atomic and molecular structure, magnetodrodynamics and plasma physics, accretion disks and spiral density waves.
Identical particles and symmetry, self-consistent field theory, spin and angular momenta, electromagnetic interactions, semiclassical radiation theory, many-body perturbation theory, topics in scattering theory. Applications to atomic, molecular, and nuclear systems.
Klein-Gordon equation, Dirac equation, solutions of Dirac equation for scattering and bound states, non-relativistic limits of Dirac solutions, hole theory, Feynman diagrams, quantum electrodynamics, renormalization procedures, non-electromagnetic processes, solutions.
Basic concepts of elementary particle physics; symmetries, groups, and invariance principles; hadron-hadron interactions; static quark model of hadrons; weak interactions; brief introduction to quantum chromodynamics.
Second quantization of free fields; second quantization of interacting fields; elementary processes - Q.E.D. and non-Q.E.D. examples; perturbation theory methods for higher order processes; renormalization theory; path integral realization of quantum field theory.
Modern formulation of quantum field theory: quantization and renormalization of gauge theories, both Abelian and non-Abelian; third quantization; applications in the Q.E.D. example; SU2L XU1 theory; quantum chromodynamics; grand unified theories; theories of everything including quantum gravity such as the superstring theory.
Continuation of 6374: Detailed theory of higher order corrections to Standard Model and beyond the Standard Model processes; detailed presentation of recent developments in superunification, superstring/M theory, superstring field theory, and other approaches to quantum general relativity, depending on instructor. May be repeated for credit by instructor for a maximum of nine credits.
Special topics which are related to specialized fields of research sponsored in the department. May be repeated once with change of content.
Research for doctoral students studying for preliminary examinations or preparing their dissertation topic proposals.
A minimum of twelve semester hours is required.