## Physics and Astronomy

### Courses of Instruction

###### Astronomy (ASTR)

The terms indicated are*expected*but are not

*guaranteed.*For the courses offered during any given term, consult the

*Schedule of Classes.*

**ASTR 100Lxg The Universe (4, FaSp)** Survey of the universe: planets, satellites, comets, stars, nebulae, galaxies. Practical component includes planetary observations and dark-sky field trip. Not available for major credit.

**ASTR 104L Special Laboratory (1, FaSp)** Laboratory component for ASTR 100Lxg for transfer students with equivalent lecture credit from another institution. For transfer students only. Graded CR/NC.

**ASTR 200Lxg Earth and Space (4)** Study of earth as a physical object and an object in space. Topics include seismic events, earth interior, other planets, formation of the sun and earth. Not available for major credit.

**ASTR 390 Special Problems (1-4)** Supervised, individual studies. No more than one registration permitted. Enrollment by petition only.

**ASTR 400 The Solar System (4, 2 years, Fa)** Earth’s motions; planets and their satellites; comets; meteorites; interplanetary matter; elementary celestial mechanics. *Prerequisite: *MATH 226.

**ASTR 410 Stellar Astronomy (4, 2 years, Sp)** The nature and dynamics of the sun, stars, star clusters, interstellar medium, and the structure of our galaxy. *Prerequisite: *MATH 126.

**ASTR 420 Galaxies and Cosmology (4, 2 years, Fa)** Galaxies and clusters of galaxies: their content, structure, dynamics, distribution, and motions; observational cosmology. *Prerequisite: *PHYS 153*L* or PHYS 163*L*.

**ASTR 440 Astrophysics (4, 2 years, Sp)** Introduction to the theory of stellar structure, stellar atmospheres, the evolution of the sun and stars. *Prerequisite: *PHYS 153*L* or PHYS 163*L*.

**ASTR 490x Directed Research (2-8, max 8)** Individual research and readings. Not available for graduate credit. *Prerequisite: *one upper division course in astronomy and departmental approval.

###### Physics (PHYS)

The terms indicated are*expected*but are not

*guaranteed.*For the courses offered during any given term, consult the

*Schedule of Classes.*

**PHYS 051x Problem Solving in Mechanics and Thermodynamics (1)** Intensive practice in solving elementary problems within a student-centered learning environment. Not available for degree credit. Graded CR/NC. *Concurrent enrollment: *PHYS 151*L.*

**PHYS 100Lxg The Physical World (4, FaSp)** The fundamentals of physics presented with emphasis on the structure and beauty of physical laws. Practical component will relate these laws to commonly encountered events. Not available for major credit.

**PHYS 125Lg Physics for Architects (4, Sp)** Fundamental laws and principles of physics with emphasis on the application of physical principles to the problems of architecture. Lecture, 4 hours; laboratory, 3 hours. (Duplicates credit in PHYS 135*abL.*) *Prerequisite: *MATH 108.

**PHYS 135abL Physics for the Life Sciences (4-4, FaSpSm)** Fundamental laws and principles of physics emphasizing areas related to life sciences; prerequisite for biological sciences, medicine, dentistry, and pharmacy. Lecture, 4 hours; laboratory, 3 hours. (Duplicates credit in PHYS 125*L.*) *Prerequisite: *Passing of Math Placement Exam or MATH 108 or MATH 125 or MATH 126 or MATH 226.

**PHYS 151Lg Fundamentals of Physics I: Mechanics and Thermodynamics (4, FaSpSm)** Gateway to the majors and minors in Physics and Astronomy. Statics and dynamics of particles and rigid bodies, conservation principles, gravitation, simple harmonic oscillators, thermodynamics, heat engines, entropy. Lecture, 3 hours; laboratory, 3 hours. *Prerequisite: *MATH 125 or MATH 126 or MATH 226.

**PHYS 152L Fundamentals of Physics II: Electricity and Magnetism (4, FaSpSm)** Electrostatics, magnetostatics, electrical circuits, wave motion, sound waves, electromagnetic waves. Lecture, 4 hours; laboratory, 3 hours. *Prerequisite: *PHYS 151*L, *MATH 126; *corequisite: *MATH 226.

**PHYS 153L Fundamentals of Physics III: Optics and Modern Physics (4, FaSpSm)** Geometrical optics, interference, diffraction, special relativity, quantum mechanics, atomic physics, solid state physics. Lecture, 3 hours; laboratory, 3 hours. *Prerequisite: *PHYS 152*L.*

**PHYS 161L Advanced Principles of Physics I (4, Sp)** Gateway to the majors and minors in Physics and Astronomy. Introductory treatment intended for well-qualified students. Dynamics of particles and rigid bodies, conservation laws, wave motion, thermodynamics, heat engines, entropy. Lecture, 3 hours; laboratory, 3 hours. *Prerequisite: *MATH 125; *corequisite: *MATH 126.

**PHYS 162L Advanced Principles of Physics II (4, Fa)** Electrostatics, magnetostatics, electrical circuits, electrical and magnetic properties of matter, Maxwell’s equations, electromagnetic waves, propagation of light. Lecture, 4 hours; laboratory, 3 hours. *Corequisite: *MATH 226; *recommended preparation: *PHYS 161*L.*

**PHYS 163L Advanced Principles of Physics III (4, Sp)** Interference and diffraction of waves, special relativity, quantum mechanics, atomic physics, nuclear physics, condensed matter physics, elementary particles. Lecture, 3 hours; laboratory, 3 hours. *Prerequisite: *PHYS 162*L.*

**PHYS 190 Freshman Colloquium (1, Fa)** Introduction to current research activities of the faculty of the Department, and topics of current and popular interest among the wider community of physicists. Graded CR/NC.

**PHYS 200Lxg The Physics and Technology of Energy: Keeping the Motor Running (4, FaSp)** Investigation of energy technologies, including development and implementation issues. Topics include the industrial revolution, electromagnetic induction, power transmission, combustion engines, fission and fusion. Not available for major credit.

**PHYS 304 Mechanics (4, Fa)** Dynamics of particles, kinematics of rotations, rigid body motion, Lagrangian and Hamiltonian formalism, theory of small vibrations. *Prerequisite: *PHYS 151*L *or PHYS 161*L, *MATH 245.

**PHYS 316 Introduction to Thermodynamics and Statistical Physics (4, 2 years, Sp)** First, second, and third thermodynamic laws; thermodynamic potentials, applications; distribution laws, kinetic theory, transport phenomena, specific heats. *Prerequisite: *PHYS 152*L *or PHYS 161*L, *MATH 226.

**PHYS 390 Special Problems (1-4)** Supervised, individual studies. No more than one registration permitted. Enrollment by petition only.

**PHYS 408ab Electricity and Magnetism (a: 4, Fa; b: 4, Sp)** *a: *Electrostatics; thermal, chemical, magnetic effects of steady currents; DC circuits. *b: *Electromagnetic induction; AC circuits; Maxwell’s equations. *Prerequisite: *PHYS 152*L *or PHYS 162*L; Corequisite: *MATH 245 (for PHYS 408

*a*), MATH 445 (for PHYS 408

*b*).

**PHYS 438ab Introduction to Quantum Mechanics and its Applications (a: 4, Sp; b: 4, Fa)** *a: *Concepts and techniques of quantum mechanics; free and bound states, the hydrogen atom. *b: *Relativity, atomic spectra, quantum statistics, nuclear models, nuclear reactions, elementary particles. *Prerequisite: *PHYS 304; *corequisite: *MATH 445.

**PHYS 440 Introduction to Condensed Matter Physics (4, Irregular, Sp)** Crystal structures, x‑ray diffraction, thermal properties of solids, diamagnetism and paramagnetism, free-electron model of metals, semiconductors, ferromagnetism, super-conductivity, imperfections in crystals. *Corequisite: *PHYS 438*a.*

**PHYS 472 Introduction to Lasers and Laser Systems (3, Fa)** (Enroll in EE 472)

**PHYS 473L Lasers and Optics Laboratory (3, Sp)** (Enroll in EE 473*L*)

**PHYS 490x Directed Research (2-8, max 8)** Individual research and readings. Not available for graduate credit.

**PHYS 492L Senior Lab (4, Fa)** Projects will include experiments in mechanics, thermodynamics, electricity and magnetism. Emphasis on laboratory work with discussion of theoretical background. Lecture, 2 hours; laboratory, 6 hours. *Prerequisite: *PHYS 152*L*.

**PHYS 493L Advanced Experimental Techniques (4, Sp)** Development of modern experimental techniques, including computer interface with data acquisition hardware and data analysis by software, applied specifically to experiments in modern physics. Emphasis on laboratory work with discussion of theoretical background. Lecture, 2 hours; laboratory, 6 hours. *Prerequisite: *PHYS 152*L*.

**PHYS 495 Senior Project (2)** An original project will be constructed applying computer technology (in either hardware or software) to produce a result useful in the physics classroom or laboratory.

**PHYS 499 Special Topics (2-4, max 4)** Lectures and discussions on specialized topics in physics.

**PHYS 500 Graduate Colloquium (1, Max 4, FaSp)** Topics of current research interest in physics and astronomy. Lectures directed to physics graduate students by faculty of the department and by outside speakers. Graded CR/NC.

**PHYS 502 Advanced Optics (3, Irregular)** Interaction of light and matter; laser oscillation condition; optical resonators; spectroscopy; pumping mechanisms; characteristics of dielectric, semiconductor, gas, and liquid lasers; topics in nonlinear optics.

**PHYS 504 Advanced Mechanics (3, Fa)** Newtonian formulation of dynamics; Hamilton’s principle; Lagrangian formulation; rigid body motion; Hamiltonian formulation; Hamilton-Jacobi theory; vibrations.

**PHYS 508ab Advanced Electricity and Magnetism (a: 3, Sp; b: 3, Fa)** *a: *Electrostatics, boundary value problems, multipole expansions, microscopic models of matter, magnetostatics. *b: *Maxwell’s equations, potentials and gauge transformations; electromagnetic waves; wave guides; electromagnetic radiation; special relativity.

**PHYS 510 Methods of Theoretical Physics (3, Fa)** Vector analysis; infinite, asymptotic Fourier series; complete sets; Dirac delta function; Fourier, Laplace transforms; Legendre functions; spherical harmonics; Sturm-Liouville theory; orthogonal polynomials; gamma-factorial function; complex variables.

**PHYS 514 Methods of Experimental Physics (3, Irregular)** Techniques of general utility in contemporary physics research, with emphasis on the use of commercially available instrumentation.

**PHYS 516 Methods of Computational Physics (3, Sp)** Introduction to algorithm development. Integration of ordinary differential equations; chaotic systems; molecular dynamics; Monte Carlo integration and simulations; cellular automata and other complex systems. *Recommended preparation: *ability to program in C or C++.

**PHYS 518 Thermodynamics and Statistical Mechanics (3, Fa)** Principles of, and relations between, thermodynamics and statistical mechanics; ensembles, partition function formalism; quantum statistics of non-interacting particles; fluctuations.

**PHYS 520 Methods for Complex Systems (3, Fa)** Probabilities, random walks, generalized central limit theorems, probabilities in thermodynamics, critical phenomena, self organized criticality, phenomenology of catastrophies, dynamical systems and examples from outside physics.

**PHYS 530 Relativity (3, Irregular)** Fundamentals of the special theory and applications to classical and quantum physics; the principle of equivalence; tensor analysis and Einstein’s theory of gravitation; relativistic cosmology. *Recommended preparation: *PHYS 504*a, *PHYS 508*a.*

**PHYS 540 Solid State Physics (3, Fa)** Fundamental concepts and techniques in solid state physics; electron gas at metallic densities; semiclassical transport; crystallography; band structure; phonons; screening; superconductivity; magnetic ordering. *Recommended preparation:* PHYS 518*a, *PHYS 558*a.*

**PHYS 558ab Quantum Mechanics (a: 3, Sp; b: 3, Fa)** *a: *General formulation of quantum mechanics with applications; theory of measurement; exactly solvable problems; angular momentum formalism. *b: *Approximation schemes and applications to atomic and molecular physics and scattering theory; identical particles; electromagnetic properties of atoms.

**PHYS 566 Neural Network Self-Organization (3, Sp)** (Enroll in CSCI 566)

**PHYS 590 Directed Research (1-12)** Research leading to the master’s degree. Maximum units which may be applied to the degree to be determined by the department. Graded CR/NC.

**PHYS 594abz Master’s Thesis (2-2-0)** Credit on acceptance of thesis. Graded IP/CR/NC.

**PHYS 640 Advanced Condensed Matter Physics (3, Sp)** Magnetism, magnons; superconductivity; transport phenomena; many-body effects; interacting electron gas; Hartree-Fock theory; neutron and x-ray scattering; and other selected topics. *Recommended preparation: *PHYS 540, PHYS 558*b.*

**PHYS 650 Topics in Current Research (2, Fa)** Course content will vary each year. It will include topics of current interest in research conducted in academia and industry.

**PHYS 668 Advanced Quantum Mechanics (3, Sp)** Relativistic wave equations; second quantization of Klein-Gordon, Dirac and Maxwell fields; applications in quantum electrodynamics and condensed matter physics. *Recommended preparation: *PHYS 558*b.*

**PHYS 669ab Group Theory and Symmetries in Physics (3-3, Irregular)** *a:* Abstract group theory; representation theory; point groups; selection rules; crystal tensors; molecular vibrations; rotation group; SU(2); Wigner-Eckart theorem; crystal-field splitting; time-reversal symmetry; gauge invariance; SU(3) and quarks. *b:* Application of group theory in field theory and particle physics: Lie groups and representations, Young tableaux, Dynkin diagrams, Poincare group, classical groups and supergroups, gauge theories. *Recommended Preparation:* PHYS 558b.

**PHYS 670 High Energy Physics (3, Irregular)** Elementary particles and the fundamental forces acting on them. Quarks, leptons, symmetries, gauge invariance, spontaneously broken symmetry, electroweak theory, quantum chromodynamics grand unified theory, strings. *Recommended preparation: *PHYS 668.

**PHYS 678 Relativistic Quantum Field Theory (3, Irregular)** Computational methods in relativistic quantum field theory: Feynman path integral, covariant perturbation theory, regularization, renormalization group, and non-perturbative techniques. *Recommended preparation: *PHYS 668.

**PHYS 680 Advanced Quantum Field Theory (3, Irregular)** Renormalization, quantization of gauge theories, non-Abelian gauge theories, quantum chromodynamics, spontaneous symmetry breaking, the standard model, anomalies. *Recommended preparation: *PHYS 678.

**PHYS 692 Internship (3 or 6, max 6, FaSpSm)** Field application of physics in a business or industry setting; part-time employment. Project to be jointly defined by student, employer and professor. Open to M.S. Physics for Business Applications degree candidates only.

**PHYS 710 Selected Topics in Experimental Physics (3, max 6)** Course content will vary yearly with current interest. Topics covered may include superconducting quantum interference devices, scanning tunneling microscopy, and laser cooling and trapping of single atoms.

**PHYS 720 Selected Topics in Theoretical Physics (3, max 6)** Course content will vary yearly with current interest. Topics covered may include field theory, many body theory, Green’s functions, dispersion theory, and group theory.

**PHYS 730 Selected Topics in Particle Physics (3, max 6)** Various advanced phases of particle physics. Content will vary yearly; emphasis on superstring theories, advanced topics in quantum gravity, and field theory. *Recommended preparation: *PHYS 678.

**PHYS 740 Selected Topics in Condensed Matter Physics (3, max 6)** Course content will vary yearly with current interest. Topics covered may include theory of superconductivity, high temperature superconductivity, Green’s functions in condensed matter physics, magnetism and transport in disordered metals.

**PHYS 750o Off Campus Studies (3, max 9)** Course work taken on campus at Caltech as part of the Caltech-USC cross-registration program. Graded CR/NC.

**PHYS 790 Research (1-12)** Research leading to the doctorate. Maximum units which may be applied to the degree to be determined by the department. Graded CR/NC.

**PHYS 794abcdz Doctoral Dissertation (2-2-2-2-0)** Credit on acceptance of dissertation. Graded IP/CR/NC.