# Ph.D. in Physics Courses

The Department of Physics & Astronomy offers a thorough graduate curriculum in physics that includes core courses and specialty electives. Ph.D. students can also take selected undergraduate courses offered in mezzanine versions (typically 5000-level).

## Core Courses

1 credit hour; required; typically taken in first year

Weekly colloquium attendance and mandatory participation in online discussion forum. Required evaluation of presentations based on content, visual aids, and delivery. [0 credit hours; students must successfully complete PHYS 8001 in six semesters]

Discussion of best teaching practices in weekly meeting with instructor. Application of teaching strategies via teaching undergraduate lab or leading homework help-desk sessions. [0 credit hours; students must successfully complete PHYS 8003 in two or more semesters]

Linear spaces and operators; matrix algebra; differential equations; Green's function; and complex analysis. May include variational calculus; perturbation methods; group theory. [3 credit hours; not required by highly recommended]

Least action principle, Lagrange formalism, conservation laws, two-body problem, small-amplitude vibrations, non-inertial reference frames, canonical formalism, rigid body motion, continuous media, and field theory. [3 credit hours; required]

Electrostatics, potentials, boundary value problems, multipole moments, polarization, magnetostatics, Maxwell's equations, electromagnetic wave propagation, dissipative and conductive media. [3 credit hours; required]

Continuation of 8020. Covariant formulation, least-action principle and Lagrange density, energy momentum tensor, charges in external fields, radiation from accelerated changes, multipole radiation. Prerequisite: 8020. [3 credit hours; not required]

Underlying assumptions. Schrodinger equation: interpretation, discrete and continuous basis, change of basis. One-dimensional examples: square potential, harmonic oscillator. Uncertainty relations, symmetries and their implications, angular momentum, hydrogen atom, spin, systems with N-degrees of freedom; time independent perturbation theory, Fermi's golden rule. [3 credit hours; required]

Continuation of Phys 8030. Variational method, degenerate second order perturbation theory. Brief introduction to group theory with rotation group and Lorentz group as examples, addition of angular momentum, Wigner-Ekhart theorem, derivation of covariant spin-half wave functions. Potential scattering theory: angular momentum decomposition, T-matrix, S-matrix, Lippman-Schwinger equation, scattering by two potentials, local and separable potentials. Dirac equation: current conservation; completeness; parity, time reversal, and charge conjugation symmetries; co-variant solution of the hydrogen atom; Feynman propagator. [3 credit hours; not required]

Phase space, entropy and reversibility; ensemble theory; Fermi and Bose Statistics; systems of interacting particles; equation of state, critical phenomena, and phase transitions; pairing and superfluidity. [3 credit hours; required]

## Elective Courses

Topics such as Lie groups and symmetry principles in quantum mechanics, quantum electrodynamics of strong field, phenomenological modes of nuclear structure. Prerequisite: consent of instructor. [3]

Current topics in experimental physics relevant to research areas in the department, such as biological, condensed- matter, elementary-particle, nuclear, and optical physics, astronomy, astrophysics and cosmology. [Variable credit: 1-3]

Physical principles applied to biological phenomena. Development of physical models of biological systems on scales ranging from molecules to organisms. Biological applications of mechanics, thermodynamics, and dynamical systems. [3]

A survey of the state of the art in quantitative physical measurement techniques applied to cellular or molecular physiology. Topics include the basis for generation, measurement, and control of the transmembrane potential; electrochemical instrumentation; optical spectroscopy and imaging; X-ray diffraction for determination of macromolecular structure; magnetic resonance spectroscopy and imaging.

Introduction to systems biology from the perspective of the emergence of complexity in toy models. Simple biological subsystems, their reductionist and equivalent models, and measurements required to specify model architecture and parameters. Multiple interconnected organs-on-chips as dynamic biological systems that can model organismal biology.

Basic experimental facts and phenomenological models (shell model and collective model). Nucleon-nucleon interaction, mean-fields theories of nuclear structure (Hartree-Fock, BSC pairing, HFB, RPA, and QRPA). Ab-initio calculations for light nuclei. Time-dependent Hartree-Fock calculations of heavy-ion reactions. Prerequisite or co-requisite 8030. [3]

Basic experimental facts and phenomenological models of ultra-relativistic heavy-ion collisions. Quark-gluon plasma formation, signatures, and properties. Thermodynamics and hydrodynamical evolution of nuclear matter in extreme conditions.

Interactions of charged particles and photons in matter, coordinate transformations, statistics of nuclear processes, radiation detectors and analyzers, and selected topics in the design and application to experiments of particle accelerators and instrumentation used in nuclear and high energy physics. [3]

Free-electron theory of metals; elementary band theory of solids; quantum theory of the harmonic crystal; elementary excitations; optical properties of materials; electronic basis of magnetic interactions; density-functional theory; relativistic band structure; electronic localization and amorphous solids; two-dimensional phase transitions and superlattices.

Relativistic quantum mechanics, canonical and path-integral field quantization, relativistic scattering theory, perturbation expansions; Feynman diagrams and radiative corrections, renormalization and regularization, with applications to quantum electrodynamics and non Abelian gauge theories.

Interaction of electromagnetic radiation with matter as a function of photon energy and flux. Mechanisms of absorption, emission, and scattering of light within the visible, infrared, ultraviolet, and x-ray wavelength regimes. Experimental and computational techniques and instrumentation for assessing and analyzing spectroscopic information. Prerequisite: 8030. [3]

Free-electron theory of metals; elementary band theory of solids; quantum theory of the harmonic crystal; elementary excitations; optical properties of materials; electronic basis of magnetic interactions; density-functional theory; relativistic band structure; electronic localization and amorphous solids; two-dimensional phase transitions and superlattices. Consent of instructor required. [3]

Evolution of elementary excitations; optical, magnetic, electronic, and mechanical characteristics of matter at nanometer length scales. Effects of one, two, and three dimensional electron confinement. Novel single-particle and collective properties of nanometer-size objects, including optical, magnetic, thermal, and transport phenomena. Prerequisite: 8030. [3]

Geometrical and electronic structure of surfaces, including surface reconstruction, density of states, and effects of adsorbates, impurities, and electronic defects. Prerequisite: 8030- 8031. [3]

Macroscopic optical properties of solids. Lorentz model of optical excitation, radiative and non-radiative relaxation. Coherence and dephasing in two-level systems. Interband transitions and luminescence. Optical properties of quantum-confined systems. Excitons, phonons, plasmons, and polaritons. Lasers, Raman and Brillouin scattering, nonlinear optical phenomenology. Prerequisite: 5651, 5640 or CHEM 5360. [3]

Laboratory introduction to nanofabrication and characterization. Preparation for independent and original research in nanotechnology and nanoscience. Review of nanomaterials, nanofabrication, characterization, nanoelectronics, and photonics. [3]

Einstein's geometric theory of gravity in terms of tensor analysis and differential geometry. Einstein's field equations are derived and solutions are discussed. Applications of general relativity are explored, including those to very strong gravitational fields, gravitational collapse, neutron stars, black holes, and quantum gravity. Topics in cosmology will include red shifts and cosmic distance relations, big bang cosmology, primordial nucleosynthesis, the very early universe and inflationary cosmologies. Prerequisite: consent of instructor. [3]

Continuation of 8160. Einstein's geometric theory of gravity in terms of tensor analysis and differential geometry. Einstein's field equations are derived and solutions are discussed. Applications of general relativity are explored, including those to very strong gravitational fields, gravitational collapse, neutron stars, black holes, and quantum gravity. Topics in cosmology will include red shifts and cosmic distance relations, big bang cosmology, primordial nucleosynthesis, the very early universe and inflationary cosmologies. Prerequisite: consent of instructor. [3]

Nonrelativistic theory of atoms, solids, and nuclei; operators in second quantization, fermions and bosons, pair correlation function, interacting electron gas (metal), propagators, Wick's theorem and Feynman diagrams, Hartree-Fock theory, shell model, pairing forces in nuclei, and superconductivity. Prerequisite: 8031. [3]

Relativistic quantum mechanics, canonical and path-integral field quantization, relativistic scattering theory, perturbation expansions; Feynman diagrams and radiative corrections, renormalization and regularization, with applications to quantum electrodynamics and non Abelian gauge theories. Prerequisite: 8010, 8020, 8030, and 8031. Corequisite: 8021. [3]

Relativistic quantum mechanics, canonical and path-integral field quantization, relativistic scattering theory, perturbation expansions; Feynman diagrams and radiative corrections, renormalization and regularization, with applications to quantum electrodynamics and non Abelian gauge theories. Prerequisite: 8170. [3]

May be repeated for credit more than once, but students may earn only up to 3 credits per semester of enrollment. [1-3]

Research prior to entry into candidacy (completion of Qualifying Examination) and for special non-degree students. [Variable credit: 0-13]

For students who have completed 72 hours and devote a half- time effort to dissertation research. [0]

Research after entry into candidacy (completion of Qualifying Examination)

## Mezzanine Courses

Temperature, work, heat, and the first law of thermodynamics. Entropy and the second law of thermodynamics. Kinetic theory of gases with applications to ideal gases and electromagnetic radiation. Serves as repeat credit for students who have completed 5207. No credit for students who have earned credit for 3200 or 3207. Prerequisite or corequisite: 5270 or 5275. [3]

Geometrical optics, including reflection, refraction, ray tracing, aberrations, and interference. Physical optics, including wave theory, absorption, dispersion, diffraction, and polarization. Properties of light from lasers and synchrotron sources. Photodetectors and optical technology. No credit for students who have earned credit for 2210. [3] (MNS)

Topics in modern physics analyzed exclusively with computer programs. Three-body solar system orbits. Random walk diffusion and entropy growth. Magnetism in the second order using model, non-equilibrium molecular dynamics. Solutions to the Schrödinger equation with numerical methods. No credit for students who have earned credit for 2237. [3]

Atomic and molecular structure, interaction of light with atoms and molecules, and spectroscopy. One three-hour laboratory per week. No credit for students who have earned credit for 2250 or 2250W. [4] (MNS)

Condensed-matter physics, biophysics, special theory of relativity, and nuclear and particle physics. One three-hour laboratory per week. No credit for students who have earned credit for 2260 or 2260W. [4]

Electrostatic fields and potentials. Gauss's law. Electrical properties of insulators, semiconductors, and metals. The Lorentz force. Magnetic fields and forces. Electromagnetic induction, Maxwell's equations, and electromagnetic waves. No credit for students who have earned credit for 2290. [3]

Continuation of 5290. Electromagnetic waves in dielectrics and conductors. Electromagnetic radiation in waveguide structures. Relativistic electrodynamics. Magnetism as a relativistic phenomenon. No credit for students who have earned credit for 2291. [3]

Crystal structure and diffraction. Phonons and lattice vibrations. Free-electron theory of metals. Elementary band theory of solids. Semiconductors. Optical properties of insulators. Applications to solid-state devices, magnetism, and superconductivity. No credit for students who have earned credit for 3640. [3]

Time-independent and time-dependent perturbation theory, matrix theory, scattering, applications to atomic physics, condensed matter physics, and astrophysics. No credit for students who have earned credit for 3652. [3]

Weak, strong, and electromagnetic forces as evidenced by the interactions of elementary particles. Classification of particles and experimental techniques. No credit for students who have earned credit for 3660. [3]

No credit for students who have earned credit for 3890. [1-3]