# PHYSICS (PHYSICS)

### Courses

**PHYSICS 15. The Nature of the Universe. 3 Units.**

The structure, origin, and evolution of the major components of the Universe: planets, stars, and galaxies. Emphasis is on the formation of the Sun and planets, the evolution of stars, and the structure and content of the Milky Way galaxy. Topics: cosmic enigmas (dark matter, black holes, pulsars, x-ray sources), star birth and death, and the origins of and search for life in the solar system and beyond.

**PHYSICS 16. Cosmic Horizons. 3 Units.**

The origin and evolution of the universe and its contents: stars, galaxies, quasars. The overall structure of the cosmos and the physical laws that govern matter, space, and time. Topics include the evolution of the cosmos from the origin of the elements and the formation of stars and galaxies, exotic astronomical objects (black holes, quasars, supernovae, and gamma ray bursts), dark matter, inflationary cosmology, and the fate of the cosmos.

**PHYSICS 17. Black Holes. 3 Units.**

Newton's and Einstein's theories of gravitation and their relationship to the predicted properties of black holes. Their formation and detection, and role in galaxies and high-energy jets. Hawking radiation and aspects of quantum gravity.

**PHYSICS 18N. Frontiers in Theoretical Physics and Cosmology. 3 Units.**

Preference to freshmen. The course will begin with a description of the current standard models of gravitation, cosmology, and elementary particle physics. We will then focus on frontiers of current understanding including investigations of very early universe cosmology, string theory, and the physics of black holes.

**PHYSICS 19. How Things Work: An Introduction to Physics. 3 Units.**

Introduction to the principles of physics through familiar objects and phenomena, including airplanes, cameras, computers, engines, refrigerators, lightning, radio, microwave ovens, and fluorescent lights. Estimates of real quantities from simple calculations. Prerequisite: high school algebra and trigonometry.

**PHYSICS 21. Mechanics and Heat. 3 Units.**

For biology, social science, and premedical students. Introduction to Newtonian mechanics, fluid mechanics, theory of heat. Prerequisite: high school algebra and trigonometry; calculus not required.

**PHYSICS 21S. Mechanics and Heat with Laboratory. 4 Units.**

For biology, social science, and premedical students. Labs are an integrated part of the summer course. Introduction to Newtonian mechanics, fluid mechanics, theory of heat. nPrerequisite: high school algebra and trigonometry; calculus not required.

**PHYSICS 22. Mechanics and Heat Laboratory. 1 Unit.**

Guided hands-on exploration of concepts in classical mechanics and thermodynamics with an emphasis on student predictions, observations and explanations. Pre- or corequisite: PHYS 21.

**PHYSICS 23. Electricity and Optics. 3 Units.**

Electric charges and currents, magnetism, induced currents; wave motion, interference, diffraction, geometrical optics. Prerequisite: PHYSICS 21.

**PHYSICS 23S. Electricity and Optics with Lab. 4 Units.**

For biology, social science, and premedical students. Labs are an integrated part of the summer courses. Electric charges and currents, magnetism, induced currents; wave motion, interference, diffraction, geometrical optics. nnPrerequisite: PHYSICS 21S or 21.

**PHYSICS 24. Electricity and Optics Laboratory. 1 Unit.**

Guided hands-on exploration of concepts in electricity and magnetism, circuits and optics with an emphasis on student predictions, observations and explanations. Introduction to multimeters and oscilloscopes. Pre- or corequisite: PHYS 23.

**PHYSICS 25. Modern Physics. 3 Units.**

Introduction to modern physics. Relativity, quantum mechanics, atomic theory, radioactivity, nuclear reactions, nuclear structure, high energy physics, elementary particles, astrophysics, stellar evolution, and the big bang. Prerequisite: PHYSICS 23 or consent of instructor.

**PHYSICS 26. Modern Physics Laboratory. 1 Unit.**

Guided hands-on and simulation-based exploration of concepts in modern physics, including special relativity, quantum mechanics and nuclear physics with an emphasis on student predictions, observations and explanations. Pre- or corequisite: PHYSICS 25.

**PHYSICS 41. Mechanics. 4 Units.**

How are the motions of objects in the physical world determined by the laws of physics? In this course, students will learn to describe the motion of objects (kinematics) and then develop an understanding of why motions have the form they do (dynamics). We will emphasize how all the important physical principles in mechanics, such as conservation of momentum and energy for translational and rotational motion, follow from just three "laws" of nature -- Newton's laws of motion. We will make clear distinctions between the fundamental laws of nature and empirical rules, which are useful approximations for more complex physics. Problems will be drawn from the many examples of mechanics in everyday life. Students will develop skills in verifying that derived results satisfy criteria for correctness, such as dimensional consistency and the expected behavior in limiting cases. Discussions will be based on the language of mathematics -- in particular, vector representations, manipulation of vectors, and calculus. Physical understanding will be fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving.nPrerequisite: High school physics or concurrent enrollment in PHYSICS 41A. MATH 41 or MATH 51 or CME 100 or equivalent. Minimum Corequisite: MATH 42 or equivalent.

**PHYSICS 41A. Mechanics Concepts, Calculations, and Context. 1 Unit.**

Additional assistance and applications for PHYSICS 41. In-class problems in physics and engineering. Exercises in the concepts and calculations of vectors, translational and rotational velocity and acceleration, equations of motion for particles and rigid bodies, and principles of energy and linear/angular momentum. In-class participation required. Highly recommended for students with limited high school physics or calculus. Co-requisite with PHYSICS 41 for students with no high school physics.

**PHYSICS 42. Classical Mechanics Laboratory. 1 Unit.**

Hands-on exploration of concepts in classical mechanics: Newton's laws, conservation laws, rotational motion. Introduction to laboratory techniques, experimental equipment and data analysis. Pre- or corequisite: PHYSICS 41.

**PHYSICS 43. Electricity and Magnetism. 4 Units.**

What is electricity? What is magnetism? And how are they related? How do these phenomena manifest themselves in the physical world? The theory of electricity and magnetism, as codified by Maxwell's equations, underlies much of the observable universe. This course will develop both conceptual and quantitative knowledge of this theory. Topics to be covered include electrostatics; magnetostatics; simple AC and DC circuits involving capacitors, inductors, and resistors; the integral form of Maxwell's equations; and electromagnetic waves. Basic principles will be illustrated in the context of modern technologies. The course will also address broader scientific questions -- How do physical theories evolve? What is the interplay between basic physical theories and their associated technologies? Discussions will be based on the language of mathematics, particularly differential and integral calculus, and vectors. Physical understanding will be fostered by peer interaction and demonstrations in lecture, and discussion sections based on interactive group problem solving. Prerequisite: PHYSICS 41 or equivalent. MATH 42 or MATH 51 or CME 100 or equivalent. Recommended corequisite: MATH 52 or CME 102.

**PHYSICS 43A. Electricity and Magnetism: Concepts, Calculations and Context. 1 Unit.**

Additional assistance and applications for PHYSICS 43. In-class problems in physics and engineering. Exercises in calculations of electric and magnetic forces and field to reinforce concepts and techniques; Calculations involving inductors, transformers, AC circuits, motors and generators.

**PHYSICS 43N. Understanding Electromagnetic Phenomena. 1 Unit.**

Preference to freshmen. Expands on the material presented in PHYSICS 43; applications of concepts in electricity and magnetism to everyday phenomena and to topics in current physics research. Corequisite: PHYSICS 43 or advanced placement.

**PHYSICS 44. Electricity and Magnetism Lab. 1 Unit.**

Hands-on exploration of concepts in electricity and magnetism and circuits. Introduction to multimeters, function generators, oscilloscopes, and graphing techniques. Pre- or corequisite: PHYSICS 43.

**PHYSICS 45. Light and Heat. 4 Units.**

Reflection and refraction, lenses and lens systems; polarization, interference, and diffraction; temperature, properties of matter and thermodynamics, introduction to kinetic theory of matter. Prerequisites: PHYSICS 41 or equivalent. MATH 21 or MATH 42 or MATH 51 or CME 100 or equivalent.

**PHYSICS 45N. Advanced Topics in Light and Heat. 1 Unit.**

Preference to freshmen. Expands on the subject matter presented in PHYSICS 45 to include optics and thermodynamics in everyday life, and applications from modern physics and astrophysics. Corequisite: PHYSICS 45 or advanced placement.

**PHYSICS 46. Light and Heat Laboratory. 1 Unit.**

Hands-on exploration of concepts in geometrical optics, wave optics and thermodynamics. Pre- or corequisite: PHYSICS 45.

**PHYSICS 50. Astronomy Laboratory and Observational Astronomy. 3 Units.**

Introduction to observational astronomy emphasizing the use of optical telescopes. Observations of stars, nebulae, and galaxies in laboratory sessions with 16- and 24-inch telescopes at the Stanford Observatory. Meets one evening per week from dusk until well after dark at the Stanford Observatory. No previous physics required. Limited enrollment. Lab.

**PHYSICS 59. FRONTIERS OF PHYSICS RESEARCH. 1 Unit.**

Recommended for prospective Physics and Engineering Physics majors, and anyone with an interest in learning about the big questions and unknowns that physicists tackle in their research at Stanford. Weekly faculty presentations, in some cases followed by tours of experimental laboratories where the research is conducted.

**PHYSICS 61. Mechanics and Special Relativity. 4 Units.**

(First in a three-part series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) Advanced freshman physics. For students with a strong high school mathematics and physics background contemplating a major in Physics or interested in a rigorous treatment of physics. Special theory of relativity and Newtonian mechanics with multi- variable calculus. Postulates of special relativity, simultaneity, time dilation, length contraction, the Lorentz transformation, causality, and relativistic mechanics. Central forces, contact forces, linear restoring forces. Momentum transport, work, energy, collisions. Angular momentum, torque, moment of inertia in three dimensions. Damped and forced harmonic oscillators. Recommended prerequisites: Mastery of mechanics at the level of AP Physics C and AP Calculus B/C or equivalent. Corequisite: MATH 51.

**PHYSICS 62. Classical Mechanics Laboratory. 1 Unit.**

Introduction to laboratory techniques, experiment design, data collection and analysis simulations, and correlating observations with theory. Labs emphasize discovery with open-ended questions and hands-on exploration of concepts developed in PHYSICS 61 including Newton's laws, conservation laws, rotational motion. Pre-or corequisite PHYSICS 61.

**PHYSICS 63. Electricity, Magnetism, and Waves. 4 Units.**

(Second in a three-part series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) Advanced freshman physics. For students with a strong high school mathematics and physics background contemplating a major in Physics or interested in a rigorous treatment of physics. Electricity, magnetism and waves with some description of optics. Electrostatics and Gauss' law. Electric potential, electric field, conductors, image charges. Other theorems of vector calculus. Electric currents, DC circuits. Moving charges, magnetic field, Ampere's law. Solenoids, transformers, induction, AC circuits, resonance. Relativistic point of view for moving charges. Displacement current, Maxwell's equations. Electromagnetic waves, dielectrics. Diffraction, interference, refraction, reflection, polarization. Prerequisite: PHYSICS 61 and MATH 51; Pre- or corequisite: MATH 52.

**PHYSICS 64. Electricity, Magnetism and Optics Laboratory. 1 Unit.**

Introduction to multimeters, breadboards, function generators and oscilloscopes. Emphasis on student-developed design of experimental procedure and data analysis for topics covered in PHYSICS 63: electricity, magnetism, circuits, and optics. Pre- or corequisite: PHYSICS 63.

**PHYSICS 65. Quantum and Thermal Physics. 4 Units.**

(Third in a three-part series: PHYSICS 61, PHYSICS 63, PHYSICS 65.) Advanced freshman physics. For students with a strong high school mathematics and physics background contemplating a major in Physics or interested in a rigorous treatment of physics. Introduction to quantum mechanics: matter waves, atomic structure, Schrödinger's equation. Thermodynamics and statistical mechanics: entropy and heat, Boltzmann statistics, quantum statistics. Prerequisites: PHYSICS 61 & PHYSICS 63. Pre- or corequisite: MATH 53.

**PHYSICS 67. Introduction to Laboratory Physics. 2 Units.**

Methods of experimental design, data collection and analysis, statistics, and curve fitting in a laboratory setting. Experiments drawn from electronics, optics, heat, and modern physics. Lecture plus laboratory format. Required for PHYSICS 60 series Physics and Engineering Physics majors; recommended, in place of PHYSICS 44, for PHYSICS 40 series students who intend to major in Physics or Engineering Physics. Pre- or corequisite: PHYSICS 65 or PHYSICS 43.

**PHYSICS 70. Foundations of Modern Physics. 4 Units.**

Required for Physics majors who completed the PHYSICS 40 series, or the PHYSICS 60 series prior to 2005-06. Special relativity, the experimental basis of quantum theory, atomic structure, quantization of light, Schrödinger equation, nuclear physics, elementary particles and cosmology. Prerequisites: PHYSICS 41, PHYSICS 43. Pre or corequisite: PHYSICS 45. Recommended: prior or concurrent registration in MATH 53.

**PHYSICS 70N. Modern Physics in Your Life. 1 Unit.**

How does modern physics intersect with your everyday life? Topics may include the quantum nature of light, atomic physics and an introduction to semiconductor physics, applications to light sources (incandescent, fluorescent, light-emitting diodes, lasers) and light sensors (photodiodes and solar cells), introduction to nuclear physics (e.g., fission, fusion, interaction of radiation with matter). Co- or pre-requisite: PHYSICS 70, PHYSICS 65, or similar high-school physics preparation.

**PHYSICS 81N. Science on the Back of the Envelope. 3 Units.**

Understanding the complex world around us quantitatively, using order of magnitude estimates and dimensional analysis. Starting from a handful of fundamental constants of Nature, one can estimate complex quantities such as cosmological length and time scales, size of the atom, height of Mount Everest, speed of tsunami, energy density of fuels and climate effects. Through these examples students learn the art of deductive thinking, fundamental principles of science and the beautiful unity of nature.

**PHYSICS 83N. Physics in the 21st Century. 3 Units.**

Preference to freshmen. Current topics at the frontier of modern physics. Topics include subatomic particles and the standard model, symmetries in nature, extra dimensions of space, string theory, supersymmetry, the big bang theory of the origin of the universe, black holes, dark matter, and dark energy of the universe. Why the sun shines. Cosmology and inflation.

**PHYSICS 91SI. Practical Computing for Scientists. 2 Units.**

Essential computing skills for researchers in the natural sciences. Helping students transition their computing skills from a classroom to a research environment. Topics include the Unix operating system, the Python programming language, and essential tools for data analysis, simulation, and optimization. More advanced topics as time allows. Prerequisite: CS106A or equivalent.

**PHYSICS 100. Introduction to Observational and Laboratory Astronomy. 4 Units.**

Designed for undergraduate physics majors but open to all students with a calculus-based physics background and some laboratory experience. Students make and analyze observations using telescopes at the Stanford Student Observatory. Topics include navigating the night sky, the physics of stars and galaxies, telescope instrumentation and operation, quantitative error analysis, and effective scientific communication. Limited enrollment. Prerequisites: prior completion of Physics 40 or PHYSICS 60 series.

**PHYSICS 105. Intermediate Physics Laboratory I: Analog Electronics. 4 Units.**

Analog electronics including Ohm's law, passive circuits and transistor and op amp circuits, emphasizing practical circuit design skills to prepare undergraduates for laboratory research. Short design project. Minimal use of math and physics, no electronics experience assumed beyond introductory physics. Prerequisite: PHYSICS 43 or PHYSICS 63.

**PHYSICS 107. Intermediate Physics Laboratory II: Experimental Techniques and Data Analysis. 4 Units.**

Experiments on lasers, Gaussian optics, and atom-light interaction, with emphasis on data and error analysis techniques. Students describe a subset of experiments in scientific paper format. Prerequisites: completion of PHYSICS 40 or PHYSICS 60 series, and PHYSICS 70 and PHYSICS 105. Recommended: PHYSICS 130, prior or concurrent enrollment in PHYSICS 120. WIM.

**PHYSICS 108. Advanced Physics Laboratory: Project. 4 Units.**

Small student groups plan, design, build, and carry out a single experimental project in low-temperature physics. Prerequisites PHYSICS 105, PHYSICS 107.

**PHYSICS 110. Advanced Mechanics. 3-4 Units.**

Lagrangian and Hamiltonian mechanics. Principle of least action, Euler-Lagrange equations. Small oscillations and beyond. Symmetries, canonical transformations, Hamilton-Jacobi theory, action-angle variables. Introduction to classical field theory. Selected other topics, including nonlinear dynamical systems, attractors, chaotic motion. Undergraduates register for PHYSICS 110 (4 units). Graduates register for PHYSICS 210 (3 units). (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor.) Prerequisites: MATH 131P, and PHYS 112 or MATH elective 104 or higher. Recommended prerequisite: PHYS 130.

Same as: PHYSICS 210

**PHYSICS 112. Mathematical Methods of Physics. 4 Units.**

Theory of complex variables, complex functions, and complex analysis. Fourier series and Fourier transforms. Special functions such as Laguerre, Legendre, and Hermite polynomials, and Bessel functions. The uses of Green's functions. Covers material of MATH 106 and MATH 132 most pertinent to Physics majors. Prerequisites: MATH 50 or 50H series, and MATH 131P or MATH 173.

**PHYSICS 113. Computational Physics. 4 Units.**

Numerical methods for solving problems in mechanics, electromagnetism, quantum mechanics, and statistical mechanics. Methods include numerical integration; solutions of ordinary and partial differential equations; solutions of the diffusion equation, Laplace's equation and Poisson's equation with relaxation methods; statistical methods including Monte Carlo techniques; matrix methods and eigenvalue problems. Short introduction to MatLab, used for class examples; class projects may be programmed in any language such as C. Prerequisites: MATH 53 and PHYS 120. Previous programming experience not required.

**PHYSICS 120. Intermediate Electricity and Magnetism I. 4 Units.**

(First in a two-part series: PHYS 120, PHYS 121.) Vector analysis. Electrostatic fields, including boundary-value problems and multipole expansion. Dielectrics, static and variable magnetic fields, magnetic materials. Maxwell's equations. Prerequisites: PHYSICS 43 or PHYS 63; MATH 52 and MATH 53. Pre- or corequisite: MATH 131P or MATH 173. Recommended corequisite: PHYS 112.

**PHYSICS 121. Intermediate Electricity and Magnetism II. 4 Units.**

(Second in a two-part series: PHYS 120, PHYS 121.) Conservation laws and electromagnetic waves, Poynting's theorem, tensor formulation, potentials and fields. Plane wave problems (free space, conductors and dielectric materials, boundaries). Dipole and quadruple radiation. Special relativity and transformation between electric and magnetic fields. Prerequisites: PHYS 120 and MATH 131P or MATH 173; Recommended: PHYS 112.

**PHYSICS 130. Quantum Mechanics. 4 Units.**

The origins of quantum mechanics and wave mechanics. Schrödinger equation and solutions for one-dimensional systems. Commutation relations. Generalized uncertainty principle. Time-energy uncertainty principle. Separation of variables and solutions for three-dimensional systems; application to hydrogen atom. Spherically symmetric potentials and angular momentum eigenstates. Spin angular momentum. Addition of angular momentum. Prerequisites: PHYSICS 65 or PHYSICS 70. Pre- or corequisites: PHYSICS 120 and MATH 131P or MATH 173.

**PHYSICS 131. Quantum Mechanics II. 4 Units.**

Identical particles; Fermi and Bose statistics. Time-independent perturbation theory. Fine structure, the Zeeman effect and hyperfine splitting in the hydrogen atom. Time-dependent perturbation theory. Variational principle and WKB approximation. Prerequisite: PHYSICS 120, PHYSICS 130, MATH 131P, or MATH 173. Pre- or PHYSICS 121.

**PHYSICS 134. Advanced Topics in Quantum Mechanics. 3-4 Units.**

Scattering theory, partial wave expansion, Born approximation. Additional topics may include nature of quantum measurement, EPR paradox, Bell's inequality, and topics in quantum information science; path integrals and applications; Berry's phase; structure of multi-electron atoms (Hartree-Fock); relativistic quantum mechanics (Dirac equation). Undergraduates register for PHYSICS 134 (4 units). Graduate students register for PHYSICS 234 (3 units); graduate students required to complete additional assignments in a format determined by the instructor. Prerequisites: PHYSICS 130, PHYSICS 131.

Same as: PHYSICS 234

**PHYSICS 152. Introduction to Particle Physics I. 3 Units.**

Elementary particles and the fundamental forces. Quarks and leptons. The mediators of the electromagnetic, weak and strong interactions. Interaction of particles with matter; particle acceleration, and detection techniques. Symmetries and conservation laws. Bound states. Decay rates. Cross sections. Feynman diagrams. Introduction to Feynman integrals. The Dirac equation. Feynman rules for quantum electrodynamics and for chromodynamics. Undergraduates register for PHYSICS 152. Graduate students register for PHYSICS 252. (Graduates student enrollees will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 130. Pre- or corequisite: PHYSICS 131.

Same as: PHYSICS 252

**PHYSICS 160. Introduction to Stellar and Galactic Astrophysics. 3-4 Units.**

Observed characteristics of stars and the Milky Way galaxy. Physical processes in stars and matter under extreme conditions. Structure and evolution of stars from birth to death. White dwarfs, planetary nebulae, supernovae, neutron stars, pulsars, binary stars, x-ray stars, and black holes. Galactic structure, interstellar medium, molecular clouds, HI and HII regions, star formation, and element abundances. Undergraduates register for PHYSICS 160. Graduate students register for PHYSICS 260. (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor.) Pre or corequisites: PHYSICS 130. Same as PHYSICS 260.

Same as: PHYSICS 260

**PHYSICS 161. Introduction to Extragalactic Astrophysics and Cosmology. 3 Units.**

Big bang theory, cosmic inflation, expansion of space. Composition of the universe. Origin of matter and the elements. The cosmic distance ladder. Observational evidence for dark matter and dark energy. Geometry of space and the standard model of cosmology. Formation of galaxies and large scale structure. Ultimate fate of the universe. Undergraduates register for PHYSICS 161. Graduates register for PHYSICS 261. (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor). Pre or corequisites: PHYSICS 121.

Same as: PHYSICS 261

**PHYSICS 170. Thermodynamics, Kinetic Theory, and Statistical Mechanics I. 3-4 Units.**

Foundations of statistical mechanics. Thermodynamic variables and basic thermodynamics. Ideal gases (including Maxwell-Boltzmann distribution). Bose and Fermi gases; examples including blackbody radiation, Debye theory of phonons, Sommerfeld theory of electrons in metals. Thermodynamic functions. Undergraduates register for PHYSICS 170 (4 units). Graduates register for PHYSICS 270 (3 units). (Graduates student enrollees will be required to complete additional assignments in a format determined by the instructor.) Recommended prerequisite: PHYSICS 130.

Same as: PHYSICS 270

**PHYSICS 171. Thermodynamics, Kinetic Theory, and Statistical Mechanics II. 3-4 Units.**

Mean-field theory of phase transitions; critical exponents. Ferromagnetism, the Ising model. The renormalization group. Dynamics near equilibrium: Brownian motion, diffusion, Boltzmann equations. Other topics at discretion of instructor. Prerequisite: PHYS 170/270. Undergraduates register for PHYSICS 171 (4 units). Graduate students register for PHYSICS 271 (3 units). (Graduates student enrollees will be required to complete additional assignments in a format determined by the instructor.) Recommended pre- or corequisite: PHYS 130. Same as PHYSICS 271.

Same as: PHYSICS 271

**PHYSICS 172. Solid State Physics. 3 Units.**

Introduction to the properties of solids. Crystal structures and bonding in materials. Momentum-space analysis and diffraction probes. Lattice dynamics, phonon theory and measurements, thermal properties. Electronic structure theory, classical and quantum; free, nearly-free, and tight-binding limits. Electron dynamics and basic transport properties; quantum oscillations. Properties and applications of semiconductors. Reduced-dimensional systems. (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor.) Undergraduates should register for PHYSICS 172 and graduate students for APPPHYS 272. Prerequisites: PHYSICS 170 and PHYSICS 171, or equivalents. Same as APPPHYS 272.

Same as: APPPHYS 272

**PHYSICS 190. Independent Research and Study. 1-9 Unit.**

Undergraduate research in experimental or theoretical physics under the supervision of a faculty member. Prerequisites: superior work as an undergraduate Physics major and consent of instructor.

**PHYSICS 205. Senior Thesis Research. 1-12 Unit.**

Long-term experimental or theoretical project and thesis in Physics under supervision of a faculty member. Planning of the thesis project is recommended to begin as early as middle of the junior year. Successful completion of a senior thesis requires a minimum of 3 units for a letter grade completed during the senior year, along with the other formal thesis and physics major requirements. Students doing research for credit prior to senior year should sign up for PHYSICS 190. Prerequisites: superior work as an undergraduate Physics major and approval of the thesis application.

**PHYSICS 210. Advanced Mechanics. 3-4 Units.**

Lagrangian and Hamiltonian mechanics. Principle of least action, Euler-Lagrange equations. Small oscillations and beyond. Symmetries, canonical transformations, Hamilton-Jacobi theory, action-angle variables. Introduction to classical field theory. Selected other topics, including nonlinear dynamical systems, attractors, chaotic motion. Undergraduates register for PHYSICS 110 (4 units). Graduates register for PHYSICS 210 (3 units). (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor.) Prerequisites: MATH 131P, and PHYS 112 or MATH elective 104 or higher. Recommended prerequisite: PHYS 130.

Same as: PHYSICS 110

**PHYSICS 211. Continuum Mechanics. 3 Units.**

Elasticity, fluids, turbulence, waves, gas dynamics, shocks, and MHD plasmas. Examples from everyday phenomena, geophysics, and astrophysics.

**PHYSICS 216. Back of the Envelope Physics. 3 Units.**

Techniques such as scaling and dimensional analysis, useful to make order-of-magnitude estimates of physical effects in different settings. Goals are to promote a synthesis of physics through solving problems, including problems that are not usually thought of as physics. Applications include properties of materials, fluid mechanics, geophysics, astrophysics, and cosmology. Prerequisites: undergraduate mechanics, statistical mechanics, electricity and magnetism, and quantum mechanics.

**PHYSICS 220. Classical Electrodynamics. 3 Units.**

Special relativity: The principles of relativity, Lorentz transformations, four vectors and tensors, relativistic mechanics and the principle of least action. Lagrangian formulation, charges in electromagnetic fields, gauge invariance, the electromagnetic field tensor, covariant equations of electrodynamics and mechanics, four-current and continuity equation. Noether's theorem and conservation laws, Poynting's theorem, stress-energy tensor. Constant electromagnetic fields: conductors and dielectrics, magnetic media, electric and magnetic forces, and energy. Electromagnetic waves: Plane and monochromatic waves, spectral resolution, polarization, electromagnetic properties of matter, dispersion relations, wave guides and cavities. Prerequisites: PHYSICS 121 and PHYSICS 210, or equivalent; MATH 106 or MATH 116, and MATH 132 or equivalent.

**PHYSICS 230. Quantum Mechanics. 3 Units.**

Fundamental concepts. Introduction to Hilbert spaces and Dirac's notation. Postulates applied to simple systems, including those with periodic structure. Symmetry operations and gauge transformation. The path integral formulation of quantum statistical mechanics. Problems related to measurement theory. The quantum theory of angular momenta and central potential problems. Prerequisite: PHYSICS 131 or equivalent.

**PHYSICS 231. Quantum Mechanics. 3 Units.**

Basis for higher level courses on atomic solid state and particle physics. Problems related to measurement theory and introduction to quantum computing. Approximation methods for time-independent and time-dependent perturbations. Semiclassical and quantum theory of radiation, second quantization of radiation and matter fields. Systems of identical particles and many electron atoms and molecules. Prerequisite: PHYSICS 230.

**PHYSICS 234. Advanced Topics in Quantum Mechanics. 3-4 Units.**

Scattering theory, partial wave expansion, Born approximation. Additional topics may include nature of quantum measurement, EPR paradox, Bell's inequality, and topics in quantum information science; path integrals and applications; Berry's phase; structure of multi-electron atoms (Hartree-Fock); relativistic quantum mechanics (Dirac equation). Undergraduates register for PHYSICS 134 (4 units). Graduate students register for PHYSICS 234 (3 units); graduate students required to complete additional assignments in a format determined by the instructor. Prerequisites: PHYSICS 130, PHYSICS 131.

Same as: PHYSICS 134

**PHYSICS 240. Introduction to the Physics of Energy. 3 Units.**

Energy as a consumable. Forms and interconvertability. World joule nnbudget. Equivalents in rivers, oil pipelines and nuclear weapons. nnQuantum mechanics of fire, batteries and fuel cells. Hydrocarbon and hydrogen synthesis. Fundamental limits to mechanical, electrical and magnetic strengths of materials. Flywheels, capacitors and high pressure tanks. Principles of AC and DC power transmission. Impossibility of pure electricity storage. Surge and peaking. Solar constant. Photovoltaic and thermal solar conversion. Physical limits on agriculture.

**PHYSICS 241. Introduction to Nuclear Energy. 3 Units.**

Radioactivity. Elementary nuclear processes. Energetics of fission and fusion. Cross-sections and resonances. Fissionable and fertile isotopes. Neutron budgets. Light water, heavy water and graphite reactors. World nuclear energy production. World reserves of uranium and thorium. Plutonium, reprocessing and proliferation. Half lives of fission decay products and actinides made by neutron capture. Nuclear waste. Three Mile Island and Chernobyl. Molten sodium breeders. Generation-IV reactors. Inertial confinement and magnetic fusion. Laser compression. Fast neutron production and fission-fusion hybrids. PREREQUISITES: Strong undergraduate background in elementary chemistry and physics. PHYS 240 and PHYS 252 recommended but not required. Interested undergraduates encouraged to enroll, with permission of instructor.

**PHYSICS 252. Introduction to Particle Physics I. 3 Units.**

Elementary particles and the fundamental forces. Quarks and leptons. The mediators of the electromagnetic, weak and strong interactions. Interaction of particles with matter; particle acceleration, and detection techniques. Symmetries and conservation laws. Bound states. Decay rates. Cross sections. Feynman diagrams. Introduction to Feynman integrals. The Dirac equation. Feynman rules for quantum electrodynamics and for chromodynamics. Undergraduates register for PHYSICS 152. Graduate students register for PHYSICS 252. (Graduates student enrollees will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 130. Pre- or corequisite: PHYSICS 131.

Same as: PHYSICS 152

**PHYSICS 260. Introduction to Stellar and Galactic Astrophysics. 3-4 Units.**

Observed characteristics of stars and the Milky Way galaxy. Physical processes in stars and matter under extreme conditions. Structure and evolution of stars from birth to death. White dwarfs, planetary nebulae, supernovae, neutron stars, pulsars, binary stars, x-ray stars, and black holes. Galactic structure, interstellar medium, molecular clouds, HI and HII regions, star formation, and element abundances. Undergraduates register for PHYSICS 160. Graduate students register for PHYSICS 260. (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor.) Pre or corequisites: PHYSICS 130. Same as PHYSICS 260.

Same as: PHYSICS 160

**PHYSICS 261. Introduction to Extragalactic Astrophysics and Cosmology. 3 Units.**

Big bang theory, cosmic inflation, expansion of space. Composition of the universe. Origin of matter and the elements. The cosmic distance ladder. Observational evidence for dark matter and dark energy. Geometry of space and the standard model of cosmology. Formation of galaxies and large scale structure. Ultimate fate of the universe. Undergraduates register for PHYSICS 161. Graduates register for PHYSICS 261. (Graduate student enrollees will be required to complete additional assignments in a format determined by the instructor). Pre or corequisites: PHYSICS 121.

Same as: PHYSICS 161

**PHYSICS 262. Introduction to Gravitation. 3 Units.**

Introduction to general relativity. Curvature, energy-momentum tensor, Einstein field equations. Weak field limit of general relativity. Black holes, relativistic stars, gravitational waves, cosmology. Prerequisite: PHYSICS 121 or equivalent including special relativity.

**PHYSICS 270. Thermodynamics, Kinetic Theory, and Statistical Mechanics I. 3-4 Units.**

Foundations of statistical mechanics. Thermodynamic variables and basic thermodynamics. Ideal gases (including Maxwell-Boltzmann distribution). Bose and Fermi gases; examples including blackbody radiation, Debye theory of phonons, Sommerfeld theory of electrons in metals. Thermodynamic functions. Undergraduates register for PHYSICS 170 (4 units). Graduates register for PHYSICS 270 (3 units). (Graduates student enrollees will be required to complete additional assignments in a format determined by the instructor.) Recommended prerequisite: PHYSICS 130.

Same as: PHYSICS 170

**PHYSICS 271. Thermodynamics, Kinetic Theory, and Statistical Mechanics II. 3-4 Units.**

Mean-field theory of phase transitions; critical exponents. Ferromagnetism, the Ising model. The renormalization group. Dynamics near equilibrium: Brownian motion, diffusion, Boltzmann equations. Other topics at discretion of instructor. Prerequisite: PHYS 170/270. Undergraduates register for PHYSICS 171 (4 units). Graduate students register for PHYSICS 271 (3 units). (Graduates student enrollees will be required to complete additional assignments in a format determined by the instructor.) Recommended pre- or corequisite: PHYS 130. Same as PHYSICS 271.

Same as: PHYSICS 171

**PHYSICS 290. Research Activities at Stanford. 1 Unit.**

Required of first-year Physics graduate students; suggested for junior or senior Physics majors for 1 unit. Review of research activities in the department and elsewhere at Stanford at a level suitable for entering graduate students.

**PHYSICS 291. Practical Training. 1-3 Unit.**

Opportunity for practical training in industrial labs. Arranged by student with the research adviser's approval. A brief summary of activities is required, approved by the research adviser.

**PHYSICS 293. Literature of Physics. 1-15 Unit.**

Study of the literature of any special topic. Preparation, presentation of reports. If taken under the supervision of a faculty member outside the department, approval of the Physics chair required. Prerequisites: 25 units of college physics, consent of instructor.

**PHYSICS 294. Teaching of Physics Seminar. 1 Unit.**

Required of all Teaching Assistants prior to the first teaching nnassignment. Weekly seminar/discussions on interactive techniques for nnteaching physics. Practicum which includes class observations, grading nnand student teaching in current courses.

**PHYSICS 295. Learning & Teaching of Science. 3 Units.**

This course will provide students with a basic knowledge of the relevant research in cognitive psychology and science education and the ability to apply that knowledge to enhance their ability to learn and teach science, particularly at the undergraduate level. Course will involve readings, discussion, and application of the ideas through creation of learning activities. It is suitable for advanced undergraduates and graduate students with some science background.

Same as: EDUC 280X

**PHYSICS 301. Astrophysics Laboratory. 3 Units.**

Open to all graduate students with a calculus-based physics background and some laboratory experience. Students make and analyze observations using telescopes at the Stanford StudentnnObservatory. Topics include navigating the night sky, the physics of stars and galaxies, telescope instrumentation and operation,nnquantitative error analysis, and effective scientific communication. The course also introduces a number of hot topics in astrophysics and cosmology. Limited enrollment.

**PHYSICS 312. Basic Plasma Physics. 3 Units.**

For the nonspecialist who needs a working knowledge of plasma physics for space science, astrophysics, fusion, or laser applications. Topics: orbit theory, the Boltzmann equation, fluid equations, magneto hydrodynamics (MHD) waves and instabilities, electromagnetic (EM) waves, the Vlasov theory of electrostatic (ES) waves and instabilities including Landau damping and quasilinear theory, the Fokker-Planck equation, and relaxation processes. Advanced topics in resistive instabilities and particle acceleration. Prerequisite: PHYSICS 220, or consent of instructor.

**PHYSICS 321. Laser Spectroscopy. 3 Units.**

Theoretical concepts and experimental techniques. Absorption, dispersion, Kramers-Kronig relations, line-shapes. Classical and laser linear spectroscopy. Semiclassical theory of laser atom interaction: time-dependent perturbation theory, density matrix, optical Bloch equations, coherent pulse propagation, multiphoton transitions. High-resolution nonlinear laser spectroscopy: saturation spectroscopy, polarization spectroscopy, two-photon and multiphoton spectroscopy, optical Ramsey spectroscopy. Phase conjugation. Four-wave mixing, harmonic generation. Coherent Raman spectroscopy, quantum beats, ultra-sensitive detection. Prerequisite: 230. Recommended: 231.

**PHYSICS 330. Quantum Field Theory I. 3 Units.**

Lorentz Invariance. S-Matrix. Quantization of scalar and Dirac fields. Feynman diagrams. Quantum electrodynamics. Elementary electrodynamic processes: Compton scattering; e+e- annihilation. Loop diagrams. Prerequisites: PHYSICS 130, PHYSICS 131, or equivalents. Foundations of Group Theory.

**PHYSICS 331. Quantum Field Theory II. 3 Units.**

Functional integral methods. Local gauge invariance and Yang-Mills fields. Asymptotic freedom. Spontaneous symmetry breaking and the Higgs mechanism. Unified models of weak and electromagnetic interactions. Prerequisite: PHYSICS 330.

**PHYSICS 332. Quantum Field Theory III. 3 Units.**

Theory of renormalization. The renormalization group and applications to the theory of phase transitions. Renormalization of Yang-Mills theories. Applications of the renormalization group of quantum chromodynamics. Perturbation theory anomalies. Applications to particle phenomenology. Prerequisite: PHYSICS 330.

**PHYSICS 351. Standard Model of Particle Physics. 3 Units.**

Symmetries, group theory, gauge invariance, Lagrangian of the Standard Model, flavor group, flavor-changing neutral currents, CKM quark mixing matrix, GIM mechanism, rare processes, neutrino masses, seesaw mechanism, QCD confinement and chiral symmetry breaking, instantons, strong CP problem, QCD axion.nnPrerequisite: PHYSICS 330; PHYSICS 331 and PHYSICS 332 recommended.

**PHYSICS 361. Advanced Topics in Radiative Processes and Stellar Astrophysics. 3 Units.**

Astronomical data on stars, star clusters, interstellar medium, and the Milky Way galaxy. Theory of stellar structure; hydrostatic equilibrium, radiation balance, and energy production. Stellar formation, Jean's mass, and protostars. Evolution of stars to the main sequence and beyond to red giants, white dwarfs, neutron stars, and black holes. Supernovae and compact sources. Structure of the Milky Way: disk and spiral arms; dark matter and the halo mass; central bulge or bar; and black hole. Prerequisite: PHYSICS 221 or equivalent. Recommended: PHYSICS 260, PHYSICS 360.

**PHYSICS 362. Advanced Extragalactic Astrophysics and Cosmology. 3 Units.**

Observational data on the content and activities of galaxies, the content of the Universe, cosmic microwave background radiation, gravitational lensing, and dark matter. Models of the origin, structure, and evolution of the Universe based on the theory of general relativity. Test of the models and the nature of dark matter and dark energy. Physics of the early Universe, inflation, baryosynthesis, nucleosynthesis, and galaxy formation. Prerequisites: PHYSICS 210, PHYSICS 211, and PHYSICS 260 or PHYSICS 360.

**PHYSICS 364. Advanced Gravitation. 3 Units.**

Classical and quantum gravity in Anti-de Sitter spacetime (AdS). History and uses of AdS. Basic classical physics of AdS: metric, conformal structure, common coordinate systems. Black holes in AdS: thermodynamics, Hawking-Page transition. Classical fields in AdS: action of conformal group, singletons. Stability of AdS and positive energy theorems. Towards the holographic correspondence: geodesics and the UV-IR relation. AdS from supergravity. Recommended: PHYSICS 330, some familiarity with general relativity.

**PHYSICS 372. Condensed Matter Theory I. 3 Units.**

Fermi liquid theory, many-body perturbation theory, response function, functional integrals, interaction of electrons with impurities. Prerequisite: APPPHYS 273 or equivalent.

**PHYSICS 373. Condensed Matter Theory II. 3 Units.**

Superfluidity and superconductivity. Quantum magnetism. Prerequisite: PHYSICS 372.

**PHYSICS 450. Conformal Field Theory. 3 Units.**

This course will be a systematic introduction to two dimensional conformal field theory. Topics to be covered include: conformal symmetry; stress tensor; operator product expansion; Virasoro algebra; unitarity; modular invariance; c-theorem; conformal bootstrap; Kac-Moody algebra; supersymmetry.

**PHYSICS 451. TOPICS IN STRING THEORY. 3 Units.**

The course will cover several topics in modern string theory including aspects of 2d conformal field theory, mirror symmetry, geometric transitions and large N dualities, and moonshine. Other topics may be discussed as time and interests dictate. Prerequisites: No formal requirements, but a familiarity with quantum field theory at the level of the 330 sequence, and some moderate mathematical maturity, will be useful.

**PHYSICS 490. Research. 1-15 Unit.**

Open only to Physics graduate students, with consent of instructor. Work is in experimental or theoretical problems in research, as distinguished from independent study of a non-research character in 190 and 293.

**PHYSICS 801. TGR Project. 0 Units.**

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**PHYSICS 802. TGR Dissertation. 0 Units.**

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