**All courses are 3 credits unless otherwise noted.**

**Course offered only when a sufficient number of interested students register.*

**PHY 501-502 Introduction to Mathematical Physics I-II**

Complex variables, ordinary and partial differential equations, special functions, Fourier series and transforms, Laplace transforms, boundary value problems, Green's functions, matrices, function spaces, group theory, tensors. LEC

**PHY 503-504 Introduction to Theoretical Physics I-II**

Recommended for students who lacked or were poorly prepared in junior/senior-level physics courses. Topics: mechanics, electromagnetic fields, interaction of electromagnetic fields with matter, special relativity. LEC

**PHY 505 Computational Physics I ** Prerequisites: classical and quantum mechanics, electrodynamics, and thermal physics at the undergraduate level; familiarity with a programming language helpful, but not required.

This course integrates the elements of numerical analysis and computer programming to study a variety of problems in classical, quantum, and statistical physics. Basic numerical operations: root finding, interpolation, matrix inversion, numerical differentiation, and quadrature. Structured and object-oriented programming of basic operations in modern languages, such as C++, FORTRAN 90, and Java. Numerical solution of ordinary linear and nonlinear differential equations of classical and quantum physics. Boundary-value and eigenvalue problems. Statistical analysis of data, the Fast Fourier Transform, and computer graphics. LEC/LAB

**PHY 506 Computational Physics II ** Prerequisite: PHY 505

More advanced numerical techniques applied to time-independent and time-dependent problems described by linear and nonlinear partial differential equations, and to the physics of systems with many degrees of freedom. Matrix operations and solution of large systems of linear equations. Random variables, importance sampling, and Monte Carlo methods. Visualization of large data sets, and animated computer graphics. Use of mathematical library routines in numerical analysis. Introduction to computer algebra and symbol manipulation programs. LEC/LAB

**PHY 507-508 Quantum Mechanics I-II ** First course deals with basic principles and formulations of quantum mechanics, classical limit and WKB method, representations and transformations, pure and mixed states, conservation laws and symmetries, central-force problems and solutions, and approximation methods for stationary states. Second course concentrates on coupling of angular momenta, rotation matrix, time-dependent perturbation and quantum transitions, many-electron systems, and scattering theory. LEC

**PHY 509 Classical Dynamics ** D'Alembert's principle; principle of virtual work; Lagrange equations and application to the dynamics of particles, rigid bodies, rotating systems, small oscillations, nonholonomic systems, principle of least action; Hamilton's principle; canonical transformations; Poisson brackets; integral invariants; Hamilton-Jacobi theory. LEC

**PHY 510 Advanced Quantum Mechanics ** Topics include classical fields; quantization of fields; quantum theory of radiation; relativistic quantum mechanics of spin-half particles; covariant perturbation theory; application of second quantization method to atomic physics, particle physics, statistical mechanics, and solid-state physics. LEC

**PHY 511-512 Quantum Theory of Fields I-II* ** Review of classical field theory; discrete and continuous symmetries, conservation laws, and Noether's theorem; canonical quantization of the free Klein-Gordon, Dirac, and electromagnetic fields; path integral quantization; interacting fields andcovariant perturbation theory; Feynman diagrams; ultraviolet and infrared divergences, regularization, and renormalization; vacuum expectation values and the S-matrix; special topics selected from the renormalization group and asymptotic behavior, solitons, spontaneous symmetry breaking, nonabelian gauge fields, lattice gauge theory, and quantum gravity; global and local symmetries and modern gauge theory of elementary particles and their interactions; the standard SU(3)xSU(2)xU(1) model of particle physics, families of quarks and leptons; electroweak unification and the Higgs mechanism; quantum chromodynamics, asymptotic freedom, and quark confinement. LEC

**PHY 513-514 Electrodynamics I-II ** First course deals with treatment of boundary-value problems in electrostatics and magnetostatics by method of images, orthogonal function expansions, Green's functions, and conformal mapping; multipoles, dielectrics, and magnetic materials. Second course concentrates on Maxwell's equations, propagation of plane waves in various media, radiating systems, special theory of relativity, radiation by moving charges, radiation damping, and scattering and absorption of radiation by a bound system. LEC

**PHY 519 Statistical Physics I ** Concept of ensembles; exactly solvable physical systems, such as Tonks and Takahashi gases; mean field theory of fluids and first-order phase transitions; second-order phase transitions; critical exponents; Ising model; lattice-gas model; fluctuations and correlations, scaling, and renormalization group analyses. LEC

**PHY 520 Statistical Physics II ** Classical dense gases and liquids, virial expansion, distribution functions, Ornstein-Zernike equation, Percus-Yevick and hypernetted chain approaches; quantum fluids, ideal and interacting Bose, and Fermi gases selected applications; description of systems in the elastic limit with applications to two-dimensional melting and analyses of inhomogeneous media; linear response theory and dynamical correlations; stochastic and memory functionbased analyses; Boltzmann equation; Navier-Stokes equation. LEC

**PHY 521 Elementary Particle Physics ** Designed to acquaint students with the broad features of particle physics, serving either as an introduction to further study or as an informative overview for specialists in other fields. Complete familiarity with special relativity and quantum mechanics is assumed. Topics: introduction to families of particles; relativistic kinematics applied to reaction cross-sections and decay rates; symmetries and conservation laws, isospin, strangeness, charm, and beauty; parity and CP violation in weak interactions; quark model of hadrons; high-energy accelerators and detectors; applications of particle physics in heavy-ion collisions, astrophysics, and the early universe. LEC

**PHY 522 Topics in High-Energy Physics* ** Topics may include particle physics at high-energy colliders and super-colliders; theories of physics beyond the standard model, including grand unification, supersymmetry, composite models, and superstring theories. LEC

**PHY 523-524 Nuclear Physics I-II* ** Topics include fundamental properties of nuclei; interactions of radiation with matter; nuclear two-body problems, including properties of deuteron, low-energy nucleon-nucleon scattering with and without tensor forces, effective range theory, polarization treatment, photodisintegration of deuteron, and n-p capture; nucleon-nucleon scattering at high energies, and meson theory of nuclear force, nuclear models, nuclear reactions, electron scattering from nuclei in Born approximation; Fermi theory of beta decay. LEC

**PHY 527-528 Solid-State Physics I-II ** Introductory graduate solid-state physics. Topics include properties of crystalline solids, reciprocal lattice, lattice vibrations, thermal properties, electronic properties, energy bands, Fermi surface, dynamics of conduction electrons, magnetic and optical properties, semiconductors, layered structures, and superconductivity. LEC

**PHY 529 Electronics ** Designed to acquaint graduate students with the concepts of circuit design that are necessary to apply modern electronics to physics research. Modern solid-state components, integrated circuits, digital circuits, and instrumentation are discussed. The course is laboratory oriented, and consists of one hour of lecture and seven hours of laboratory per week. LAB

**PHY 534-535 Atomic and Molecular Physics I-II* ** Topics include many-electron atoms, various angular momentum couplings, variational and Hartree-Fock methods of energy calculations, selection rules, atoms in external fields, configuration interactions, and theories of atomic orbitals and molecular orbitals. Hyperfine structure and nuclear properties, molecular beam studies of nuclear properties, atomic problems in astrophysics, theory of atomic collision. LEC

**PHY 536 Kinetic Theory of Gases and Plasmas* ** Kinetic theory of plasmas, Vlasov equation and its applications, Landau damping, theories of Bogoliubov and of Frieman and Sandri, stability of plasmas, transport properties of plasmas. LEC

**PHY 538-539 Quantum Theory of Solids I-II ** Topics include periodic structures, Bloch theorem, and Brillouin zones; phonons and lattice dynamics; electron states, nearly free electron models, and other models; static properties of the classification of solids; electron-electron interactions; dynamics of electrons, mass tensor, excitons, electron-phonon interactions, transport properties, electrical and thermal conductivities, relaxation times, general transport coefficients; optical properties, Fermi surfaces, cyclotron resonance, magneto-acoustic oscillations, de Haasvan Alphen effect; magnetism, superconductivity. LEC

**PHY 546 Many-Body Theory* ** Second quantization, Green's functions and diagram techniques, and path integrals; applications to electron gas, liquid helium, and superconducting systems. LEC

**PHY 551-552 Graduate Physics Laboratory I-II ** Laboratory course dealing with experimental techniques, and applications to experiments in superconductivity, Josephson effect, light scattering, infrared spectroscopy, X-ray diffraction, scanning tunneling microscopy, nuclear medicine resonance, semiconductor spectroscopy, atomic and molecular spectroscopy, laser optics, and Pi-Muon scattering. LAB

**PHY 555-556 Relativity and Fields I-II* ** Implications of special relativity from experiment, Lorentz transformation and the Poincare group, relativistic mechanics of point particles, field equations in special relativity, features of spinor-vector tensor field. Noether's theorem and the conservation equations; introduction to general relativity; differential geometry; Einstein's field equations and the Newtonian limit; the Schwarzschild solution and crucial tests; spinor, vector, and tensor field equations; equations in curved space; cosmology. LEC

**PHY 581-582 Topics in Advanced Modern Physics ** Introduces graduate students to advanced topics in physics. Different topics are covered each semester. The topics are selected based upon faculty interests and the current importance of the subjects. Faculty members are selected to teach each of these separate courses on the basis of their expertise in the field. Examples of topics include modern optics of solids, physics of semiconductor nanostructures, advanced nonequilibrium statistical physics, and physics of molecular conductors. Topics are not duplicated in consecutive years. LEC

**PHY 597 Experimental Techniques ** Lecture course dealing with experimental techniques and applications to experiments in vacuum generation and measurement; magnetic measurements; electrical transport; lock-in amplifiers; bridges; cryogenics; thermal measurements; X-ray diffraction and spectroscopies; spectroscopic techniques in the visible and infrared; Raman spectroscopy; and high-pressure production, measurement, and applications. LEC

**PHY 598 Independent Study ** (1-6 credits)

Designed to suit the specific needs of individual students who want to study certain topics in physics at the graduate level. TUT

**PHY 599 Supervised Teaching ** (1-3 credits)

Registration only by consent of the department chair. Teaching assignments within the department are delegated to each registrant. Assignment is supervised by a member of the department staff. May be taken more than once for credit. TUT

**PHY 600 Graduate Research ** (1-12 credits)

An original investigation to be pursued under the guidance of one or more faculty members. TUT

**PHY 602A Departmental Colloquium ** (1 credit)

**PHY 602B Departmental Colloquium ** (1 credit)

Faculty members present introductory talks every Tuesday at 10am. Mandatory for 1st-year graduate students. LEC