Graduate Courses
- Physics 501: Methods of Theoretical Physics
- A two semester review of some of the mathematical methods that are essiential for the study of Physics. Theory of functions of complex variables, including analyticity, Cauchy's integral formula, residue theory; review of ordinary differential equations, introduction to partial differential equations, Fourier series, Sturm-Liouville theory, integral transforms. Introduction to function spaces; self-adjoint and unitary operators; eigenvalue problems. Partial differential equations of hyperbolic, elliptic, and parabolic type; special functions. Perturbation theory; integral equations; introduction to group theory.
- Credit: 3 units. (top)
- Physics 502: Methods of Theoretical Physics
- Continuation of Physics 501
- Credit: 3 units. (top)
- Physics 503: Advanced Mathematical Methods for Physicists and Engineers I
- An organized approach for solving hard problems approximately. A self-contained and general examination of asymptotics and perturbation theory, regular and singular perturbation theory, local and global analysis of differential and difference equations, summation methods, asymptotic expansion of integrals. Emphasis calculational rather than theoretical.
- Credit: 3 units. (top)
- Physics 504: Advanced Mathematical Methods for Physicists and Engineers II
- A self-contained continuation of Physics 503. General presentation of perturbation theory. Matched asymptotic expansions. Boundary layer theory, WKB theory, multiple scale analysis. Variational methods, integral equations.
- Credit: 3 units. (top)
- Physics 505: Classical Electrodynamics
- Classical electromagnetism via Maxwell's equations. Electric and magnetic fields from static charge and current distributions. Mathematical techniques for solving electrostatic and magnetostatic problems. Electrostatic and magnetostatic forces and energies.
- Credit: 3 units. (top)
- Physics 506: Classical Electrodynamics
- Time-varying electric and magnetic fields. Electromagnetic waves and radiation; simple antennas. Waveguides and effects of dispersion. Retardation effects and special relativity.
- Credit: 3 units. (top)
- Physics 507: Classical Mechanics
- Lagrangian and Hamiltonian formulation of the equations of motion, action principles and the Hamilton-Jacobi equation. Applications to celestial mechanics, satellite motion, rigid body motion, the many-body problem, and the "old" quantum mechanics. Perturbation theory and general relativity are discussed briefly.
- Credit: 3 units. (top)
- Physics 509: Nonlinear Dynamics
- The course will treat the theoretical foundations of nonlinear dynamics, and its applications to phenomena in diverse fields including physics, biology, and chemistry. Topics will include phase plane analysis, stability analysis, bifurcations, chaos, and iterated maps.
- Prerequisite: Knowledge of multivariate calculus and ordinary differential equations at the level of Mathematics 217; and Physics 117-118 (mechanics at the level of 411 is desirable but not essential).
- Credit: 3 units. (top)
- Physics 523: Quantum Mechanics
- Review of wave mechanics, scattering theory. Measurement algebra and the foundations of nonrelativistic quantum theory. Mathematical techniques for solution, perturbation theory. Applications to atomic, molecular, nuclear, and solid state problems. Introduction to relativistic quantum theory and quantized wave fields.
- Credit: 3 units. (top)
- Physics 524: Quantum Mechanics
- Continuation of Physics 523
- Credit: 3 units. (top)
- Physics 529: Statistical Mechanics
- Gibbs' formalism of statistical mechanics and applications to thermodynamics. Quantum statistical mechanics and degenerate matter. General theory of equilibrium including phase transitions and critical phenomena. Interacting particles, including non-ideal gases, ferromagnetism and superconductivity. Transport theory, irreversible processes.
- Credit: 3 units. (top)
- Physics 530: Advanced Topics in Statistical Mechanics
- Critical phenomena and renormalization group theory; scaling, universality, exact solutions, series expansions, computer simulations, e-expansion. Role of solitons and instantons in phase transitions. Quantum fluids: superfluidity and superconductivity. Linear response theory and disordered systems.
- Credit: 3 units. (top)
- Physics 534: Magnetic Resonance
- Quantum mechanical and classical aspects of paramagnetism and of nuclear and electronic magnetic resonance. Phenomenological equations of motion, spin interactions, spin temperature, thermal relaxation, dynamic polarization, multiple resonance phenomena.
- Credit: 3 units. (top)
- Physics 537: Thermodynamics & Kinetics of Materials
- A general discussion of phase formation and transformation in solids and liquids. Topics include equilibrium and nonequilibrium thermodynamics, equilibrium and metastable phase diagrams, nucleation and growth, spinodal transformations, diffusion and interface limited processes, shear-type and order/disorder transformations. Simple characterization techniques.
- Credit: 3 units. (top)
- Physics 539: Structure and Diffraction in Materials
- Topics of interest for the study of materials using diffraction techniques. Includes an introduction to crystallography, defects in crystals and quasi-crystals, and an introduction to diffraction from materials, electron microscopy of materials touching on electron optics, scanning and transmission electron microscopy and the interaction of high-energy elctrons with matter, and an introduction to x-ray techniques.
- Prerequisite: Permission of the instructor
- Credit: 3 units. (top)
- Physics 540: Quantum Theory of Many-Particle Systems
- Develops modern approaches to quantitative microscopic description of strongly-interacting quantum many-particle systems, including the helium liquids, nuclear matter, neutron-star matter, nuclei, and strongly-coupled electron systems. Emphasis is placed on the method of correlated basis functions method and the self-consistent Green's function method and their relationships. Cluster analysis, hypernetted-chain procedures, Monte Carlo sampling algorithms, diagram resummation, and field-theoretic techniques are introduced. The microscopic basis for pairing in superfluids and superconductors is examined.
- Credit: 3 units. (top)
- Physics 542: Nuclear Physics
- Topics at the forefront of both experimental and theoretical research in nuclear physics. Background survey of classic topics includes independent particle models, collective motion in nuclei, nucleon interaction, RPA and Hartree-Fock methods, pairing phenomena, giant resonances, and statistical models for the decay of excited nuclei.
- Credit: 3 units. (top)
- Physics 546: Galactic Astrophysics
- A critical survey of the astrophysical information derivable from investigations of the cosmic radiation detectable at the Earth; electromagnetic and nuclear interactions and their role in radiation detectors and in cosmic-ray physics; properties of the primary particle radiation; primary x- and gamma rays; theory of origin, acceleration, and propagation; radioastronomy as related to cosmic ray phenomena; the sun as a source of cosmic rays.
- Credit: 3 units. (top)
- Physics 547: Introduction to Elementary Particle Physics
- An introduction to the Standard Model of elementary particle physics. The non-Abelian SU(3)xSU(2)xU(1) gauge theory and its relation to phenomenology and experiments.
- Credit: 3 units. (top)
- Physics 549: Solid State Physics I
- Quantum theory of phonons in solids, thermodynamical properties. Band theory of solids. Transport properties. Superconductivity
- Credit: 3 units. (top)
- Physics 550: Solid State Physics II
- Nonequilibrium properties. Magnetism. Optical properties. Disordered systems. Selected topics of current interest.
- Credit: 3 units. (top)
- Physics 551: Relativistic Quantum Mechanics
- Introduction to Quantum Field Theory using simple 1-dimensional and/or scalar field examples. Canonical quantization and path integrals; Feynman diagrams; Lorentz group; discrete symmetries; LSZ theorem. Introduction to regularization and renormalization.
- Credit: 3 units. (top)
- Physics 552: Relativistic Quantum Field Theory
- Path-integral quantization of spin 1/2 and spin 1 particles. Quantum electrodynamics. Ward densities and renormalization. Computation of the electron anomalous magnetic moment and the Lamb shift. Non-Abelian gauge theories and their quantization. Quantum chromodynamics and asymptotic freedom. Spontaneous symmetry breaking and the Standard Model.
- Credit: 3 units. (top)
- Physics 553: Elementary Particles
- Properties and classification scheme of underlying entities on the basis of symmetry arguments. Calculus of observations based on Hilbert space, the S-matrix formulation of elementary particle interactions, space time symmetries of the Poincaré group, and various internal symmetries. General S-matrix theory, analytic properties exemplified by the Mandelstam and Regge representations, current algebra and soft-pion techniques, vector dominance model applied to analysis of vertex functions, and relativistic scattering amplitudes of elementary particle interactions.
- Credit: 3 units. (top)
- Physics 554: Elementary Particles
- Continuation of Physics 553
- Credit: 3 units. (top)
- Physics 556: Stellar Astrophysics
- A quantitative study of physical processes in stars; stellar populations; birth, evolution, and death of stars; internal stellar structure and dynamics; energy generation; nucleosynthesis; variable stars and standard candles; supernovae; collapsed stars; compact binary sources.
- Credit: 3 units. (top)
- Physics 557: Gravitation and Cosmology
- Special relativity, equivalence principle, and fundamental experiments. Mathematics of curved space-time. General structure of Einstein's equations. Observational tests. Applications of general relativity, relativistic stellar structure, gravitational collapse, and black holes. Cosmology.
- Credit: 3 units. (top)
- Physics 558: Relativistic Astrophysics
- Cosmology, the Standard Model, physical processes in the early universe including baryogenesis, nucleosynthesis, and the microwave background. Inflationary scenario and the particle physics/cosmology interface. Origin of galaxies and large-scale structure. Physics of compact objects: equations of state, white dwarfs, neutron stars, and pulsars. Supernovae, relativistic jets, and gravitational lenses.
- Credit: 3 units. (top)
- Physics 560: X-ray & Gamma-ray Astrophysics
- The goal of this course is to provide an up to date coverage of X-ray and gamma-ray astronomy, as an integral part of high-energy astrophysics. Generation and observational techniques of energetic particles and radiations from accreting neutron stars and black holes, supernova and supernova remnants, active galactic nuclei, interstellar and intergalactic matter, as well as related physics and model building will be discussed. The course will thus explore the most energetic phenomena in the universe and will also provide insight into diverse topics ranging from planetary exploration to dark matter and cosmology.
- Credit: 3 units. (top)
- Physics 563: Topics in Theoretical Biophysics
- Application of physical theory to a broad range of biological problems. Topics include the statistical mechanics of biopolymers and membranes, the transduction of chemical energy into motion, robustness of biological networks, and the spontaneous formation of spatiotemporal patterns in nonequilibrium systems.
- Prerequisite: Thermodynamics or statistical mechanics at the level of Physics 463
- Credit: 3 units. (top)
- Physics 565: Magnetism & Superconductivity
- Fundamental and applied aspects of magnetism and superconductivity in solids. The magnetic state in magnetically dilute and concentrated systems. Exotic forms of magnetism. Conventional, high-Tc, fullerene and organic superconductors. Superfluidity. Coexistence of magnetism and superconductivity. Applications include: SQUID sensors, energy storage, magnetic resonance imaging, magnetic cooling.
- Credit: 3 units. (top)
- Physics 576: Astrophysics
- Physical processes in stars; stellar populations; birth, evolution, and death of stars; energy generation; nucleosynthesis; variable stars; supernovae; collapsed objects; selected topics in galactic astrophysics, cosmology, and exobiology. Additional reading assignments for students registered for 576.
- Prerequisite: Physics 411, 421, and 463, or permission of instructo
- Credit: 3 units. (top)
- Physics 580: Special Topics in Physical Chemistry: Algebraic and Diagrammatic Methods for Many-Fermion Systems
- This course focuses on an important current topic in physical chemistry. Open to undergraduates with permission of the instructor. Quantum theory course on many-body methods for electronic and other many-fermion system. Topics include second quantization, hole-particle formalism, diagrammatic techniques, Wicks, Thouless, linked-cluster, and connected-cluster theorems, independent particle models, many-body perturbation theory, and coupled-cluster theory. Emphasis on mastering algebraic and diagrammatic techniques for many-fermion systems and their application to derive and analyze many-body perturbation theory and coupled-cluster theory, which are widely exploited in ab initio quantum chemistry and nuclear structure calculations.
- Prerequisite: Chem 401 and 402
- Credit: 3 units. (top)
- Physics 582: Research Seminar
- Designed to introduce students to current developments in physics and to research carried out by faculty. Topics vary each year. Each member of the department addresses issues in their particular specialty. Required of all first-year graduate students.
- Credit: 1 units. (top)
- Physics 584: Computational Methods
- This course provides an introduction to the computational techniques that are most widely used in both theoretical and experimental research in physics. Each lecture will use a realistic research problem to introduce the algorithms, software packages and numerical techniques that will be used by the students to develop a solution on the computer. Topics include Monte Carlo techniques, symbolic analysis with Mathematica, data acquisition software used in the laboratory, the numerical solution of quantum mechanical problems, and an introduction to general purpose frameworks based on Python.
- Prerequisite: Prior or concurrent enrollment in L31 471 or L31 422 or permission of the instructor.
- Credit: 1 units. (top)
- Physics 589: Selected Topics in Physics I
- Topics and credit by arrangements
- Credit: Credits by arrangement units. (top)
- Physics 589.1: Seminar on the Physics of Ultrasonic Imaging in Cardiovascular Medicine-Section 1
- In this course, students prepare, deliver, and revise Power Point-illustrated presentations of aspects of cardiovascular physiology and pathophysiology based in part upon echocardiographic imaging and tissue characterization. Joining in on the discussions and active class participation are central to the seminar format of this course.
- Credit: 1.5 units. (top)
- Physics 589.2: Analysis of Biological Data
- "Data science" is most commonly associated with topics in computer science; however, efficient algorithms, specific software packages, or "deep learning" are only tools, and are easily misused. In a research setting, working with data is primarily an exercise in critical thinking. The purpose of this interactive, hands-on course is to learn from mistakes by making them in a safe environment. After covering/reviewing probability theory; Bayesian inference; elements of information theory and random matrix theory, the course will focus on case studies of real-world biological data, such as quantitative imaging data, next-generation sequencing (metagenomics), and neural recordings. These modules will involve critical reading of research papers and working through puzzle-based assignments. The primary modules will be supplemented by shorter presentations on topics chosen by students. Fair warning: this is explicitly NOT a course on "big data" or machine learning, although students may choose to explore some of these topics in their presentations (required for credit). Experience with MatLab or Python strongly encouraged or will need to be acquired during the course.
- Credit: Credits by arrangement units units. (top)
- Physics 590: Special Topics in Physics
- Topics and credit by arrangements
- Credit: Credit by arrangements units. (top)
- Physics 590.1: Seminar on the Physics of Ultrasonic Imaging in Cardiovascular Medicine-Section 1
- In this course, students prepare, deliver, and revise Power Point-illustrated presentations of aspects of cardiovascular physiology and pathophysiology based in part upon echocardiographic imaging and tissue characterization. Joining in on the discussions and active class participation are central to the seminar format of this course.
- Credit: 1.5 units. (top)
- Physics 590.2: Group Theory And Symmetries In Physics
- Symmetries offer beautiful explanations for many otherwise incomprehensible physical phenomena in Nature. Group theory is the underlying mathematical framework to study symmetries, with far-reaching applications in many areas of physics, including solid state physics, atomic and molecular physics, gravitational physics, and particle physics. We will discuss many of the fascinating mathematical aspects of group theory, but highlighting its physics applications. The following topics will be covered: general properties of groups (definition, subgroups and cosets, quotient group, homo- and iso-morphism), representation theory (general group actions, direct sums and tensor products, Wigner-Eckart theorem, Young tablelaux), discrete groups (cyclicity, characters, examples), Lie groups and Lie algebra (Cartan-Weyl basis, roots and weights, Dynkin diagrams, Casimir operators, Clebsch-Gordan coefficients, classification of simple Lie algebras), space-time symmetries (translation and rotation, Lorentz and Poincare groups, conformal symmetry, supersymmetry and superalgebra), gauge symmetries (Abelian and non-Abelian, Standard Model, Grand Unified Theories).
- Credit: 3 units. (top)
- Physics 590.3: Elements of Phase Transitions and Critical Phenomena
- Phase transitions and critical phenomena are main active areas in Statistical Physics. A number of important concepts and methods have been developed that turned out to be valuable tools in both theoretical and experimental physics. The course will aim to teach the essentials, based on a recent book by Professors Ortiz and Nishimori, "Elements of Phase Transitions and Critical Phenomena" (Oxford University Press), to understand how and why states of matter may change their defining properties and transition to other states of matter. How do collective properties emerge? What characterizes the different phases of matter?
- Credit: 3 units. (top)
- Physics 591: Cardiovascular Biophysics Journal Club
- This journal club is intended for beginning graduate students, advanced undergraduates, and MSTP students with a background in the quantitative sciences (engineering, physics, math, chemistry, etc). The subjects covered are inherently multidisciplinary. We will review landmark and recent publications in quantitative cardiovascular physiology, mathematical modeling of physiologic systems and related topics such as chaos theory and nonlinear dynamics of biological systems. Familiarity with calculus, differential equations, and basic engineering/thermodynamic principles is assumed. Knowledge of anatomy/physiology is optional.
- Credit: 1 units. (top)
- Physics 593: Introduction to Methods in Physics
- Five hours per week of tutorial training in modern experimental and/or theoretical methods in physics. Instruction by faculty members or, with faculty supervision and assistance, by graduate teaching interns who are enrolled in and earning credit for Phys 597-598.
- Credit: Variable units. (top)
- Physics 594: Introduction to Methods in Physics
- Five hours per week of tutorial training in modern experimental and/or theoretical methods in physics. Instruction by faculty members or, with faculty supervision and assistance, by graduate teaching interns who are enrolled in and earning credit for Phys 597-598.
- Credit: Variable units. (top)
- Physics 595: Research
- The department regularly conducts seminars for review of current progress in research. Fields in which it is active: (a) Space Physics and Astrophysics, (b) Nuclear Physics, (c) Theoretical Physics, (d) Condensed Matter and Magnetic Resonance, (e) Applications of Ultrasound to medical, biological, and physical problems.
- Credit: Credit variable, max 9 units units. (top)
- Physics 596: Research
- The department regularly conducts seminars for review of current progress in research. Fields in which it is active: (a) Space Physics and Astrophysics, (b) Nuclear Physics, (c) Theoretical Physics, (d) Condensed Matter and Magnetic Resonance, (e) Applications of Ultrasound to medical, biological, and physical problems.
- Credit: Credit variable, max 9 units units. (top)
- Physics 597: Teaching Methods in Physics
- May be taken more than once. Supervised instructional experience as graduate teaching intern. (Typically for five contact hours per week and associated preparation and evaluation.) The teaching requirement for the Ph.D. degree may be met through satisfactory completion of 8 units of Physics 597-598.
- Credit: 1 units. (top)
- Physics 598: Teaching Methods in Physics
- May be taken more than once. Supervised instructional experience as graduate teaching intern. (Typically for five contact hours per week and associated preparation and evaluation.) The teaching requirement for the Ph.D. degree may be met through satisfactory completion of 8 units of Physics 597-598.
- Credit: 2 units. (top)