# All Courses

This page contains descriptions of the courses currently offered by the Department of Physics on a regular or semi-regular basis.

**Undergraduate Courses**

- Regularly Offered: courses required for the major and minor plus regularly offered electives
- Special Topics: elective courses that are only occasionally offered
- Physical Science Sequences

**Graduate Courses****

- Regularly Offered: standard first-year courses plus those that satisfy the category A, B, C, and D requirements
- Special Topics: elective courses that are only occasionally offered

** For graduate courses we prefer a model in which the faculty have some flexibility in what topics to cover and how to cover them. This approach keeps the courses fresh, modern, and up-to-date. Therefore, the description of graduate courses are in several forms. Each description should be viewed as an *example* of how the course might be taught, not as a list of required topics taught in a specific order.

## Regularly Offered Undergraduate Courses

** 12100-12200-12300, 13100-13200-13300, and 14100-14200-14300. ***PQ: For all three sequences, a first-year calculus sequence (MATH 13100-13200-13300, 15100-15200-15300, or 16100-16200-16300) and appropriate placement recommendation. (NOTE: MATH 15100-15200-15300 or 16100-16200-16300 may be taken concurrently.) Calculus is used in all three sequences. The first two courses of any sequence meets the general education requirement in physical sciences. *Although the essential physics content of these sequences is similar, PHYS 13100-13200-13300 and 14100-14200-14300 prepare students for further courses in the Department of Physics, while PHYS 12100-12200-12300 includes a broader emphasis on interdisciplinary applications, such as in biology. Two sections are offered for both the PHYS 13100-13200-13300 sequence and the PHYS 14100-14200-14300 sequence.

12100-12200-12300. General Physics I, II, III.PQ: Second-year standing.This is a one-year sequence in the fundamentals of physics. Topics include classical mechanics, fluids, electricity and magnetism, wave motion, optics, and modern physics.Autumn, Winter, Spring. L.

13100-13200-13300. Mechanics - Electricity and Magnetism - Waves, Optics and Heat.PQ: More advanced mathematical abilities and training recommended.This is a one-year sequence in the fundamentals of physics. Topics include classical mechanics, special relativity, electricity and magnetism, wave motion, optics, and heat.Autumn, Winter, Spring. L.

14100-14200-14300. Honors Mechanics - Honors Electricity and Magnetism - Honors Waves, Optics and Heat.PQ: Recommended to physics majors. Advanced knowledge of mathematics and good high school physics course helpful.This is a one-year sequence in the fundamentals of physics. Topics include classical mechanics, special relativity, electricity and magnetism, wave motion, optics, and heat. Multivariable and vector calculus is used.Autumn, Winter, Spring. L.

** 15400. Modern Physics. ***PQ: PHYS 14300, or PHYS 13300 and MATH 22000.* Topics in this introduction to quantum physics include Einstein’s quantum theory of light, the wave nature of particles, atomic structure, the Schrödinger equation, quantum mechanics in one- and three-dimensions, barrier penetration and tunneling, and the hydrogen atom. Applications to nuclear and solid-state physics are presented. *Autumn. L.*

** 18500. Intermediate Mechanics. ***PQ: PHYS 13100 or 14100, and PHYS 22100 or MATH 20300.* Topics include a review of Newtonian mechanics, the calculus of variations, Lagrangian and Hamiltonian mechanics, generalized coordinates, canonical momenta, phase space, constrained systems. central-force motion, noninertial reference frames, and rigid-body motion. *Winter.*

** 19700. Statistical and Thermal Physics. ***PQ: PHYS 23400, and PHYS 22100 or MATH 20500. *This course develops a statistical description of physical systems. Topics include elements of probability theory, equilibrium and fluctuations, thermodynamics, canonical ensembles, the equipartition theorem, quantum statistics of ideal gases, and kinetic theory.* Autumn.*

** 21100. Experimental Physics. ***PQ: PHYS 23400. Open only to physics majors. Credit is granted in Spring Quarter after successful completion of the year’s work.* This is a yearlong laboratory course, offering experiments in atomic, molecular, solid-state, nuclear, and particle physics. Additional material will be presented, as needed, in supplemental lectures. Content varies from quarter to quarter. *Autumn, Winter, Spring. L.*

** 22000. Introduction to Mathematical Methods in Physics. ***PQ: MATH 15200 or 16200 and PHYS 13200.* This course, with concurrent enrollment in PHYS 13300, is required of students who plan to major in physics. Topics include infinite series and power series, complex numbers, linear equations and matrices, partial differentiation, multiple integrals, vector analysis, and Fourier series. Applications of these methods include Maxwell's equations, wave packets, and coupled oscillators. *Spring.*

** 22100. Mathematical Methods in Physics. ***PQ: MATH 22000 and PHYS 13300, or PHYS 14200 and 14300.* Topics include linear algebra and tensor analysis, ordinary and partial differential equations, calculus of variations, special functions, series solutions of differential equations, and integral transforms. *Autumn.*

** 22500, 22700. Intermediate Electricity and Magnetism I, II. ***PQ: PHYS 13200 or 14200, and PHYS 22100 or MATH 20500.* Topics include electrostatics, magnetostatics, electromagnetic induction, electric and magnetic fields in matter, plane electromagnetic waves, reflection and refraction of electromagnetic waves, and electromagnetic radiation.* Winter, Spring.*

** 22600. Electronics. ***PQ: PHYS 12200, 13200, or 14200; or equivalent. *The goal of this hands-on experimental course is to develop confidence, understanding, and design ability in modern electronics. This is *not* a course in the physics of semiconductors. In two lab sessions a week, students explore the properties of diodes, transistors, amplifiers, operational amplifiers, oscillators, field effect transistors, logic gates, digital circuits, analog-to-digital and digital-to-analog converters, phase-locked loops, and more. Lectures supplement the lab. *Spring. L.*

** 23400. Quantum Mechanics I. ***PQ: PHYS 15400, and PHYS 22100 or MATH 20400. *A study of wave-particle duality leading to the basic postulates of quantum mechanics is presented. Topics include the uncertainty principle, applications of the Schrödinger equation in one and three dimensions, the quantum harmonic oscillator, rotational invariance and angular momentum, the hydrogen atom, and spin. *Spring. *

** 23500. Quantum Mechanics II. ***PQ: PHYS 23400.* A review of quantum mechanics is presented, with emphasis on Hilbert space, observables, and eigenstates. Topics include spin and angular momentum, time-independent perturbation theory, fine and hyperfine structure of hydrogen, the Zeeman and Stark effects, many-electron atoms, molecules, the Pauli exclusion principle, and radiative transitions. *Autumn. *

** 23600. Solid State Physics. ***PQ: PHYS 23500 and 19700. *Topics include a review of quantum statistics, crystal structure and crystal binding, lattice vibrations and phonons, liquid helium, the free-electron model of metals, the nearly-free-electron model, semi-conductors, and optical properties of solids. *Winter. *

** 23700. Nuclei and Elementary Particles. ***PQ: PHYS 23500. *This course covers topics such as nuclear structure, processes of transformation, observables of the nucleus, passage of nuclear radiation through matter, accelerators and detectors, photons, leptons, mesons, and baryons, hadronic interactions, and the weak interaction. *Spring. *

** 25000. Computational Physics.** *PQ: PHYS 13300 or 14300*. Knowledge of computer programming not required. This course introduces the use of computers in the physical sciences. After an introduction to programming basics, we cover numerical solutions to fundamental types of problems, techniques for manipulating large data sets, and computer simulations of complex systems. Additional topics may include an introduction to graphical programming, with applications to data acquisition and device control. *Autumn. L*.

** 26400. Spacetime and Black Holes. ***PQ: PHYS 18500, and PHYS 22100 or MATH 20400 or consent of instructor.* This course is an introduction to general relativity. After a review of special relativity and four-dimensional spacetime, the basic tools of physics in a curved spacetime are introduced. The Schwarzschild solution describing both black holes and the exteriors of stars and planets is presented, and the behavior of objects in a Schwarzschild spacetime are extensively studied. The course concludes by introducing the dynamical equations relating energy and momentum to spacetime curvature (Einstein’s equations). *Autumn.*

** 29100-29200-29300. Bachelor’s Thesis. ***PQ: Open to physics majors with fourth-year standing and consent of instructor. Students are required to submit the College Reading and Research Course Form in Autumn Quarter. Students receive a grade in each quarter of registration: *P/F* grading in Autumn and Winter Quarters, and quality grading in Spring Quarter. *This yearlong sequence of courses is designed to involve the student in current research. Over the course of the year, the student works on a research project in physics or a closely related field (e.g., astrophysics) leading to the writing of a bachelor’s thesis. A student who submits a satisfactory thesis, earns a grade of *B* or higher based on the project, and achieves a GPA of 3.0 or higher in the required undergraduate physics courses is awarded a B.A. with honors. The project may be one suggested by the instructor or one proposed by the student and approved by the instructor. In either case, all phases of the project (including the literature search, design and construction of the experiments, and analysis) must be done by the student. The instructor, faculty adviser, postdocs, and graduate students are, of course, available for consultation. *Autumn, Winter, Spring*.

## Undergraduate Special Topics Courses

** 22300. Topics in Mathematical Physics.*** PQ: PHYS 18500; and MATH 20500 or 20900*. This course covers selected topics in mathematical physics. Possible topics include differential geometry, group theory, Hilbert spaces, functional analysis, and topology.

** 23800. Modern Atomic Physics. ***PQ: PHYS 23500. *This course is an introduction to modern atomic physics. Topics include atomic structure, fundamental symmetries in atoms, interactions of atoms with radiation, laser spectroscopy, trapping and cooling, Bose-Einstein condensates, and quantum information.

** 25100. Chaos, Complexity, and Computers.** (=CMSC 27900, MATH 29200) *PQ: One year of calculus, two quarters of physics at any level, and PHYS 25000 or prior programming experience.* This course presents the mathematical bases for the complex, scale-independent behavior seen in chaotic dynamics and fractal patterns. It illustrates these principles from physical and biological phenomena. It explores these behaviors concretely using extensive computer simulation exercises, thus developing simulation and data analysis skills.* L.*

**25300. Materials of Tomorrow**. *PQ: PHYS 23400 *(*may be taken concurrently with consent of instructor*). This course focuses on the science and engineering of technologically advanced materials from a historical perspective that includes design considerations. We emphasize the relationship between microstructure and macroscopic response with an explicit discussion of processing strategies. Students work in conjunction with the instructor to develop and present a lab project.

** 25500. Biological Physics.*** PQ: PHYS 19700 or CHEM 26200.* This course introduces the physics of living matter. Our goal is to convey an understanding of the design principles from physics that characterize the condensed and organized matter of living systems. The first part of the course focuses on the physics of molecular motors, the dynamics of single molecules, and the mechanical properties of individual DNA molecules. The second part studies examples of stochastic processes in intracellular regulatory networks.

** 26000. Fluid Dynamics.** *PQ: PHYS 18500, and PHYS 22100 or MATH 20400*. This course introduces the dynamics of liquids and gases. Starting with the basic equations of motion, we consider the behavior of an ideal fluid, vorticity, viscous dissipation, shock formation, chaos, and turbulence, as well as other phenomena associated with both slow and fast fluid flow.

** 26100. Introduction to Structured Fluids. ***PQ: PHYS 19700 or CHEM 26200. *This course presents an overview of the fundamental physical concepts governing the behavior of the major categories of structured fluids: colloids, polymers, and surfactant assemblies. This course discusses how the characteristic spatial dimensions, response times, and interaction energies scale with the number of atoms in these structures. It is intended for students of physical and biological science who wish to understand the statistical mechanics underlying structure and motion in these liquids.

** 28000. Current Research Topics in Physics. ***PQ: PHYS 23500.* This course covers several research topics of current interest in physics. Topics, which are chosen by the instructors, may include neutrino masses, the quantum Hall effect, dark matter and dark energy, the physics of grains and glasses, the search for supersymmetry, and nanophysics, as well as other topics. The course is intended to acquaint students with forefront research in physics and to show how ideas from different areas of physics are combined in dealing with real-world problems.

** 29700. Participation in Research. ***PQ: Consent of instructor and departmental counselor. Open to physics majors with third- or fourth-year standing. Students are required to submit the College Reading and Research Course Form. With consent of instructor, this course is available for either quality grades or *P/F*. *By mutual agreement, students work in a faculty member’s research group. Participation in research may take the form of independent work (with some guidance) on a small project, or of assistance in research to an advanced graduate student or research associate. A written report must be submitted at the end of the quarter. Students may register for PHYS 29700 for as many quarters as they wish; students need not remain with the same faculty member each quarter.* Summer, Autumn, Winter, Spring. L.*

## Regularly Offered Graduate Courses

** 31600. Advanced Classical Mechanics. ***PQ: PHYS 18500. *This course begins with variational formulation of classical mechanics of point particles, including discussion of the principle of least action, Poisson brackets, and Hamilton-Jacobi theory. These concepts are generalized to continuous systems with infinite number of degrees of freedom, including a discussion of the transition to quantum mechanics.* Autumn.*

** 32200-32300. Advanced Electrodynamics I, II. ***PQ: PHYS 22700 and 23500. *This two-quarter sequence covers electromagnetic properties of continuous media, gauge transformations, electromagnetic waves, radiation, relativistic electrodynamics, Lorentz theory of electrons, and theoretical optics. There is considerable emphasis on the mathematical methods behind the development of the physics of these problems.* Winter, Spring.*

** 33000. Mathematical Methods of Physics. ***PQ: PHYS 22700. *Topics include complex analysis, linear algebra, differential equations, boundary value problems, and special functions.* Autumn.*

** 34100-34200. Quantum Mechanics I, II. ***PQ: PHYS 23500 and PHYS 22100 or MATH 27300. *This two-quarter sequence covers wave functions and their physical content, one-dimensional systems, WKB method, operators and matrix mechanics, angular momentum and spin, two- and three-dimensional systems, the Pauli principle, perturbation theory, Born approximation, and scattering theory.* Autumn, Winter.*

** 35200. Statistical Mechanics. ***PQ: PHYS 19700 and 23500.* This course covers principles of statistical mechanics and thermodynamics, as well as their applications to problems in physics and chemistry. *Spring.*

**33400. Advanced Experimental Physics.**

**33500. Advanced Experimental Physics Project.**

**35300. Advanced Statistical Mechanics.**

**36100. Introduction to Solid State Physics.**

**36300. Introduction to Particle Physics.**

**36400. General Relativity.**

**36600. Advanced Solid State Physics.**

**36700. Soft Condensed Matter Physics.**

**37100. Introduction to Cosmology.**

**37200. Space Physics and Astrophysics.**

**44300. Introduction to Quantum Field Theory I.**

**44400. Introduction to Quantum Field Theory II.**

**44500. Introduction to Quantum Field Theory III.**

## Graduate Special Topics Courses

** 31700. Symplectic Methods of Classical Dynamics.**

** 38500. Advanced Mathematical Methods of Physics.**

** 38600. Advanced Methods of Data Analysis.** This course emphasizes the practical over the formal. Students will gain facility with standard techniques in reducing and simulating data, an increased ability to understand the significance of a result they hear presented, and they develop a thirst for uncovering systematic effects in data. Such abilities are crucial for both data analysis and for designing new experiments. Class participation will be an important component of the course. Topics include: Probability distributions and their characteristics; Covariance and the Propagation of Errors; Bayesian vs. Frequentist approaches; Estimation of Errors, Curve fitting and Parameter estimation, Fitting in the presence of background; Maximum Likelihood Estimators; Fisher information matrix; Measures of Goodness of Fit; Confidence Interval Estimation; Fitting for a variance; Time stream analysis, 1/f noise; Fourier methods; Using Monte-Carlo Markov Chains.

** 40900. Synchrotron Radiation and Free Electron Lasers.** Synchrotron radiation is the electromagnetic radiation emitted by high-energy electrons travelling in curved trajectories. Its high intensity, coherence, wide spectral coverage, and other properties make synchrotron radiation a powerful tool for basic and applied studies of physical and biological systems. In the future, the intensity and coherence will be further enhanced by developing free-electron lasers. This course will provide an introduction to the basic principles of these radiation devices.

** 41600. X-ray and Neutron Scattering.** Description TBA

** 41900. Non-equilibrium Statistical Mechanics.** Linear response theory, Green-Kubo theory of transport coefficients, generalized Brownian motion, dynamic critical phenomena, Nambu-Goldstone modes, and introduction to non-linear dynamics.

** 42000. Superconductivity and Superfluidity.** Review of BCS theory, mean field theory of superconductors, superconducting response functions, Landau-Ginsberg theory, superconducting tunneling and Josephson effect, BCS-BEC crossover theory, Gross-Pitaevskii and Bogoliubov theory for bosonic superfluids, applications in ultracold atomic gases.

** 42600. Topics in Fluid Mechanics.** This course provides an introduction to the fundamentals of fluid mechanics with detailed examinations of a few research topics. The goal is to develop intuition about nonlinear flows via dimensional analysis, scaling arguments and simple, quantitative models. Some topics are: motion and deformation of liquid drops, boundary layer, formation of shocks and dydraulic jumps with possible analogs to ganular flows.

** 45200. Quantum Optics and Quantum Gases.** Atom-photon interaction and optical Bloch vector, Dressed atom description and radiative processes near resonance, Quantization of electromagnetic field, Nonlinear quantum optics, EPR paradox and quantun entanglement of macroscopic systems, Mechanical effects of radiative process, Atomic interactions and resonant scattering, Bose-Einstein condensation and degenerate Fermi gas, Superfluidity of quantum gases.

** 45500. Computing: Quantum and Otherwise.** (1) *Computability*: Notion of a computable problem; computable and noncomputable numbers; turing machines; diagonal arguments; halting problem; unsolvable problems in mathematics. (2) *Probabilistic computing*: Computations invoking a random-number generator; what this means, and what it means, e.g., to "solve" a problem with such a computer. (3) *Efficiency*: Notion of the "number of steps" required to solve a problem; results that are independent of the detailed efficiency measure; attempt to find a natural, canonical notion of the number of steps required. (4) *Physical computers*: "Classical" computers; "quantum" computers; discussion of the claim that quantum computers can be essentially more efficient than classical; examples.

**47100. Introduction to Modern Atomic Physics.**

**48300 - 48500. String Theory I - III.**

**48800. Introduction to Supersymmetry.**

**49100. Biological Physics.**

## Physical Science Sequences

** PHSC 11100-11200. Foundations of Modern Physics I, II.** *PQ: MATH 10600, or placement in MATH 13100 or higher. Must be taken in sequence.*

11100. Foundations of Modern Physics I.This algebra-based course presents an introduction to Newton’s laws of mechanics, including a study of planetary motion. The course also discusses wave motion as applied to sound and light. It concludes with an introduction to the special theory of relativity, in which the Newtonian concepts of space and time are reconsidered.Autumn. L.

11200. Foundations of Modern Physics II.PQ: PHSC 11100. With the advent of quantum mechanics, physicists found a successful alternative to Newton’s laws for explaining atomic phenomena. In doing so, a completely new philosophy concerning the laws of physics had to be adopted. In this course, we explore the basic tenets of quantum mechanics, and consider the quantization of energy, the indeterminacy of physical events, and other concepts unique to the quantum view of nature.Winter. L.

** PHSC 11400–11500. Life in the Universe I, II.** *PQ: MATH 10600, or placement into MATH 13100 or higher.* *Must be taken in sequence; course I is prequisite for course II*. This two-quarter, algebra-based sequence treats our current understanding of the role that the laws of physics play in the development, existence, persistence, and prevalence of life in the universe. The main goal of this sequence is for students to learn about these laws within the overarching context of this theme. The subject matter includes all the major branches of physics as well as certain aspects of cosmology, stellar evolution, planetary science, as well as chemical and biological evolution.

11400: Life in the Universe I: Development of Life on Earth

Starting with the big bang theory of the early universe, students will study how the laws of physics guided the evolution of the universe through the processes most likely to have produced life on earth as it exists today. Physics topics include: the fundamental interactions and the early universe, nuclear, atomic, and molecular structure, Newton's laws and the formation of stars, galaxies, and planetary systems, thermonuclear fusion in stars, the physical origin of the chemical elements, the laws of electricity and magnetism and electromagnetic radiation, the laws of thermodynamics, atmospheric physics, and physical processes on primordial earth.Summer. L.

11500: Life in the Universe II: Extraterrestrial LifeBuilding upon the topics in

Life in the Universe I, this course goes on to consider what the laws of physics has to say about life elsewhere in the universe.Life in the Universe IIbegins with an analysis of the prospects for life on other bodies in the solar system, especially Mars. This is followed by a treatment of the physics behind the search for extraterrestrial intelligence and the feasibility of human interstellar and intergalactic spaceflight. The course concludes with a critical examination of speculative ideas in the popular media such as the suggestion that the universe itself is a living organism. Physics topics include: extended applications of the topics fromLife in the Universe I, optics and electromagnetic communication, rocket propulsion and advanced propulsion systems, the theories of special and general relativity, quantum physics, complexity, and emergence.Summer. L.