# Physics Graduate Courses

Courses numbered 300 and above may be used for graduate credit for non-physics majors, e.g. in filling out a Master's program, as part of a minor in Physics, or for residence credits. Courses numbered 500 and above are graduate level for both physics and non-physics majors.

For a complete list of courses and programs at UW-Madison see the Guide

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### Courses Carrying Graduate Credit for Non-Physics Majors

- Physics 307: Intermediate Laboratory-Mechanics and Modern Physics
- Physics 311: Mechanics
- Physics 321: Electric Circuits and Electronics
- Physics 322: Electromagnetic Fields
- Physics 323: Electromagnetic Fields
- Physics 325: Optics
- Physics 371: Acoustics for Musicians
- Physics 407: Advanced Laboratory
- Physics 415: Thermal Physics
- Physics 448: Atomic and Quantum Physics
- Physics 449: Atomic and Quantum Physics
- Physics 472: Scientific Background to Global Environmental Problems
- Physics 498: Directed Study
- Physics 499: Directed Study
- Physics 563: Radionuclides in Medicine and Biology

**307 Intermediate Laboratory-Mechanics and Modern Physics.**I, II; 2 cr (P-A).*Experiments in modern physics, with discussion of statistical uncertainties and error analysis. Propagation of error. Available labs include gamma-ray spectroscopy, X-ray physics and diffraction, blackbody radiation, and Cavendish measurement of the gravitational constant G.*Prerequisites: Physics 202, 208, or 248.**311 Mechanics.**I, II; 3 cr (P-A). Origin and development of classical mechanics; mathematical techniques, especially vector analysis; conservation laws and their relation to symmetry principles; brief introduction to orbit theory and rigid-body dynamics; accelerated coordinate systems; introduction to the generalized-coordinate formalisms of Lagrange and Hamilton.*Prerequisites: Physics 202, 208 or 248, and Math 234 or 375.***321 Electric Circuits and Electronics.**I; 4 cr.(P-A). Direct current circuits, circuit theorems, alternating current circuits, transients, non-sinusoidal sources, Fourier analysis, characteristics of semiconductor devices, typical electronic circuits, feedback, non-linear circuits; digital and logic circuits; three lectures and one three-hour lab per week.*Prerequisites: Physics 202, 208 or 248.***322 Electromagnetic Fields.**I, II; 3 cr. (P-A).*Electrostatic fields, capacitance, multi-pole expansion, dielectric theory; magnetostatics; electromagnetic induction; magnetic properties of matter; Maxwell's equations.**Prerequisites: Physics 202, 208 or 248, and Math 234 or 375.***323 Electromagnetic Fields.**I, II; 3 cr (P-A). Special relativity, electromagnetic momentum, electromagnetic waves: propagation, interference, scattering, reflection and refraction at a dielectric interface, waves in a conductor. Wave packets and group velocity, dispersion. Waveguides and transmission lines. Retarded potentials. Radiation. Prerequisite: Physics 322.**325 Optics.**II; 3 cr (Advanced, Physical Sciences, C). Classical and modern optics, including imaging, polarization optics, optical telescopes, optical microscopes, interference and interferometers, optical fibers and fiber-optic communication, optical resonators, lasers, optical modulators, introduction to quantum and nonlinear optics. Concepts covered in lecture reinforced by weekly laboratory experiments. Prerequisites: Physics 202, 208, or 248, and Physics 322 or concurrent enrollment in Physics 322.**371 Acoustics for Musicians.**I or II; 2 cr. An introduction. Some elementary physics principles to describe such phenomena as wave and sound propagation, the operation of wind and string instruments, and the acoustics of rooms. May not be taken by Physics majors to count as physics credit. P: Advanced Undergrad or Grad st in music, HS algebra.**407 Advanced Laboratory.**II; 2-4 cr (P-A).*Advanced experiments in classical and modern physics. Possible experiments include beta decay, muon lifetime, nuclear magnetic resonance, Stern-Gerlach atomic beam, Mossbauer scattering, velocity of light, Zeeman effect, and Compton scattering. Techniques for the statistical analysis of experimental data are emphasized. Two (four) credit students will typically perform four (eight) experiments.*Prerequisites: Physics 307 or 308.**415 Thermal Physics.**I, II; 3 cr. Thermodynamics, kinetic theory of gases, and statistical mechanics. P: Physics 241, 244, or 205 & 311.**448 Atomic and Quantum Physics.**I; 3 cr. First semester of a two-semester senior course. Review of atomic and other quantum phenomena and special relativity; introduction to quantum mechanics treating the more advanced topics of atomic physics and applications to molecular, solid state, nuclear, and elementary particle physics and quantum statistics. Experiments underlying this course are covered in Physics 407. P: Physics 205, 241, or 244, and Physics 311 and 322. Not open to those who have had Physics 531.**449 Atomic and Quantum Physics.**II; 3 cr. A continuation of 448. P: Physics 448.**472 Scientific Background to Global Environmental Problems.**(Crosslisted with Atm Ocn) I or II; 3 cr (P-D). A one-semester course designed to provide those elements of physics, atmospheric sciences, chemistry, biology and geology which are essential to a scientific understanding of global environmental problems. Specific examples of such problems include global warming, stratospheric ozone depletion, acid rain and environmental toxins. Three lectures per week. P: Physics 103, 201, 207 or 247, or Chemistry 103, 108, 109, 115, or 116.**498 Directed Study.**I, II; 1-3 cr. P: Cons inst.**499 Directed Study.**I, II; 1-3 cr. P: Cons inst.**563 Radionuclides in Medicine and Biology**. (Cross-listed with Med Phys) I; 2-3 cr (P-I) Physical principles of radioisotopes used in medicine and biology and operation of related equipment; lecture and lab. P: Physics 205, 241, or 249, or Graduate Standing### Graduate Level Courses for Both Physics and Non-Physics Majors

- Physics 501: Radiological Physics and Dosimetry
- Physics 507: Advanced Laboratory
- Physics 525: Introduction to Plasmas
- Physics 527: Plasma Confinement and Heating
- Physics 531: Intro to Quantum Mechanics
- Physics 535: Introduction to Particle Physics
- Physics 545: Introduction to Atomic Structure
- Physics 546: Lasers
- Physics 551: Solid State Physics
- Physics 563: Radionuclides-Med & Biology
- Physics 601: Scientific Presentation
- Physics 603: Workshop in College Physics Teaching
- Physics 619: Microscopy of Life
- Physics 623: Electronic Aids to Measurement
- Physics 625: Applied Optics
- Physics 681: Senior Honors Thesis
- Physics 682: Senior Honors Thesis
- Physics 691: Senior Thesis
- Physics 692: Senior Thesis
- Physics 701: Introductory Seminars
- Physics 707: Quantum Computing Laboratory
- Physics 709: Intro to Quantum Computing
- Physics 711: Theoretical Physics-Dynamics
- Physics 715: Statistical Mechanics
- Physics 716: Statistical Mechanics II
- Physics 717: Relativity
- Physics 721: Theoretical Physics-Electrodynamics
- Physics 724: Waves and Instabilities in Plasmas
- Physics 725: Plasma Kinetic Theory and Radiation Processes
- Physics 726: Plasma Magnetohydrodynamics
- Physics 731: Quantum Mechanics
- Physics 732: Quantum Mechanics
- Physics 735: Particle Physics
- Physics 736: Experimental Techniques in Particle Physics
- Physics 746: Quantum Electronics
- Physics 748: Linear Waves
- Physics 749: Coherent Generation and Particle Beams
- Physics 751: Advanced Solid State Physics
- Physics 752: Many-Body Problems in Solid State Physics
- Physics 772: High Energy Astrophysics
- Physics 775: Advanced Ultrasound Physics
- Physics 799: Independent Study
- Physics 801: Special Topics in Theoretical Physics
- Physics 805: Special Topics in Physics
- Physics 831: Advanced Quantum Mechanics
- Physics 832: Advanced Quantum Mechanics
- Physics 833: Advanced Math in Quantum Field Theory
- Physics 835: Collider Physics Phenomenology
- Physics 848: Nonlinear Waves
- Physics 900: Colloquium
- Physics 903: Seminar-Theoretical Physics
- Physics 910: Seminar in Astrophysics
- Physics 922: Seminar in Plasma Physics
- Physics 951: Seminar-Solid State Physics
- Physics 990: Research

**501 Radiological Physics and Dosimetry.**(Crosslisted with H Oncol, Physics, BME) 3 cr. Interactions and energy deposition by ionizing radiation in matter; concepts, quantities and units in radiological physics; principles and methods of radiation dosimetry. P: Calculus and modern physics.**507 Advanced Laboratory.**II; 2-4 cr. Advanced experiments in classical and modern physics. Possible experiments include beta decay, muon lifetime, nuclear magnetic resonance, Stern-Gerlach atomic beam, Mossbauer scattering, velocity of light, Zeeman effect, and Compton scattering. Techniques for the statistical analysis of experimental data are emphasized. Two (four) credit students will typically perform four (eight) experiments.**525 Introduction to Plasmas.**(Also ECE, Engr. Physics 525.) I, II; 3 cr. Theory of plasmas. Plasma kinetic theory, collisional processes, orbit theory, and hydrodynamic theory. Applications to plasmas and their measurement. P: One course each in electromagnetic fields and in mechanics beyond elementary physics.**527 Plasma Confinement and Heating.**(Also Engr. Phys., ECE 527.) I; 3 cr. Principles of magnetic confinement and heating of plasmas for controlled thermonuclear fusion: magnetic field structures, single particle orbits, equilibrium, stability, collisions, transport, heating, modeling and diagnostics. Discussion of current leading confinement concepts: tokamaks, tandem mirrors, stellarators, reversed field pinches, etc. P: Engr. Physics/Physics/ECE 525 or equiv.**531 Introduction to Quantum Mechanics.**II; 3 cr. Historical background and experimental basis, de Broglie waves, correspondence principle, uncertainty principle, Schrodinger equation, hydrogen atom, electron spin, Pauli principle; applications of wave mechanics. P: Physics 311 & 322 & a course in modern physics, or equiv, or cons inst. Not open to those who have had Physics 448.**535 Introduction to Particle Physics.**II; 3 cr. Introduction to particles, antiparticles and fundamental interactions; detectors and accelerators; symmetries and conservation laws; electroweak and color interactions of quarks and leptons; unification theories. P: Physics 448 or 531 or equiv.**545 Introduction to Atomic Structure.**I; 3 cr. Nuclear atom; hydrogen atom; Bohr-Sommerfeld model, wave model, electron spin, description of quantum electron spin, description of quantum electrodynamic effects; external fields; many-electron atoms; central field, Pauli principle, multiplets, periodic table, x-ray spectra, vector coupling, systematics of ground states; nuclear effects in atomic spectra. P: A course in quantum mechanics or cons inst.**546 Lasers.**(Crosslisted with ECE) II; 2-3 cr. General principles of laser operation; laser oscillation conditions; optical resonators; methods of pumping lasers, gas discharge lasers, e-beam pumped lasers, solid state lasers, chemical lasers, and dye lasers; gain measurements with lasers; applications of lasers. P: Physics 322 or ECE 420 or equiv; Physics 545, or 449 or 531.**551 Solid State Physics.**I, II; 3 cr. Mechanical, thermal, electric, and magnetic properties of solids; band theory; semiconductors; crystal imperfections. P: A course in quantum mechanics or cons inst.**563 Radionuclides-Med&Biology**Physical principles of radioisotopes used in medicine and biology and operation of related equipment; lecture and lab.**601 Scientific Presentation**I, II; 2 cr. Oral and written reports to give practice in the presentation of scientific papers. P: Grad st or Sr st in the Honors program or cons inst.

P: At least 9 cr in intmed physics.**603 Workshop in College Physics Teaching.**II; 1-2 cr (P-A) Discussion, practice, and occasional lectures on various aspects of the teaching of physics. Course planning; course materials; lecture, demonstration, and discussion techniques; laboratory; problem solving; examinations, grading, and evaluation. Problems arising in the teaching of physics; levels of difficulty, differences in talents and backgrounds; methods of presentation of various specific topics.**619 Microscopy of Life.**(Crosslisted with Anatomy, BME, Chem, Med Phys, Phmcol M, Radiol) 3 cr. Survey of state of the art microscopic, cellular and molecular imaging techniques, beginning with subcellular microscopy and finishing with whole animal imaging. P: 2nd semester intro physics including light & optics (e.g. 104, 202, 208) or cons inst.**623 Electronic Aids to Measurement.**(Crosslisted with Atm Ocn) I; 4 cr. Fundamentals of electronics, electronic elements, basic circuits; combinations of these into measuring instruments. Three lectures and one three-hour lab per week. P: Physics 321 or cons inst.**625 Applied Optics.**II; 4 cr. Optical methods in research and technology. Reflection, refraction, absorption, scattering. Imaging. Sources and sensors. Schlieren methods. Interferometry. Instrumental spectroscopy. Fourier optics, image processing, holography. Laser technology, Gaussian beams, nonlinear optics. P: Three semesters of calculus level physics or equiv. Sr or Grad st or cons inst.**681 Senior Honors Thesis.**2-3 cr.**682 Senior Honors Thesis.**2-3 cr.**691 Senior Thesis.**2 cr.**692 Senior Thesis.**2 cr.**701 Introductory Seminars**Designed to give new students an introduction to the broad range of modern research going on at UW Physics, and to help students find research opportunities in the department. Each week, faculty from each major research area will present their research in a seminar setting. The research areas will include selected topics both in theory and experiment from biophysics; atomic, molecular, and optical physics; plasma; condensed matter; quantum information and computation; high energy and nuclear physics; particle physics, astrophysics, and cosmology.**707 Quantum Computing Laboratory**Provides an intensive introduction to the experimental techniques of quantum computing. Students will do 8 experiments chosen from: Bell violation with entangled photons, Stern-Gerlach, Pulsed NMR, Optical pumping of Rb, Nanofabrication, Fiber optics communication, Diode pumped YAG laser, and Acousto-optic modulator.**709 Intro to Quantum Computing**A detailed introduction to quantum computation and quantum information processing. Basic topics of quantum mechanics that are most relevant to quantum computing, particularly measurement theory. Specialized topics such as entanglement, other measures of quantum correlation and the Bell inequalities. Classical and quantum information theory, classical and quantum complexity theory. Qubits, quantum gates, quantum circuits. Teleportation, quantum dense coding, quantum cryptography. Quantum algorithms: Deustch, Simon, Shor, Grover, and adiabatic algorithms. Basic quantum error correction: 5-qubit, Steane and Shor codes.**711 Theoretical Physics-Dynamics.**I; 3 cr. Lagrange's equations, Hamilton's principle, orbits and scattering, kinematics of rotation, dynamics of rigid bodies, small oscillation problems and normal coordinates, Lorentz transformations and relativistic mechanics, Hamiltonian formulation of mechanics, canonical transformations, symmetries and conservation laws, Hamilton-Jacobi theory. P: Physics 311 or equiv.**715 Statistical Mechanics.**II; 3 cr. Statistical foundations, Liouville's theorem, ensembles, classical and quantum distribution functions, entropy and temperature, connection with thermodynamics, partition functions, quantum gases, non-ideal gases, phase transitions and critical phenomena, non-equilibrium problems, Boltzmann equation and the H-theorem, transport properties, applications of statistical mechanics to selected problems. P: Physics 711, 531 & 415, or equiv.**716 Statistical Mechanics II.**I; 3 cr. Symmetries and symmetry breaking, phase transitions, mean field theory, critical exponents, scaling hypothesis, renormalization group, diagrammatic expansion, epsilon-expansion, exact solution of the 2d Ising model. Boltzman kinetic equation, H-theorem, Fokker-Planck and Langevin equations, Born-Markov master equation, Lindblad superoperators, classical and quantum noise, theory of amplifiers. P: Physics 715.**717 Relativity.**II, Even Yrs; 3 cr. Special and general theories of relativity, relativistic electrodynamics, cosmology, unified field theories. P: Physics 721.**721 Theoretical Physics-Electrodynamics.**I, II; 3 cr. Electrostatics, magnetostatics, Green functions, boundary value problems, macroscopic media, Maxwell's equations, the stress tensor and conservation laws, electromagnetic waves, wave propagation, dispersion, waveguides, radiation, multipole expansions, diffraction and scattering, special relativity, covariance of Maxwell's equations, Lienard-Wiechert potentials, radiation by accelerated charges. P: Physics 322 or equiv.**724 Waves and Instabilities in Plasmas.**(Crosslisted with Engr. Physics, ECE) II; 3 cr. Waves in a cold plasma, wave-plasma interactions, waves in a hot plasma, Landau damping, cyclotron damping, magneto-hydrodynamic equilibria and instabilities, microinstabilities, introduction to nonlinear processes, and experimental applications. P: Engr. Physics/ECE/Physics 525 & Physics 721 or ECE 740 or cons inst.**725 Plasma Kinetic Theory and Radiation Processes..**(Also Engr. Physics, ECE 725.) I; 3 cr. Boltzmann equation, Fokker-Planck methods, dynamical friction, neoclassical and pseudoclassical diffusion, collision integrals, radiation processes, including stimulated and spontaneous emission, bremsstrahlung, atomic processes, experimental applications. P: Physics, ECE, Engr. Physics 525 & Physics 721 or ECE 740 or cons inst.**726 Plasma Magnetohydrodynamics.**(Crosslisted with Engr. Physics, ECE) II; 3 cr. MHD equations and validity in hot plasmas; magnetic structure and magnetic flux coordinates; equilibrium in various configurations; stability formulation, energy principle, classification of instabilities; ideal and resistive instability in various configurations, evolution of nonlinear tearing modes; force-free equilibria, helicity, MHD dynamo; experimental applications. P: Engr. Physics/ECE/Physics 525 & Physics 721 or ECE 740 or cons inst.**731 Quantum Mechanics.**I; 3 cr. Schrodinger equation, operator theory, matrix mechanics, transformation theory, Heisenberg representation, orbital angular momentum, bound-state problems, scattering theory, stationary perturbation theory, degenerate systems, time-dependent perturbation theory, Born approximation, other approximation methods. P: Physics 711, & 449 or 531, or equiv.**732 Quantum Mechanics.**II; 3 cr. Interaction of electromagnetic radiation with matter, quantization of the electromagnetic field, spontaneous transitions, identical particles and spin, addition of angular momenta, tensor operators, complex atoms, Hartree approximation, molecules, Dirac equation, relativistic effects in atoms. P: Physics 721 & 731.**735 Particle Physics.**II; 3 cr. Structure of elementary particles, quarks and gluons, introduction to calculational techniques of particle interactions (Feynman diagrams), constituent models of electroweak and strong interactions and associated phenomenological techniques. P: Physics 535, 731 or equiv or cons inst.**736 Experimental Techniques in Particle Physics.**Irr; 3 cr. Interaction of particles with matter; gas detectors (proportional and drift chambers); low noise electronics; techniques of calorimetry; triggering; event recording and data handling; motion of charged particles in accelerators and storage rings; colliding beam machines and detectors. P: Physics 535 or cons inst.**746 Quantum Electronics.**(Crosslisted with ECE) I, Even Yrs; 3 cr. Elementary aspects of Lagrange theory of fields and field quantization; Bose, Fermi and Pauli operators; interaction of fields; quantum theory of damping and fluctuations; applications to lasers, nonlinear optics, and quantum optics. P: ECE-Physics 546; Physics 721 or ECE 740.**748 Linear Waves.**(Also ECE 748.) I; 3 cr. General considerations of linear wave phenomena; one dimensional waves; two and three dimensional waves; wave equations with constant coefficients; inhomogenous media; random media. Lagrangian and Hamiltonian formulations; asymptotic methods. P: ECE 440 or Physics 322 or cons inst.**749 Coherent Generation and Particle Beams.**(Crosslisted with ECE, Engr) 3 cr. Fundamental theory and recent advances in coherent radiation charged particle beam sources (microwave to X-ray wavelengths) including free electron lasers, wiggler/wave-particle dynamics, Cerenkov masers, gyro-trons, coherent gain and efficiency, spontaneous emission, beam sources and quality, related accelerator concepts experimental results and applications. P: ECE 740 or Physics 721, or equiv, or cons inst.**751 Advanced Solid State Physics.**I, Odd Yrs; 3 cr. Lattice dynamics; band theory; Fermi surfaces; electrodynamics of metals; optical properties; transport properties. P: Physics 731 and 551 or equiv.**752 Many-Body Problems in Solid State Physics.**II, Odd Yrs; 3 cr. Introduction to many-body problems in solids: phonons, magnons, homogeneous electron gas, superconductivity, disordered systems. P: Physics 731.**772 High Energy Astrophysics.**Spring semester of odd calendar years; 3 cr. Interactions among the particles, fields, and radiations of interstellar and intergalactic space. Gamma ray, x-ray, and cosmic ray production, propagation, and detection. P: Physics 721 or 322, basic knowledge of spec relativity, basic diff equations, or cons inst.**775 Advanced Ultrasound Physics.**Foundations of acoustic wave equations, diffraction phenomena and acoustic beam formation, models for acoustic scattering from discrete structures and inhomogeneous continua, speckle statistics including speckle correlation, applications of these topics in medical imaging.**799 Independent Study**I, II; 1-3 cr. P: Cons inst.**801 Special Topics in Theoretical Physics.**I, II; 1-3 cr. Can be repeated for credit. P: Cons inst.**805 Special Topics in Physics.**I, II; 1-3 cr. Can be repeated for credit. P: Cons inst.**831 Advanced Quantum Mechanics.**I; 3 cr. Quantum theory of free and interacting fields, formal scattering theory, dispersion theory. P: Physics 732.**832 Advanced Quantum Mechanics.**II; 3 cr. Continuation of 831. P: Physics 831.**833 Advanced Math in Quantum Field Theory.**Irr; 3 cr. The use in physics, most specifically nonabelian gauge field theory, of differential forms, homology, cohomology, homotopy, index theorems, fiber bundles, parallel transport, connections, curvature, characteristic classes, moduli space, Morse theory, and assorted other mathematics, is motivated, developed, and illustrated. P: Physics 731, 732 and 831; or cons inst.**835 Collider Physics Phenomenology.**I; 2-3 cr. Standard gauge model. Applications to e+e-, proton-antiproton, pp, and ep colliders. Jets. Weak boson, heavy-quark, and Higgs boson production and decay. Neutrino counting. Neutral B meson mixing. Quarkonia. Supersymmetry. Fourth generation. P: Physics 735 or equiv or cons inst.**848 Nonlinear Waves.**(Also ECE 848.) II; 3 cr. General considerations of nonlinear wave phenomena; nonlinear hyperbolic waves; nonlinear dispersion; nonlinear geometrical optics; Whitham?s variational theory; nonlinear and parametric instabilities; solitary waves; inverse scattering method. P: ECE 748 or cons inst**900 Colloquium.**I, II; 0-1 cr. Lectures by staff and visitors. P: Cons inst if taken for 1 cr.**903 Seminar-Theoretical Physics.**I, II; 0-1 cr.**910 Seminar in Astrophysics.**(Crosslisted with Astron) 0-1 cr. Current topics. P: Cons inst.**922 Seminar in Plasma Physics.**(Crosslisted with ECE, Engr) 0-1 cr.**951 Seminar-Solid State Physics.**I, II; 0-1 cr.**990 Research.**I, II, SS; 1-12 cr.