# Core Graduate Courses

#### CAS PY 501 Mathematical Physics

**Undergraduate Prerequisites**: CAS MA 226 and CAS PY 403; or equivalent.

**Graduate Prerequisites**: CAS MA 226 and CAS PY 403; or equivalent.

Introduction to complex variables and residue calculus, asymptotic methods,
and conformal mapping; integral transforms; ordinary and partial differential
equations; non-linear equations; integral equations.

#### CAS PY 502 Computational Physics

Prereq: consent of instructor. Fundamental methods of computational physics and applications; numerical algorithms; linear algebra, differential equations; computer simulation; vectorization, parallelism, and optimization. Examples and projects on scientific applications. 4 cr, 1st sem.

#### CAS PY 511 Quantum Mechanics I

Prereq: CAS PY 451 and PY 452. General theory of quantum mechanics, including the Schrödinger, Heisenberg, and interaction pictures. The path integral formulation. Angular momentum: orbital and spin angular momentum, addition of angular momenta, Wigner-Eckart theorem. Scattering theory: time-independent, partial waves and phase shift, identical particles, time dependent, and propagators. 4 cr, 1st sem.

#### CAS PY 512 Quantum Mechanics II

Prereq: CAS PY 511. Continuation of CAS PY 511. Degenerate and nondegenerate 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, Dirac equation. 4 cr, 2nd sem.

#### CAS PY 521 Electromagnetic Theory I

**Undergraduate Prerequisites**: CAS PY 405.

**Graduate Prerequisites**: CAS PY 405.

Magnetostatics, dipole moments, magnetic materials, and dielectric materials. Electromagnetic induction and electromagnetic energy. Maxwell Equations in materials. Electromagnetic waves in materials, reflection and refraction. Waveguides. Scattering and diffraction. Special relativity, Lorentz Transformations and covariant electrodynamics. Radiation, Lienard-Wiechert potentials, antennas.

#### CAS PY 522 Electromagnetic Theory II

**Undergraduate Prerequisites**: CAS PY 521.

**Graduate Prerequisites**: CAS PY 521.

Continuation of CAS PY 521. Gaussian optics, cavity resonators, lasers. Synchrotron radiation, accelerators, free electron lasers. Interaction of relativistic charged particles with matter. Stopping power. Bremmstrahlung, Cherenkov radiation, transition radiation. Spectroscopy. Numerical methods. Metamaterials.

#### CAS PY 536 Quantum Computing

Prereq: CAS CS 330 OR CAS PY 354 or equivalent. Quantum physics as a powerful computational paradigm. Quantum bits (qubits), qubit operations and quantum gates, computation, and algorithms. Computational complexity classes, and efficiency of classical vs. quantum computers. Quantum Fourier transform and Shor's factorization algorithm. Physical implementation of quantum computation. Also offered as CAS CS 536. 4 cr. On Demand.

#### CAS PY 538 Econophysics

Prereq: CAS PY 355 or equivalent. The key concepts of the newly emerged interdisciplinary field of econophysics. The methods now available in the field of economics for analyzing large data sets, and for extracting new empirical "laws," such as the famous inverse cubic distribution of price fluctuations.

#### CAS PY 541 Statistical Mechanics I

Prereq: CAS PY 410. Probability theory. Ensembles. Steepest descent methods. Paramagnetism, ideal gas, Einstein model, adsorption isotherms. Thermodynamics, Maxwell relations, heat capacity. Bose and Fermi gases. Electrons in metals, white dwarf stars, black-body radiation, phonons, Bose-Einstein condensation. Interacting systems, virial expansion, Van der Waals gas. Phase transitions: mean-field theories, spin systems. 4 cr, 1st sem.

#### CAS PY 542 Statistical Mechanics II

Prereq: CAS PY 541 or equivalent. Continuation of CAS PY 541; emphasis on applications. Phase transitions: thermodynamic theory of phase transitions, mean field theories (Landau theory). Fluctuations: equilibrium fluctuations, instabilities, fluctuation dissipation theories. Elementary kinetic theory: mean free path approach, Boltzmann equation. Stochastic mathematics: probability theory, Markoff processes, Gaussian processes. Brownian motion: Langevin equations, Fokker-Planck equation. 4 cr, 1st sem.

#### CAS PY 543 Introduction to Solid State Physics

Prereq: CAS PY 406, PY 410, PY 451, or consent of instructor. An introduction to crystal structure; lattice vibrations; electronic energy bands and Fermi surfaces; semiconductors, conductors, and insulators; superconductivity and magnetism. 4 cr, 2nd sem.

#### CAS PY 551 Introduction to Particle Physics

Prereq: CAS PY 451 and PY 452. Fundamental particles and their symmetries. Isospin and flavor. Discrete symmetries. Phenomenology of weak and strong interactions. Introduction to detector techniques. 4 cr, 2nd sem.

#### CAS PY 555 Cosmological Physics

Prereq: CAS PY 406, PY 408. Recommended: PY 410. Early universe cosmology: inflation, thermodynamics in an expanding universe with radiation, matter, vacuum energy. Growth of density perturbations, cosmic microwave background, large scale structure. The cosmological standard model and open questions, dark matter, dark energy, neutrinos.

#### CAS PY 561 Introduction to Nuclear Physics

Prereq: CAS PY 511. 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, and the like). 4 cr.

#### CAS PY 571 Introduction to Biological Physics

Prereq: CAS PY 410 or may be taken concurrently as a co-requisite. Introduction to biomolecular forces, energy flow, information and thermodynamics in biological systems. Nucleic acid, protein, and biomembrane structure. Mechanisms of transport and signaling in biological membranes. Biophysical techniques including spectroscopy. Emphasis on the physical principles underlying biological structure and function. 4 cr.

#### CAS PY 581 Advanced Laboratory

Prereq: CAS PY 351. 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, Mössbauer studies, and flux quantization, positron annihilation. 4 cr, 1st sem.