# Physics

211 Interdisciplinary Sciences Building

(831) 459-3744

http://physics.ucsc.edu/

## Lower-Division Courses

**1.** **Conceptual Physics.** **W**

Topics in classical and quantum physics and their relation to physical phenomena in the world around us, including modern electronics. Concepts are stressed, but some practical calculational techniques are developed. Working knowledge of high school algebra and geometry is essential. (General Education Code(s): SI, IN, Q.) The Staff

**2.** **Elementary Physics of Energy.** **S**

The physics of energy developed in a course accessible to non-science majors as well as science majors. Fundamental principles and elementary calculations, at the level of basic algebra, developed and applied to the understanding of the physics of energy. Topics include fossil fuels, renewable energy, solar cells and waste energy, waste-energy recovery, nuclear power, and global greenhouse effects. (General Education Code(s): PE-E.) S. Bailey

**5A.** **Introduction to Physics I.** **F,W**

Elementary mechanics. Vectors, Newton's laws, inverse square force laws, work and energy, conservation of momentum and energy, and oscillations. Prerequisite(s): concurrent enrollment in course 5L and Mathematics 19A or 20A is required. Enrollment restricted to biochemistry and molecular biology, chemistry, Earth sciences, engineering, and physics majors, minors, and proposed majors. (General Education Code(s): MF, IN, Q.) A. Durand, J. Nielsen

**5B.** **Introduction to Physics II.** **W**

A continuation of 5A. Wave motion in matter, including sound waves. Geometrical optics, interference and polarization, statics and dynamics of fluids. Prerequisite(s): courses 5A/L and Mathematics 19A or 20A; concurrent enrollment in course 5M is required. Corequisite: Mathematics 19B or 20B. (General Education Code(s): SI, IN.) A. Steinacker

**5C.** **Introduction to Physics III.** **S**

Introduction to electricity and magnetism. Electromagnetic radiation, Maxwell's equations. Prerequisite(s): courses 5A/L and Mathematics 19B or 20B. Concurrent enrollment in course 5N is required. (General Education Code(s): SI, IN.) A. Sher

**5D.** **Introduction to Physics IV.** **F**

Introduces temperature, heat, thermal conductivity, diffusion, ideal gases, laws of thermodynamics, heat engines, and kinetic theory. Introduces the special theory of relativity and the equivalence principle. Includes the photoelectric effect, the Compton effect, matter waves, atomic spectra, and the Bohr model. (Formerly Heat, Thermodynamics, and Kinetics) Prerequisite(s): courses 5A/L or 6A/L and Mathematics 19B or 20B. T. Jeltema

**5I.** **Introduction to Physics Honors I** **(2 credits).** *****

Weekly 90-minute section covering advanced and modern topics. Topics may include the theory of relativity; complicated dynamics (air resistance, planetary dynamics, etc.); fallacies in perpetual-motion machines; the Euler disk and unusual tops; elasticity of materials applied to structures. Concurrent enrollment in course 5A is required. The Staff

**5J.** **Introduction to Physics Honors II** **(2 credits).** *****

Weekly 90-minute section covering advanced and modern topics. Topics may include nonlinear oscillators and chaos; waves in deep water and inside the earth; redshift in astronomy; negative refractive index materials; photons and matter waves; holography; viscosity; and turbulence. Concurrent enrollment in course 5B is required. The Staff

**5K.** **Introduction to Physics Honors III** **(2 credits).** *****

Weekly 90-minute section covering advanced and modern topics. Topics may include atmospheric electricity; shielding; tensor polarization; alternative energy sources; semiconductor devices; particle accelerators and relativistic electrodynamics; Thomson scattering; digital and analog communication. Concurrent enrollment in course 5C is required. The Staff

**5L.** **Introduction to Physics Laboratory** **(1 credit).** **F,W**

Laboratory sequence illustrating topics covered in course 5A. One three-hour laboratory session per week. Prerequisite(s): concurrent enrollment in course 5A is required. The Staff

**5M.** **Introduction to Physics Laboratory** **(1 credit).** **W**

Laboratory sequence illustrating topics covered in course 5B. One three-hour laboratory session per week. Prerequisite(s): courses 5A/L; concurrent enrollment in course 5B is required. The Staff

**5N.** **Introduction to Physics Laboratory** **(1 credit).** **S**

Laboratory sequence illustrating topics covered in course 5C. One three-hour laboratory session per week. Prerequisite(s): courses 5A/L. Concurrent enrollment in 5C is required. Courses 5B/M recommended. The Staff

**6A.** **Introductory Physics I.** **F,W,S**

Elementary mechanics. Vectors, Newton's laws, inverse square force laws, work and energy, conservation of momentum and energy, and oscillations. Prerequisite(s): Concurrent enrollment in course 6L required. Corequisite(s): Mathematics 11A or 19A or 20A or Applied Mathematics and Statistics 15A. (General Education Code(s): MF, IN, Q.) (W) Z. Schlesinger, (FS) A. Steinacker

**6B.** **Introductory Physics II.** **W,S**

A continuation of 6A. Geometric optics; statics and dynamics of fluids; introduction to thermodynamics, including temperature, heat, thermal conductivity, and molecular motion; wave motion in matter, including sound waves; introduction to electricity and magnetism. Prerequisite(s): course 5A/L or 6A/L; and Mathematics 11A or 19A or 20A or Applied Mathematics and Statistics 15A . Corequisite(s): Mathematics 11B or 19B or 20B. (General Education Code(s): SI, IN.) S. Bailey

**6C.** **Introductory Physics III.** **F,S**

Introduction to electricity and magnetism. Elementary circuits; Maxwell's equations; electromagnetic radiation; interference and polarization of light. Prerequisite(s): courses 5A/L or 6A/L, and Mathematics 11B or 19B or 20B or Applied Mathematics and Statistics 15B. (General Education Code(s): SI, IN.)(F) S. Bailey, (S) A. Steinacker

**6L.** **Introductory Physics Laboratory** **(1 credit).** **F,W,S**

Laboratory sequence illustrating topics covered in course 6A. One three-hour laboratory session per week. Prerequisite(s): Previous or concurrent enrollment in course 6A required. The Staff

**6M.** **Introductory Physics Laboratory** **(1 credit).** **W,S**

Laboratory sequence illustrating topics covered in course 6B. One three-hour laboratory session per week. Prerequisite(s): courses 5A, 6A, or 7A and 5L, 6L or 7L; and previous or concurrent enrollment in course 6B. The Staff

**6N.** **Introductory Physics Laboratory** **(1 credit).** **F,S**

Laboratory sequence illustrating topics covered in course 6C. One three-hour laboratory session per week. Prerequisite(s): courses 6A and 6L; previous or concurrent enrollment in course 6C; courses 6B and 6M are recommended. The Staff

**11.** **The Physicist in Industry** **(2 credits).** **W**

One two-hour meeting per week. Subjects include roles of the physicist in industry, the business environment in a technical company, economic considerations, job hunting, and discussions with physicists with industrial experience. Enrollment by permission of instructor. Priority given to applied physics upper-division students; other majors if space available. Enrollment limited to 15. S. Carter

**42.** **Student-Directed Seminar.**

Seminars taught by upper-division students under faculty supervision. (See course 192.) The Staff

**99.** **Tutorial.** **F,W,S**

Students submit petition to sponsoring agency. The Staff

## Upper-Division Courses

**102.** **Modern Physics.** **F,W**

Topics in quantum physics including the Schrodinger equation; angular momentum and spin; the Pauli exclusion principle; and quantum statistics. Applications in multi-electron atoms and molecules, and in solid-state, nuclear, and particle physics. Prerequisite(s): courses 5A/L, and 5B/M, and 5C/N and 5D; or 6A/L, and 6B/M, and 5D; or equivalent. R. Johnson, D. Belanger

**105.** **Mechanics.** **F**

Particle dynamics in one, two, and three dimensions. Conservation laws. Small oscillations, Fourier series and Fourier integral solutions. Phase diagrams and nonlinear motions, Lagrange's equations, and Hamiltonian dynamics. Prerequisite(s): courses 5A/L and 116A-B. J. Deutsch

**107.** **Introduction to Fluid Dynamics.** **F**

Covers fundamental topics in fluid dynamics: Euler and Lagrange descriptions of continuum dynamics; conservation laws for inviscid and viscous flows; potential flows; exact solutions of the Navier-Stokes equation; boundary layer theory; gravity waves. Students cannot receive credit for this course and Applied Mathematics and Statistics 217. (Also offered as Applied Math and Statistics 107. Students cannot receive credit for both courses.) Prerequisite(s): Mathematics 107 or Physics 116C or Earth and Planetary Sciences 111. The Staff

**110A.** **Electricity, Magnetism, and Optics.** **W**

Maxwell's equations, electrostatics, magnetostatics, induction, electromagnetic waves, physical optics, and circuit theory. Prerequisite(s): 116A-B-C. S. Ritz

**110B.** **Electricity, Magnetism, and Optics.** **S**

Maxwell's equations, electrostatics, magnetostatics, induction, electromagnetic waves, physical optics, and circuit theory. Prerequisite(s): courses 110A and 116C. D. Lederman

**112.** **Thermodynamics and Statistical Mechanics.** **W**

Consequences of the first and second laws of thermodynamics, elementary statistical mechanics, thermodynamics of irreversible processes. Prerequisite(s): course 5D, and course 116C or Applied Mathematics and Statistics 5 or Mathemathics 23A/B. Concurrent enrollment in course 101B or 102 or 116A is required. R. Johnson

**115.** **Computational Physics.** **S**

This course will apply efficient numerical methods to the solutions of problems in the physical sciences which are otherwise intractable. Examples will be drawn from classical mechanics, quantum mechanics, statistical mechanics, and electrodynamics. Students will apply a high-level programming language, such as Mathematica, to the solution of physical problems and develop appropriate error and stability estimates. Prerequisite(s): courses 101B or 102, and 105 and 116A-B-C, or equivalent. Basic programming experience in C or Fortran. No previous experience with Mathematica is required. O. Narayan

**116A.** **Mathematical Methods in Physics.** **W**

Infinite series, topics in linear algebra including vector spaces, matrices and determinants, systems of linear equations, eigenvalue problems and matrix diagonalization, tensor algebra, and ordinary differential equations. Prerequisite(s): Mathematics 23A and 23B. T. Jeltema

**116B.** **Mathematical Methods in Physics.** **S**

Complex functions, complex analysis, Fourier series and transforms, Dirac-delta function, Green's functions, asymptotic series and expansions, special functions defined by integrals, and calculus of variations. Prerequisite(s): course 116A and Mathematics 23A and 23B. A. Ramirez

**116C.** **Mathematical Methods in Physics.** **F**

Series solutions of ordinary equations, Legendre polynomials, Bessel functions, sets of orthogonal functions, partial differential equations, probability and statistics. Prerequisite(s): courses 116A-B and Mathematics 23A and 23B. A. Aguirre

**120.** **Polymer Physics.** *****

Statistical properties polymers; scaling behavior, fractal dimensions; random walks, self avoidance; single chains and concentrated solutions; dynamics and topological effects in melts; polymer networks; sol-gel transitions; polymer blends; application to biological systems; computer simulations will demonstrate much of the above. Students cannot receive credit for this course and course 240. Prerequisite(s): courses 112 and 116B. Offered in alternate academic years. J. Deutsch

**129.** **Nuclear and Particle Astrophysics.** **W**

The standard model of particle physics; general relativistic cosmology; the early universe and Big Bang nucleaosynthesis; dark matter and structure formation; formation of heavy elements in stars and supernovae; neutrino oscillations; high-energy astrophysics: cosmic rays and gamma-ray astronomy. (Formerly Nuclear and Particle Physics.) Prerequisite(s): courses 5D, and 101B or 102, and Mathematics 23B; students with equivalent coursework may contact instructor for permission to enroll. M. Hance

**133.** **Intermediate Laboratory.** **F,W**

Demonstration of phenomena of classical and modern physics. Development of a familiarity with experimental methods. Special experimental projects may be undertaken by students in this laboratory. Prerequisite(s): course 101A or 102. (General Education Code(s): SR.) (F) A. Ramirez, (W) B. Schumm

**134.** **Physics Advanced Laboratory.** **W,S**

Individual experimental investigations of basic phenomena in atomic, nuclear, and solid state physics. Prerequisite(s): courses 133, and 101B or 102. May be repeated for credit. (W) A. Ramirez, (S) S. Carter

**135.** **Astrophysics Advanced Laboratory.** *****

Introduction to the techniques of modern observational astrophysics at optical and radio wavelengths through hands-on experiments. Offered in some academic years as a multiple-term course: 135A in fall and 135B in winter, depending on astronomical conditions. (Also offered as Astronomy and Astrophysics 135. Students cannot receive credit for both courses.) Prerequisite(s): course 133 and at least one astronomy course. Intended primarily for juniors and seniors majoring or minoring in astrophysics. The Staff

**135A.** **Astrophysics Advanced Laboratory** **(3 credits).** **F**

Introduction to techniques of modern observational astrophysics at optical and radio wavelengths through hands-on experiments. Intended primarily for juniors and seniors majoring or minoring in astrophysics. Offered in some academic years as single-term course 135 in fall, depending on astronomical conditions. (Also offered as Astronomy and Astrophysics 135A. Students cannot receive credit for both courses.) Prerequisite(s): course 133 and at least one astronomy course. G. Brown

**135B.** **Astrophysics Advanced Laboratory** **(2 credits).** **W**

Introduction to techniques of modern observational astrophysics at optical and radio wavelengths through hands-on experiments. Intended primarily for juniors and seniors majoring or minoring in astrophysics. Offered in some academic years as single-term course 135 in fall, depending on astronomical conditions. (Also offered as Astronomy and Astrophysics 135B. Students cannot receive credit for both courses.) Prerequisite(s): course 133 and at least one astronomy course. G. Brown

**136.** **Advanced Astronomy Laboratory.** **S**

Introduces the techniques of modern observational astrophysics at optical wavelengths through hands-on experiments and use of remote observatories. Students develop the skills and experience to pursue original research. Course is time-intensive and research-oriented. Prerequisite(s): Earth Sciences 119 and Physics 133. Enrollment restricted to junior and senior astrophysics majors. Enrollment limited to 12. J. Prochaska

**139A.** **Quantum Mechanics.** **S**

The principles and mathematical techniques of nonrelativistic quantum mechanics: the Schrödinger equation, Dirac notation, angular momentum, approximation methods, and scattering theory. Offered in spring. Prerequisite(s): courses 101B or 102, and 116A-B-C. S. Ritz

**139B.** **Quantum Mechanics.** **F**

The principles and mathematical techniques of nonrelativistic quantum mechanics: the Schrödinger equation, Dirac notation, angular momentum, approximation methods, and scattering theory. Offered in fall. Prerequisite(s): courses 101B or 102, and 139A and 116ABC. M. Dine

**143.** **Supervised Teaching** **(2 credits).** *****

Supervised tutoring in selected introductory courses. Students should have completed course 101A and 101B as preparation. Students submit petition to sponsoring agency. The Staff

**152.** **Optoelectronics.** *****

The first half of the course covers the theory of optoelectronics including wave, electromagnetic, and photon optics, modulation of light by matter, and photons in semiconductors. The second half covers applications including displays, lasers, photodetectors, optical switches, fiber optics, and communication systems. Prerequisite(s): courses 101B or 102, and 110A. The Staff

**155.** **Solid State Physics.** **W**

Interatomic forces and crystal structure, diffraction, lattice vibrations, free electron model, energy bands, semiconductor theory and devices, optical properties, magnetism, magnetic resonance, superconductivity. Prerequisite(s): courses 112 and 139A; students with equivalent coursework may contact instructor for permission to enroll. Z. Schlesinger

**156.** **Applications of Solid State Physics.** *****

Emphasizes the application of condensed matter physics to a variety of situations. Examples chosen from subfields such as semiconductor physics, lasers, superconductivity, low temperature physics, magnetism, and defects in crystals. Prerequisite(s): courses 101B or 102. A. Ramirez

**160.** **Practical Electronics.** *****

Provides a practical knowledge of electronics that experimentalists generally need in research. The course assumes no previous knowledge of electronics and progresses according to the interest and ability of the class. Based on weekly lectures. However, with the aid of the instructor, the students are expected to learn mainly through the design, construction, and debugging of electronics projects. Students are billed a materials fee. Prerequisite(s): courses 5C and 5N or 6C and 6N. The Staff

**171.** **General Relativity, Black Holes, and Cosmology.** **F**

Special relativity is reviewed. Curved space-time, including the metric and geodesics, are illustrated with simple examples. The Einstein equations are solved for cases of high symmetry. Black-hole physics and cosmology are discussed, including recent developments. (Also offered as Astronomy and Astrophysics 171. Students cannot receive credit for both courses.) Prerequisite(s): courses 105, 110A, 110B, and 116A/B. H. Haber

**180.** **Biophysics.** **S**

Physical principles and techniques used in biology: X-ray diffraction; nuclear magnetic resonance; statistics, kinetics, and thermodynamics of macromolecules; viscosity and diffusion; DNA/RNA pairing; electrophoresis; physics of enzymes; biological energy conversion; optical tweezers. Prerequisite(s): course 112; students who have a biochemistry background may contact instructor for permission. Enrollment restricted to juniors and seniors. (General Education Code(s): PR-E.) J. Deutsch

**182.** **Scientific Communication for Physicists.** **F,W**

Explores the communication of physics to a wide range of audiences, including writing articles from the popular to the peer-reviewed level; critically analyzing the communication of scientific discoveries in the media; structuring the physics senior thesis; writing grant applications; assembling a personal statement for job and graduate school application; and assembling and critiquing oral presentations. Prerequisite(s): satisfaction of Entry Level Writing and Composition requirements. Enrollment restricted to junior and senior majors in physics, astrophysics, applied physics, or physics education. Enrollment limited to 35. (General Education Code(s): W.) (F) D. Belanger, (W) A. Steinacker

**191.** **Teaching Practicum.** **F,W,S**

Designed to provide upper-division undergraduates with an opportunity to work with students in lower division courses, leading discussions, reading and marking submissions, and assisting in the planning and teaching of a course. Prerequisite(s): excellent performance in major courses; instructor approval required; enrollment restricted to senior physics majors. The Staff

**192.** **Directed Student Teaching.** **F,W,S**

Teaching of a lower-division seminar under faculty supervision. (See course 42.) Prerequisite(s): upper-division standing; submission of a proposal supported by a faculty member willing to supervise. The Staff

**199.** **Tutorial.** **F,W,S**

Students submit petition to sponsoring agency. May be repeated for credit. The Staff

**199F.** **Tutorial** **(2 credits).**

Tutorial. May be repeated for credit. The Staff

## Graduate Courses

**205.** **Introduction to Research in Physics** **(2 credits).** **W**

Introduction to current research opportunities at UCSC for graduate students. Topics include: elementary particle physics, condensed matter and solid state physics, high energy astrophysics, biophysics, and cosmology. Selected topics related to career development may also be included. Enrollment restricted to graduate students or by permission of instructor. R. Johnson

**210.** **Classical Mechanics.** **F**

Generalized coordinates, calculus of variations, Lagrange's equations with constraints, Hamilton's equations, applications to particle dynamics including charged particles in an electromagnetic field, applications to continuum mechanics including fluids and electromagnetic fields, introduction to nonlinear dynamics. Enrollment restricted to graduate students only, except by permission of instructor. A. Sher

**212.** **Electromagnetism I.** **F**

Electrostatics and magnetostatics, boundary value problems with spherical and cylindrical symmetry, multipole expansion, dielectric media, magnetic materials, electromagnetic properties of materials, time-varying electromagnetic fields, Maxwell's equations, conservation laws, plane electromagnetic waves and propagation, waveguides and resonant cavities. Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. J. Deutsch

**214.** **Electromagnetism II.** **W**

Lorentz covariant formulation of Maxwell's equations, dynamics of relativistic charged particles and electromagnetic fields, scattering and diffraction. Topics in classical radiation theory: simple radiating systems radiation by moving charges, multipole radiation, synchrotron radiation, Cerenkov radiation, bremsstrahlung and radiation damping. Prerequisite(s): course 212. Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. O. Narayan

**215.** **Introduction to Non-Relativistic Quantum Mechanics.** **W**

Mathematic introduction; fundamental postulates; time evolution operator, including the Heisenberg and Schrodinger pictures; simple harmonic oscillator and coherent states; one-dimensional scattering theory, including S-matrix resonant phenomena; two-state systems, including magnetic resonance; symmetries, including rotation group, spin, and the Wigner-Eckart theorem; rotationally invariant problems, including the hydrogen atom; gauge invariance, including Landau levels; introduction to path integral. Enrollment restricted to graduate students only, except by permission of instructor. S. Profumo

**216.** **Advanced Topics in Non-Relativistic Quantum Mechanics.** **S**

Approximate methods: time-independent perturbation theory, variational principle, time-dependent perturbation theory; three-dimensional scattering theory; identical particles; permutation symmetry and exchange degeneracy, anti-symmetric and symmetric states; many-body systems and self-consistent fields: variational calculations; second quantized formalism, including Fock spaces/number representation, field operators and Green functions; applications: electron gas; quantization of the electromagnetic field and interaction of radiation with matter: absorption, emission, scattering, photoelectric effect, and lifetimes. Prerequisite(s): course 215. Enrollment restricted to graduate students only, except by permission of instructor. J. Nielsen

**217.** **Quantum Field Theory I.** **F**

Lorentz invariance in quantum theory, Dirac and Klein-Gordon equations, the relativistic hydrogen atom, Green functions and canonical approach to field theory, quantum electrodynamics, Feynman diagrams for scattering processes, symmetries and Ward identities. Students learn to perform calculations of scattering and decay of particles in field theory. Prerequisite(s): course 216. Enrollment restricted to graduate students only, except by permission of instructor. S. Profumo

**218.** **Quantum Field Theory II.** **W**

Path integral approach to quantum field theory. Theory of renormalization and the renormalization group, introduction to gauge theories and spontaneously broken field theories. Applications to the standard model of strong, weak, and electromagnetic interactions. Prerequisite(s): course 217. Enrollment restricted to graduate students only, except by permission of instructor. H. Haber

**219.** **Statistical Physics.** **S**

The basic laws of thermodynamics, entropy, thermodynamic potentials, kinetic theory of gases, quantum and classical statistical mechanics, virial expansion, linear response theory. Applications in condensed matter physics. Enrollment restricted to graduate students only, except by permission of instructor. O. Narayan

**220.** **Theory of Many-Body Physics.** **S**

Finite temperature Green functions, Feynman diagrams, Dyson equation, linked cluster theorem, Kubo formula for electrical conductivity, electron gas, random phase approximation, Fermi surfaces, Landau fermi liquid theory, electron phonon coupling, Migdal's theorem, superconductivity. Prerequisite(s): courses 216 and 219. Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. S. Shastry

**221A.** **Introduction to Particle Physics I.** **F**

First quarter of a two-quarter graduate level introduction to particle physics, including the following topics: discrete symmetries, quark model, particle classification, masses and magnetic moments, passage of radiation through matter, detector technology, accelerator physics, Feynman calculus, and electron-positron annihilation. Prerequisite(s): course 217 or concurrent enrollment. Enrollment restricted to graduate students only, except by permission of instructor. B. Schumm

**221B.** **Introduction to Particle Physics II.** **W**

Second quarter of a two-quarter graduate level introduction to particle physics, including the following topics: nucleon structure, weak interactions and the Standard Model, neutrino oscillation, quantum chromodynamics, CP violation, and a tour of the Stanford Linear Accelerator Center. Prerequisite(s): course 221A; course 217 or concurrent enrollment. Enrollment restricted to graduate students only, except by permission of instructor. J. Nielsen

**222.** **Quantum Field Theory III.** **S**

Focuses on the theoretical underpinnings of the standard model, including the spontaneous symmetry breaking, the renormalization group, the operator product expansion, and precision tests of the Standard Model. Prerequisite(s): courses 218 and 221B. Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. M. Dine

**224.** **Particle Astrophysics and Cosmology.** **S**

Particle physics and cosmology of the very early universe: thermodynamics and thermal history; out-of-equilibrium phenomena (e.g., WIMPs freeze-out, neutrino cosmology, Big Bang nucleosynthesis, recombination); baryogenesis; inflation; topological defects. High-energy astrophysical processes: overview of cosmic ray and gamma ray astrophysics; radiative and inelastic processes; astroparticle acceleration mechanisms; magnetic fields and cosmic ray transport; radiation-energy density of the universe; ultrahigh-energy cosmic rays; dark-matter models; and detection techniques. (Formerly Origin and Evolution of the Universe.) (Also offered as Astronomy and Astrophysics 224. Students cannot receive credit for both courses.) Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. A. Aguirre

**226.** **General Relativity.** **W**

Develops the formalism of Einstein's general relativity, including solar system tests, gravitational waves, cosmology, and black holes. (Also offered as Astronomy and Astrophysics 226. Students cannot receive credit for both courses.) Enrollment restricted to graduate students only, except by permission of instructor. A. Aguirre

**227.** **Advanced Fluid Dynamics.** *****

Fundamentals of heat transfer and fluid flow: thermal convection, gravity waves, vortex dynamics, viscous flows, instabilities, turbulence, and compressible flows. Students develop computer program for simulating thermal convection and gravity waves. Vector calculus and computer programming experience required. (Formerly Fluid Dynamics.) An introductory course in fluid dynamics recommended as preparation. Enrollment restricted to graduate students. Offered in alternate academic years. The Staff

**231.** **Introduction to Condensed Matter Physics.** **F**

Crystal structures, reciprocal lattice, crystal bonding, phonons (including specific heat), band theory of electrons, free electron model, electron-electron and electron-phonon interactions, transport theory. Prerequisite(s): course 216. Enrollment restricted to graduate students only, except by permission of instructor. S. Shastry

**232.** **Condensed Matter Physics.** **W**

Magnetism (para, ferro, anti-ferro, ferri), spin waves, superconductivity, introduction to semiconductors. Prerequisite(s): course 231. Enrollment restricted to graduate students only, except by permission of instructor. S. Shastry

**233.** **Advanced Condensed Matter Physics.** *****

A special topics course which includes areas of current interest in condensed matter physics. Possible topics include superconductivity, phase transitions, renormalization group, disordered systems, surface phenomena, magnetic resonance, and spectroscopy. Prerequisite(s): course 231. Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. S. Carter

**234.** **Soft Condensed Matter Physics.** *****

A selection of topics from: liquid crystals, biological systems, renormalization group and critical phenomena, stochastic processes, Langevin and Fokker Planck equations, hydrodynamic theories, granular materials, glasses, quasicrystals. Prerequisite(s): courses 219 and 232. Enrollment restricted to graduate students. A. Young, O. Narayan

**240.** **Polymer Physics.** *****

Statistical properties polymers. Scaling behavior, fractal dimensions. Random walks, self avoidance. Single chains and concentrated solutions. Dynamics and topological effects in melts. Polymer networks. Sol-gel transitions. Polymer blends. Application to biological systems. Computer simulations demonstrating much of the above. Students cannot receive credit for this course and course 120. Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. J. Deutsch

**242.** **Computational Physics.** **S**

This course will apply efficient numerical methods to the solution of problems in the physical sciences which are otherwise intractable. Examples will be drawn from classical mechanics, quantum mechanics, statistical mechanics, and electrodynamics. Students will apply a high-level programming language such as Mathematica to the solution of physical problems and will develop appropriate error and stability estimates. Prerequisite(s): basic programming experience in C or Fortran. No previous experience with Mathematica is required. Enrollment restricted to graduate students only, except by permission of instructor. Z. Schlesinger

**250.** **Mathematical Methods.** *****

Probability theory with applications to data analysis, complex variables, Cauchy's residue theorem, dispersion relations, saddle-point type asymptotic methods for integrals, integral transforms, ordinary differential equations and orthogonal polynomials, partial differential equations and boundary value problems, and Greens functions. Integral equations also included if time permits. Enrollment restricted to graduate students. A. Young

**251.** **Group Theory and Modern Physics.** *****

Finite and continuous groups, group representation theory, the symmetric group and Young tableaux, Lie groups and Lie algebras, irreducible representations of Lie algebras by tensor methods, unitary groups in particle physics, Dynkin diagrams, Lorentz and Poincaré groups. Enrollment restricted to graduate students only, except by permission of instructor. Offered in alternate academic years. H. Haber

**290.** **Special Topics.** *****

A series of lectures on various topics of current interest in physics at UC Santa Cruz. Enrollment restricted to graduate students only, except by permission of instructor. May be repeated for credit. The Staff

**291A.** **Cosmology** **(2 credits).** **F,W,S**

Intensive research seminar on cosmology and related topics in astrophysics: nature of dark matter; origin of cosmological inhomogeneties and other initial conditions of the big bang; origin and evolution of galaxies and large scale structure in the universe. Enrollment restricted to graduate students only, except by permission of instructor. J. Primack

**291B.** **X-rays and Magnetism** **(2 credits).** **F,W,S**

Research seminar on x-ray studies of the properties and behavior of magnetic materials. Topics include: the underlying physical interactions, experimental techniques, and selected examples from current research. This course includes a visit to the Advanced Light Source in Berkeley. Enrollment is restricted to graduate students. May be repeated for credit. P. Fischer

**291C.** **Developments in Theoretical Particle Physics** **(2 credits).** **F,W,S**

Seminar on the current literature of elementary particle physics, ranging from strong and weak interaction phenomenology to Higgs physics, supersymmetry, and superstring theory. Students may present their own research results. Prerequisite(s): course 218; enrollment restricted to graduate students. May be repeated for credit. M. Dine, H. Haber

**291D.** **Experimental High-Energy Collider Physics** **(2 credits).** **F,W,S**

Seminar on current results in experimental high-energy particle physics. Topics follow recently published results, including design of experiments, development of particle detector technology, and experimental results from new particle searches, quantum chromodynamics, and properties of heavy flavor quarks. Enrollment restricted to graduate students. May be repeated for credit. J. Nielsen

**291E.** **Applied Physics** **(2 credits).** **F,W,S**

Intensive research seminar on applied physics and related topics in materials science, including semiconductor devices, optoelectronics, molecular electronics, magnetic materials, nanotechnology, biosensors, and medical physics. Students may present their own research results. Enrollment restricted to graduate students. May be repeated for credit. G. Alers, S. Carter

**291F.** **Experimental High-Energy and Particle Astrophysics Seminar** **(2 credits).** **F,W,S**

Survey of current research in experimental high-energy and particle astrophysics. Recent observations and development in instrumentation for x-rays, gamma rays, and neutrinos, and evidence for dark matter and other new particles. Students lead discussion of recent papers. Enrollment restricted to graduate students. Enrollment limited to 15. May be repeated for credit. D. Smith

**291G.** **Condensed Matter Physics Research Seminar** **(2 credits).** **F,W,S**

Weekly seminar series covering topics of current interest in condensed matter physics. Local and external speakers discuss their work. Enrollment restricted to graduate students. May be repeated for credit. A. Young

**292.** **Seminar** **(no credit).** **F,W,S**

Weekly seminar attended by faculty and graduate students. Directed at all physics graduate students who have not taken and passed the qualifying examination for the Ph.D. program. Enrollment restricted to graduate students only, except by permission of instructor. The Staff

**297.** **Independent Study.** **F,W,S**

Enrollment restricted to graduate students only, except by permission of instructor. The Staff

**298.** **Theoretical and Experimental Research Project.** **F,W,S**

Enrollment restricted to graduate students only, except by permission of instructor. The Staff

**299.** **Thesis Research.** **F,W,S**

Enrollment restricted to graduate students only, except by permission of instructor. The Staff

Revised: 09/01/15