LSA Graduate Course Guide - Select the appropriate term, check "graduate", and highlight "LSA: Physics" under Step 3: Subjects. Make sure to un-check the boxes for courses at level 100-400.

### Service Courses

**UC 415: Ethics in Research**

*Offered one ½ term each semester. Typically attended in the 2nd year. Credits: (1). All Graduate Students in Physics must attend this course (or equivalent training)*

Informal discussion of ethics in research. Some issues: sharing of research credit, falsification of data, duties to report, financial management.

**Physics 501: Mini-Colloquium**

*Two semesters: fall and winter. Both terms are mandatory for all Graduate Students in Physics. Credits: (1 for each term)*

Mini lectures introducing the research conducted by Physics faculty. Almost always taken in the first year of graduate study.

### Foundations of Physics

Foundational courses on the traditional core subjects of physics. All of these courses satisfy 3 credits per term.

**Physics 505/506: Electricity and Magnetism I and II**

*Offered each fall/winter. *

1st term: Electrostatics, magnetostatics, quasi-static fields, electromagnetic waves.

2nd term: Scattering and diffraction, wave guides, radiation theory, covariant formulation of electrodynamics.

**Physics 507 Mechanics**

*Offered most winter terms. *

This course develops mechanics at the graduate level. Topics covered include generalized coordinates, constraints, Lagrange’s equations and applications, Lagrange multipliers, calculus of variations, Hamilton’s principle, central force and particle scattering, rigid-body coordinates and movement, Euler angles, damped driven oscillations, relativistic classical mechanics, Hamilton equation of motion, canonical transformations, Poisson brackets, and Hamilton-Jacobi theory.

**Physics 510: Statistical Physics**

*Offered each fall. *

Review of thermodynamics. Statistical basis of the second law of thermodynamics, entropy and irreversibility, equipartition, the Gibbs paradox. Quantum statistics, ideal Fermi gas, ideal Bose-Einstein condensation, phase equilibrium, phase transitions, fluctuations, and transport theory.

**Physics 511/512: Quantum Theory and Atomic Structure I and II.**

*Offered each fall/winter. *

This is a two term sequence on the quantum theory on graduate level and its applications to non-relativistic atomic, molecular, nuclear and condensed matter systems. Physics 511 (Fall term) covers fundamental concepts and mathematical structure of quantum mechanics, exactly solvable quantum systems, and symmetries analysis in quantum mechanics based on group theory (angular momentum etc.). Physics 512 (Winter term) covers approximation methods in quantum theory including time independent and time dependent perturbation, variational method, semi-classical theory and adiabatic theorem; applications of quantum mechanics to understand atomic and molecular structures, scattering theory, and non-relativistic quantum many-body systems.

**Physics 513/523: Advanced Quantum Mechanics I and II**

*Offered each fall/winter. *

Introduction to the methods of relativistic quantum field theory with applications relevant to high energy physics. Topics include: Feynman diagrams, calculations of cross sections for simple processes in scalar and spin or field theories, and the electron gas problem.

**Physics 514: Computational Physics**

*Offered each fall. *

Introduction to computational physics: classical and quantum physics. The first part of the course is an introduction to computational methods for classical physics: ODE and PDE, classical few- and N-body systems, criticality, percolation, and magnetism. The second part of the course contains an introduction to methods for single- and many-body quantum physics: Hartree Fock and extensions, density functional theory, density matrix renormalization group theory and quantum Monte Carlo.

### Specialty Courses

Specialty courses each provide comprehensive graduate-level introductions to one of the main areas of physics research.

All of these courses satisfy 3 credits per term.

**Physics 520/540: Condensed Matter Physics I and II**

*Offered each winter/fall. Prerequisites: PHYS 510, 511. *

1st term: basic phenomena and fundamental concepts of condensed matter physics. Classical and quantum descriptions of the electron gas and its transport properties using the Drude theory and the Sommerfeld theory, crystal structures and their symmetries, phonon excitations, electronic band structures and the corresponding classification of materials into conductors, insulators and semi-conductors, phenomena and theories of conventional superconductors, magnetization.

2nd term: an advanced course in condensed matter physics that focuses on correlation effects (beyond the free system). Green’s functions and Feynman diagrams are developed in the context of weakly-correlated electronic systems and the Fermi liquid theory of Landau, transport and localization, phase transitions, spontaneous symmetry breaking, and the optical properties of solids. We then proceed to discuss strongly-correlated electronic systems and non-Fermi liquids such as the quantum Hall effect and topological insulator.

**Physics 521/541: Elementary Particle Physics I and II**

*Offered each winter/fall. *

1st term: presentation of the standard model of particle physics. Quantum Electrodynamics, Weak and strong interactions,

2nd term: further development of particle physics in the detail appropriate for students planning to carry out research in this area. QCD, phenomenology of supersymmetric theories, grand unification and precision tests of the electroweak theory.

**Physics 525/526: Cosmology I and II - Early Universe/Late Universe**

*Offered each fall and winter, respectively*

1st term:

This course focuses on the cosmology of the early universe, from the big bang to the epoch of the cosmic microwave background.

Physics of the expanding universe, Einstein and Boltzmann equations, inflation, big bang nucleosynthesis, cosmological perturbations, recombination and early universe probes of inhomogeneities up to the CMB epoch. If time allows, some topics in early universe particle physics such as baryogenesis and dark matter genesis will also be covered.

2nd term:

This course focuses on the cosmology of the late universe, from the cosmic microwave background until today.

Review of the expanding universe. Observational aspects of the cosmic microwave background and formation of large scale structure from the CMB epoch until today. Late universe probes of dark energy and dark matter. Broad overview of astrophysics, stars and galaxies and their connection to late universe probes of dark matter, dark energy and structure formation.

**Physics 535 General Relativity **

*Offered each fall. *

This course is a thorough introduction to the theory of general relativity, covering both its mathematical underpinnings and its implications for gravitational physics. Topics include: tensor analysis, curved manifolds and differential geometry, the Einstein field equations, gravitational radiation, black holes, experimental tests of general relativity and standard cosmological models.

The graduate version of this course is a “meet-together” with an undergraduate course and as such there are no prerequisites. The instructor introduces additional challenges for graduate students.

**Physics 542 Quantum Optics **

*Offered each winter. *

Intended to give students a solid background in the interaction of optical radiation with atoms. The course begins with a detailed study of the interaction of “two-level” atoms with classical radiation fields. A density matrix formalism is developed that allows one to explore a wide range of problems including absorption, atom optics, laser cooling, saturation spectroscopy, dark states and slow light, coherent optical transients, and atom interferometry. The next part of the course is devoted to properties of the quantized radiation field, including coherent states, squeezed states, photon statistics, and field correlation functions. Finally, a range of problems involving the interaction of the quantized radiation field with atoms is studied, including spontaneous emission, dressed states of the atoms and the field, light scattering, and the Heisenberg approach to matterfield interactions. Additional topics may be covered as time permits. The prerequisites for this course are Quantum Mechanics (Phys 512) and Electromagnetism (Phys 506), or their equivalent. It is assumed that students have a good working knowledge of non-relativistic quantum mechanics using both wave function and Dirac notation.

### Advanced Courses

The offerings of 600-level courses change on a term-by-term basis. Refer to the Schedule of Classes to see what courses are offered in a given term.

All of these courses satisfy 3 credits.

**Physics 611: Nonlinear Optics**

*Prerequisites: EECS 537 or 538 or 530. *

Formalism of wave propagation in nonlinear media; susceptibility tensor; second harmonic generation and three-wave mixing; phase matching; third order nonlinearities and four-wave mixing processes; stimulated Raman and Brillouin scattering. Special topics: nonlinear optics in fibers, including solitons and self-phase modulation.

**Physics 620: Solid State Physics **

*This course can be repeated up to three times.*

An advanced course in condensed matter physics that introduces subjects not covered in Physics 520 and 540. 2nd term: an advanced course in condensed matter physics that focuses on correlation effects (beyond the free system). Green’s functions and Feynman diagrams are developed in the context of weakly-correlated electronic systems and the Fermi liquid theory of Landau. We then proceed to discuss the rich phenomena in condensed matter systems, including transport and localization, phase transitions, spontaneous symmetry breaking, the quantum Hall effect and topological insulators, optical properties of solids, strongly-correlated electronic systems and non-Fermi liquids.

**Physics 621: Quantum Theory of Fields**

This course continues the study of quantum field theory initiated in PHY 513 and PHY523 by developing one or more advanced topics. The focus will generally be different in each version of the course. Some past topics have been “the Renormalization Group”, “Supersymmetry”, or “Non-perturbative methods”.

*This course can be repeated up to three times.*

**Physics 644: Advanced Atomic Physics**

The course is focused on the following topics: Atom-field and atom-laser interactions. Absorption, emission, and saturation. Mechanical effects of light on atoms (atom cooling and trapping methods, BEC). Atom interferometry. Rydberg-atom physics and quantum defect theory. AC Stark shifts and ponderomotive effects. Floquet theory. Quantum optics phenomena (such as electromagnetically induced transparency and Autler-Townes effect). The prerequisites for this course are Quantum Mechanics (Phys 511/512) and Electromagnetism (Phys 505/506), or their equivalent. It is assumed that students have a good working knowledge of non-relativistic quantum mechanics.

**Physics 646: String Theory**

An introduction to the quantum theory of relativistic strings and its modern applications. Focus is on perturbative techniques based on conformal field theory in two dimensions. Important examples are D-branes, toroidal compactification and orbifolds. The course provides the foundation needed for applications of string theory to strongly gravitating systems such as black holes and cosmology as well as to particle physics.

**Physics 630: Biological Physics**

An introduction to biological physics at the cellular and supra-cellular scales, with an emphasis on understanding how robust biological function emerges from the interactions of systems of molecules, genes, and cells. Topics will be drawn from research literature of the past 20 years including signal transduction and cellular information processing, the effects of noise in living cells, the active mechanics of the cytoskeleton, and pattern formation and morphogenesis in animal development. We will pay particular attention to the process of model-building and the role that quantitative, physical models can play in shaping our understanding of biological systems. Physical and mathematical background developed as needed.

**Physics 650: Optical Waves in Crystals**

*Prerequisite: EECS 434.*

Propagation of laser beams: Gaussian wave optics and the ABCD law. Manipulation of light by electrical, acoustical waves; crystal properties and the dielectric tensor; electro-optic, acousto-optic effects and devices. Introduction to nonlinear optics; harmonic generation, optical rectification, four-wave mixing, self-focusing, and self-phase modulation.

### Research for Credit

**Physics 515: Research/Pre-Candidate**

*Credits: 4-6.*

Independent Study with student’s research advisor. Can be repeated for credit.

**Physics 995: Dissertation Research/Candidate**

*Credits: 8 (full term) or 4 (half term)*

Independent Study with student’s research advisor. Can be repeated for credit.