Academics
Graduate Information
Graduate Classes
Academics
Graduate Information
Graduate Classes
CAS PY501 Mathematical Physics
Introduction to complex variables and residue calculus,
asymptotic methods, and conformal mapping; integral transforms;
ordinary and partial differential equations; non-linear
equations; integral equations. 4 cr.
CAS PY502 Computational Physics
Fundamental methods of computational physics and applications;
numerical algorithms, linear algebra, differential equations;
computer simulation; vectorization, parallelism, and optimization
and examples and projects on scientific applications. 4 cr.
CAS PY511 Quantum Mechanics I
General theory of quantum mechanics, including the Schrodinger,
Heisenberg, and interaction pictures. The path intefral
formulation. Angular momentum: orbital and spin angular momentum,
addition of angular momenta, Wigner-Echart theorem. Scattering
theory: time-independent, partial waves and phase shift,
identical particles, time dependent and propagators. 4 cr.
CAS PY512 Quantum Mechanics II
Degenerate and non-degenerate perturbation theory. Second
quantization of nonrelativistic systems with applications to
scattering, lifetime of excited atomic states, many-body
problems. Relativistic quantum mechanics: Klein-Gordon equation.
4 cr.
CAS PY521 Electromagnetic Theory I
Structure of Maxwell's equations, conservation of charge,
uniqueness of solutions; electrostatics boundary value problems,
Maxwell's equations in matter definition and discussion of P.M.;
conservation laws, plane waves, wave propagation; reflection;
refraction and diffraction; wave guides. 4 cr.
CAS PY522 Electromagnetic Theory II
Lorentz transformations, tensor analysis, covariant form of
electrodynamics, conservation laws; elementary Green's function
treatment of the scalar wave equation; radiation theory: Raleigh
scattering; absorption and emission of radiation in matter;
dispersion relations; radiation by moving charges, synchrotron
radiation; scattering of radiation by particles. 4 cr.
CAS PY531 Classical Mechanics
Contact transformations; Lagrangian and Hamiltoniam formalisms;
the Kepler problem; rigid-body motion; canonical transformations;
Poisson brackets; Hamilton-Jacoby theory; harmonic oscillators
and small oscillations; continuous medium. 4 cr.
CAS PY541 Statistical Mechanics I
Introduction to thermodynamics and statistical physics. Phase
space, microcanonical, canonical, and grand canonical ensembles.
Applications. Equilibrium fluctuations, relation to thermodynamic
functions. Quantum statistical mechanics, density matrix. Ideal
Bose and Fermi gases. Phase transitions: thermodynamic theory of
phase transitions, mean-field theories. Kinetic theory, transport
processes. 4 cr.
CAS PY542 Statistical Mechanics II
Emphasis on non-equilibrium statistical mechanics. Fluctuations:
equilibrium fluctuations, instabilities, fluctuation dissipation
theories. Elementary kinetic theory: mean free path approach,
Boltzmann equation. Stochastic mathematics: probability theory,
Markoff processes, Gaussian processes, first-passage processes.
Brownian motion: Langevin equations, Fokker-Planck equation. 4
cr.
CAS PY543 Introduction to Solid State Physics
An introduction to crystal structure; lattice vibration;
electronic energy bands and Fermi surfaces: semiconductors,
conductors, and insulators; superconductivity and magnetism. 4
cr.
CAS PY551 Introduction to Particle Physics
Fundamental particles and their symmetries. Isospin and flavor.
Discrete symmetries. Phenomenology of weak and strong
interactions. Introduction to detector techniques. 4 cr.
CAS PY561 Introduction to Nuclear Physics
A general introduction to nuclear physics. Topics covered include
an introduction to the nucleus, nuclear forces, theories of
nuclear structure, decay and reaction processes, and special
topics of interest (nuclear energy, origin of nuclei, etc.) 4 cr.
CAS PY581 Advanced Laboratory
Classical experiments in atomic and nuclear physics, development
of new experiments, basic research projects. Experiments include
magnetic resonance, nuclear-decay studies, Zeeman effect,
holography, black-body radiation, x-ray diffraction, Mossbauer
studies, and flux quantization, positron annihilation. 4 cr.
GRS PY621- Advanced Scientific Computing in Physics
Introduces advances computational techniques for research problems in physics, with emphasis on computationally intensive applications in a massively parallel supercomputing environment. Corequisite laboratory meets together CAS CS 512 (or CAS CS 551), CH 455, and ENG EK 521, focusing algorithms and computational tools with cross-disciplinary application. 4cr, 2nd sem.
GRS PY681-Electronics for Scientist
Prereq: CAS PY 212 or PY 252, and CAS MA 124; or consent of instructor. A survey of practical electronics for all science students who wish to gain a working knowledge of electronic instrumentation and, in particular, its construction. Two four-hour laboratory-lecture sessions per week. 4cr, 2nd sem.
GRS PY 701,702-Advanced Mathematical Physics
Prereq: CAS PY 501 or equivalent. Mathematical structures; algebraic systems, topological spaces, measure theory, and integration. Functional analysis: Banach and HIlbert spaces, linear functionals, operators, and spectral theory. Other applications at discretion of instructor. (Course offered only upon sufficient demand.) 4cr, 1st sem & 2nd sem.
GRS PY 711-Advanced Quantum Theory for Condensed Matter
Prereq: CAS PY 511, PY 512. Scattering and multiple scattering theory. Field quantization, Green's function, time-ordering, and Wick's theorem. Perturbation theory and Feynman diagrams. Correlation functions and density matrices. Spontaneous symmetry breaking and Goldstone's theorem. (Course offered only upon sufficient demand.) 4 cr, 1st sem.
GRS PY 713-Quantum Field Theory I
Prereq: CAS PY 511 and PY 512. For particle physics students concurrent enrollment in CAS PY 551 or GRS PY 751 is strongly recommended. Provides an introduction to the techniques of quantum field theory with applications to high-energy and condensed-matter physics. Topics include field equations and quantization of many-body systems; Green function and linear response theory; S-matrix and scattering theory; path integration; perturbation expansions and the Feynman rules; renormalization and effective field theories; expansion and critical exponents. 4cr, 2nd sem.
GRS PY 714-Quantum Field Theory II
Prereq: GRS PY 713 and PY 751 or equivalent. A continuation of GRS PY 713 for particle physicist. Topics include relativistic fields; LSZ formalism; the Lorentz group; quantum electrodynamics; nonabelian gauge symmetry; spontaneous symmetry breaking; Goldtone's theorem; the Higgs mechanism; the Glashow=Weinberg=Salam model. 4 cr, 2nd sem.
GRS PY 731-Theory of Relativity
Prereq: CAS PY 521, PY 522, and PY 531, or consent of instructor. Space-times, space-time structures and gravitation. Affine spaces, pseudo-metric spaces and special-relativistic space-time. Manifolds, connections, and curvature. Four-dimensional formulation of Newton's Theory of Gravitation. Physics in locally special-relativistic space-times. Gravitational field equations. Weak gravitational fields. Schwarzchild solution. Variational principles and initial value problems. Gravitational radiation. (Course offered only upon sufficient demand.) 4 cr, 1st sem.
GRS PY 741-Solid-State Physics I
Prereq: CAS PY 511, PY 512, PY 541, and PY 542, or equivalent. Methods and properties of electron and phonon band structures--local density functional, Green functions (APW and KKR) and phase shift, pseudopotentials, tight binding. Representative systems: covalent, ionic, simple metals, transition metals, Transition metal compounds, and correlation gaps. Screening, dielectric function and applications: optical properties and photoemission, excitons, electron-photon interaction, Kohn anomalies, lattice instabilities. Electrons and phonons at surfaces. Transport equations. 4cr, 1st sem.
GRS PY 742-Solid-State Physics II
Prereq: GRS PY 741. Continuation of CAS PY 741; applications of quantum theory to solid-state systems with many-body effects: electron-phonon interaction and the Frolich Hamiltonian, polarons, superconductivity; microscopic theory of magnetism, spin waves, and magnons. Quantum transport theory and the Kubo formula. Scattering theory, localized states, averaging over disorder; Anderson localization. Various topics of current interest: quantum antiferromagnets, charge and spin density waves, heavy fermions, surface physics, quantum Hall effect, metal-insulator transition. 4cr, 2nd sem.
GRS PY 743-Low-Temperature Physics
Prereq: CAS PY 512, PY 542. Superconductivity, superfluidity, and properties of HE and HE at low temperatures. Techniques and measurement of physical quantities near absolute zero. (Offered alternate years.) 4cr, 1st sem.
Prereq: CAS PY 541 or GRS CH 653, and consent of instructor. Introduction to polymer physics, focusing on the structure, phase behavior, and dynamics of isolated chains, polymer solutions, and gels. Development of underlying theoretical formalism and comparison with experimental results. Discussion of applications to novel polymeric materials. 4 cr.
GRS PY 747-Advanced Statistical Mechanics
Prereq: CAS PY 501, PY 512, PY 531, and PY 542. Classical and quantum statistical ensembles and their physical interpretations; connection between statistical and thermodynamic quantities. Irreversible process: Boltzmann equation, transport theory, thermal fluctuations, introduction to stochastic process theory. Application, e.g., imperfect gases, phase transitions, cooperative phenomena, and liquid helium. (Offered alternate years.) . 4cr, either sem.
GRS PY 751, 752-High-Energy Physics
Prereq: CAS PY 511 and PY 512, or consent of instructor. Yearlong course on phenomenological aspects of modern high-energy physics. Principal topics are the standard model of strong and elector-weak symmetry breaking. Intended for both theoretical and experimental students and emphasizes current calculations techniques. (Offered alternate year; Second semester offered only upon sufficient demand.) 4cr, 1st sem.
Prereq: CAS PY 511 and PY 512. Nuclear properties. Experimental methods of nuclear physics. Electron scattering and nuclear form fractors. Muonic atoms. Symmetries and conservation laws in nuclear physics. Nuclear models. The nucleon-nucleon force and the nuclear forces. Weak interactions and decay. (Course offered only upon sufficient demand.) 4cr, 1st sem.
GRS PY 762-Intermediate Energy Physics
Prereq: CAS PY 511 and PY 512; GRS PY 711; GRS PY 761 and consent of instructor. The pion-nucleon system, pion physics, muon physics and weak interactions, photo productions of mesons of nucleons and nuclei, exotic atoms, and hypernuclei. Hadron scattering at intermediate and high energies. (Course offered only upon sufficient demand.) 4cr, 2nd sem.
Prereq: facility with calculus; a BA in Physics, Chemistry or the equivalent; and consent of instructor. Introduction to biomolecular forces, energy flow, and thermodynamics in biological systems. Hydrophobic interactions and membrane structure. Feedback and control mechanisms; allosteric enzymes. Mechanism of transport in biological membranes. Emphasis on the physical principle underlying biological structure and function. (Offered alternate years.) 4cr, 1st sem.
GRS PY 811-Advanced Quantum Field Theory
Prereq: GRS PY 713 and PY 714; GRS PY 731. Covers advanced methods in quantum field theory. Topics include QCD, confinement and chiral symmetry breaking, renormalization group, monopoles and instantons, the U (1) problem. (Course offered only upon sufficient demand.) 4cr.
GRS PY 841-Symmetry in Solid-State Physics
Prereq: GRS PY 741, PY 842, or consent of instructor. Theory of finite groups, crystalline point groups, crystal double groups, crystal field theory, selection rules, perturbation theory, Kramer's theorem, applications to solid-state physics. (Course offered only upon sufficient demand.) 4cr, 1st sem.
GRS PY 842-Many-Body Topics in Solid-State Physics
Prereq: GRS PY 741, PY 742, and PY 711 or PY 713, and PY 747. Applications of many-body techniques in classical and quantum mechanics including graphical techniques and Green's functions. Thermodynamic Green's functions. Includes normal and super-conducting Fermi systems, superfluid Boson systems, quantum magnetism, transport theory, localization. (Course offered only upon sufficient demand.) 4cr
GRS PY 891, 892-Seminar: Philosophical Foundations of Physics
Prereq: consent of instructor. Logical and historical analysis of concepts and theories of classical and modern physics. 4cr, 1st & 2nd sem.
GRS PY 895, 896-Seminar: Special Topics in Theoretical Physics
Prereq: consent of instructor. Theoretical research topics include general relativity, quantum field theory, high energy and particle physics, phase transitions, renormaliztion group, laser physics, kinetic equations, biophysics, computational physics, and selected topics in mathematical physics. Variable cr, 1st & 2nd sem.
GRS PY 897, 898-Seminar: Special Topics in Experimental Physics
Surface physics; intermediate energy nuclear physics
experiments; low temperature techniques, liquid and solid helium,
and magnetism at low temperatures. Raman effect, gels, and
biophysics. High-energy physics experimental techniques. Variable
cr, 1st & 2nd sem.