Physics

Ph 1 abc. Classical Mechanics and Electromagnetism. 9 units (4-0-5); first, second, third terms. The first year of a two-year course in introductory classical and modern physics. Topics: Newtonian mechanics in Ph 1 a; electricity and magnetism, and special relativity, in Ph 1 b, c. Emphasis on physical insight and problem solving. Ph 1 b, c is divided into two tracks: the Practical Track emphasizing practical electricity with take-home lab kits, and the Analytic Track, which has no lab component but teaches and uses methods of multivariable calculus. Students will be given information helping them to choose a track at the end of fall term. Lecturers: Goodstein, Martin, Politzer.

Ph 2 ab. Statistical Physics, Waves, and Quantum Mechanics. 9 units (4-0-5); first, second terms. Prerequisites: Ph 1 abc, Ma 1 abc, or equivalents. The second year of a five-term introductory course in classical and modern physics. Topics to be covered include statistical physics and classical waves first term, introductory quantum mechanics second term. s Lecturers: Lange, Harrison.

Ph 3. Physics Laboratory. 6 units; first, second, third terms. Prerequisite: Ph 1 a or instructor’s permission. An introduction to experimental technique, commonly used in the physical sciences. A variety of topics is presented, including the Maxwell top, electrical and mechanical resonant systems, and radioactivity. Special emphasis is given to data analysis techniques based on modern statistical methods. The course consists of one three-hour laboratory session a week, conferences with the instructor, prelaboratory preparation, and analysis of experimental results. Graded pass/fail; seniors receive letter grades. Only one term may be taken for credit. Instructors: Sannibale, Rice, Kimble.

Ph 5. Physics Laboratory. 9 units; first term. Prerequisites: Ph 1 abc, Ph 3, or equivalents. A laboratory course dealing with “operational’’ electronics with emphasis on analog electronics. The following topics are studied: RC circuits, electrical oscillations, operational amplifiers, diodes, and transistors. Combining diodes, transistors, and operational amplifiers; computer data acquisitions. The course culminates in a two-week project of the student’s choosing. Instructors: Rice, Sannibale, Kimble.

Ph 6. Physics Laboratory. 9 units; second term. Prerequisites: Ph 1 abc, Ph 2 b or Ph 12 b (or taken concurrently), and Ph 3 or equivalent. Experiments in electromagnetic phenomena such as electromagnetic induction, properties of magnetic materials, and high-frequency circuits. Mobility of ions in gases; precise measurement of the value of e/m of the electron. Instructors: Rice, Sannibale, Kimble.

Ph 7. Physics Laboratory. 9 units; third term. Prerequisite: Ph 6 or equivalent. Experiments in atomic and nuclear physics, including studies of the Balmer series of hydrogen and deuterium, the decay of radioactive nuclei, absorption of X rays and gamma rays, ratios of abundances of isotopes, and the Stern-Gerlach experiment. Instructors: Rice, Sannibale, Kimble.

Ph 10. Frontiers in Physics. 3 units (2-0-1); first term. Open for credit to freshmen and sophomores. Weekly seminar by a member of the physics department or a visitor, to discuss his or her research at an introductory level; the other class meetings will be used to explore background material related to seminar topics and to answer questions that arise. The course will also help students find faculty sponsors for individual research projects. Graded pass/fail. Instructor: Soifer.

Ph 11 abc. Research Tutorial. 6 units (2-0-4); second and third terms of freshman year and first term of sophomore year. A small number of students will be offered the opportunity to enroll in this tutorial, the purpose of which is to demonstrate how research ideas arise, and are evaluated and tested, and how those ideas that survive are developed. This is accomplished by doing individual, original projects. There will be weekly group meetings and individual tutorial meetings with the instructor. Support for summer research at Caltech between the freshman and sophomore years will be automatic for those students making satisfactory progress. Graded pass/fail. Instructor: Tombrello.

Ph 12 abc. Waves, Quantum Physics, and Statistical Mechanics. 9 units (4-0-5); first, second, third terms. Prerequisites: Ph 1 abc, Ma 1 abc, or equivalents. A one-year course primarily for students intending further work in the physics option. Topics include classical waves; wave mechanics, interpretation of the quantum wave-function, one-dimensional bound states, scattering, and tunneling; thermodynamics, introductory kinetic theory, and quantum statistics. May be taken to fulfill the Institute Ph 2 requirement. Students may transfer from Ph 12 b to Ph 2 b any time during the term, before the last day for dropping courses. The final grade will be based on the combined record in the two courses. Instructors: Kimble, Filippone, Ooguri.

Ph 20, 21, 22. Freshman/Sophomore Computational Physics Laboratory. A series of courses on the application of computational techniques to simulate or solve simple physical systems, with the intent of aiding both physics understanding and programming ability. Instructors: Mach, Prince, Libbrecht.

20. 6 units (0-6-0); first, second, third terms. Prerequisite: CS 1 or equivalent experience in programming. Introduction to scientific computing with applications to physics. Use of simple numerical algorithms and symbolic manipulation packages for solution of physical problems. Numerical integration and numerical solution of differential equations of motion. Simulation of orbital mechanics.

21. 6 units (0-6-0); second, third terms. Prerequisite: Ph 20 or equivalent experience with programming and simple numerical techniques. Introduction to numerical algorithms for scientific computing. Root-finding, Runge-Kutta methods, Monte Carlo techniques, numerical solution of partial differential equations, minimization techniques such as neural networks. Applications to problems in classical mechanics and discrete-element electromagnetism.

22. 6 units (0-6-0); third term. Prerequisite: Ph 20 or equivalent experience with programming and simple numerical techniques. Introduction to scientific computing on parallel computers. Introduction to parallel computing and multiprocessing. Message passing on networked workstations. Algorithm decomposition and parallelization. Numerical solution of N-body systems on multiprocessor computers. Additional information concerning this course can be found at http://www.pma. caltech.edu/~physlab.

Ph 70. Oral and Written Communication. 6 units (2-0-4); first, third terms. Provides practice and guidance in oral and written communication of material related to contemporary physics research. Students will choose a topic of interest, make presentations of this material in a variety of formats, and, through a guided process, draft and revise a technical or review article on the topic. The course is intended for senior physics majors. Fulfills the Institute scientific writing requirement. Instructor: Hitlin.

Ph 77 abc. Advanced Physics Laboratory. 9 units (0-5-4); first, second, third terms. A three-term laboratory course to familiarize students with equipment and procedures used in the research laboratory. Experiments illustrate fundamental physical phenomena in atomic, optical, condensed-matter, nuclear, and particle physics, including NMR, laser-based atomic spectroscopy, gamma and X-ray spectroscopy, muon decay, weak localization, superconductivity, positron annihilation, and others. Instructors: Black, Libbrecht.

Ph 78 abc. Senior Thesis, Experimental. 9 units; first, second, third terms. Prerequisite: To register for this course the student must obtain approval of the chair of the Physics Undergraduate Committee (Steven Frautschi). Open only to senior physics majors. This research must be supervised by a faculty member, the student’s thesis adviser. Laboratory work is required for this course. Two 15-minute presentations to the Physics Undergraduate Committee are required, one at the end of the first term and the second at the midterm week of the third term. The written thesis must be completed and distributed to the committee one week before the second presentation. Not offered on a pass/fail basis. See Note, below.

Ph 79 abc. Senior Thesis, Theoretical. 9 units; first, second, third terms. Prerequisite: to register for this course the student must obtain approval of the chair of the Physics Undergraduate Committee (Steven Frautschi). Open only to senior physics majors. This research must be supervised by a faculty member, your thesis adviser. Two 15-minute presentations to the Physics Undergraduate Committee are required, one at the end of the first term and the second at the midterm week of the third term. The written thesis must be completed and distributed to the committee one week before the second presentation. Not offered on a pass/fail basis. See Note, below.

Note: Students wishing assistance in finding an adviser and/or a topic for a senior thesis are invited to consult with the chair of the Physics Undergraduate Committee, or any other member of this committee. A grade will not be assigned in Ph 78 or Ph 79 until the end of the third term. P grades will be given the first two terms, and then changed at the end of the course to the appropriate letter grade.

Ph 101. Order-of-Magnitude Physics. 9 units (3-0-6); third term. Emphasis will be on using basic physics to understand complicated systems. Examples will be selected from properties of materials, geophysics, weather, planetary science, astrophysics, cosmology, biomechanics, etc. Not offered 2005–06.

Ph 103 ab. Topics in Contemporary Physics. 9 units (3-0-6); second, third terms. Prerequisite: instructor’s permission. A series of introductory one-term, independent courses. Students may register for any particular term or terms.

a. Atomic and Molecular Spectroscopy. Second term. This course will review the basic spectroscopy of atoms and molecules, with applications to astrophysics, the terrestrial atmosphere, and the laboratory. Species to be discussed include hydrogen and simple multielectron atoms such as carbon, diatomic and polyatomic molecules, and some solids. Mechanisms and effects determining linewidths and lineshapes will be discussed for laboratory, atmospheric, and astrophysical conditions. Instructor: Phillips.

Ph/Bi 103 b. Neuroscience for Physicists and Engineers. Third term. A reading and discussion course on topics ranging from the function of single neurons to methods for studying multineural activity in synapses; electrical recording; vision; positron and NMR topography; and neural modeling. Preference is given to physics seniors. Instructor: Pine.

Ph 105. Analog Electronics for Physicists. 9 units; first term. Prerequisites: Ph 1 abc, Ph 3, or equivalents (the take-home lab of Ph 1 bc may be substituted for Ph 3). A laboratory course dealing with “operational’’ electronics with emphasis on analog electronics. The following topics are studied: RC circuits, electrical oscillations, operational amplifiers, diodes, and transistors. Combining diodes, transistors, and operational amplifiers; computer data acquisition. The course culminates in a two-week project of the student’s choosing. Instructors: Rice, Sannibale, Kimble.

Ph 106 abc. Topics in Classical Physics. 9 units (3-0-6); first, second, third terms. Prerequisites: Ph 2 ab or Ph 12 abc, Ma 2. An intermediate course in the application of basic principles of classical physics to a wide variety of subjects. Roughly half of the year will be devoted to mechanics, and half to electromagnetism. Topics include Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, boundary-value problems, multipole expansions, and various applications of electromagnetic theory. Instructors: Golwala, Eisenstein.

Ph/EE 118 ab. Low-Noise Electronic Measurement. 9 units (3-0-6); first, second terms. Prerequisite: Ph 105 or equivalent. An introduction to ultralow-noise electrical measurements and sensor technology as applied to experimental research. Topics include physical noise processes, signal transduction, synchronous and lock-in detection, digital signal transforms, and other aspects of precision measurements. Specific sensor technologies will include SQUID sensors, single electron transistors, transition-edge sensors, tunnel junction detectors, micro- and nanomechanical detectors, and biosensors. Instructor: Roukes.

Ph 125 abc. Quantum Mechanics. 9 units (3-0-6); first, second, third terms. Prerequisites: Ma 2 ab, Ph 12 abc or Ph 2 ab, or equivalents. A one-year course in quantum mechanics and its applications, for students who have completed Ph 12 or Ph 2. Wave mechanics in 3-D, scattering theory, Hilbert spaces, matrix mechanics, angular momentum, symmetries, spin-¹/₂ systems, approximation methods, identical particles, and selected topics in atomic, solid-state, nuclear, and particle physics. Instructors: Wise, Kamionkowski.

Ph 127 abc. Statistical Physics. 9 units (3-0-6); first, second, third terms. Prerequisites: Ph 12 c or equivalent, and a basic understanding of quantum and classical mechanics. A course in the fundamental ideas and applications of classical and quantum statistical mechanics. Topics to be covered include the statistical basis of thermodynamics; ideal classical and quantum gases (Bose and Fermi); lattice vibrations and phonons; weak interaction expansions; phase transitions; and fluctuations and dynamics. Instructor: Refael.

Ph 129 abc. Mathematical Methods of Physics. 9 units (3-0-6); first, second, third terms. Prerequisites: Ph 106 abc and ACM 95/100 abc or Ma 108 abc, or equivalents. Mathematical methods and their application in physics. First term includes analytic and numerical methods for solving differential equations, integral equations, and transforms, and other applications of real analysis. Second term focuses on probability and statistics in physics. Third term covers group theoretic methods in physics. The three terms can be taken independently. Instructors: Porter, Gottschalk.

Ph 134. String Theory. 9 units (3-0-6); third term. Prerequisites: Ph 125 ab, Ph 106 ab. A basic course in string theory designed to be accessible to a broad audience. The main topics include the motion of relativistic point particles and strings, actions, world-sheet symmetries and currents, light-cone quantization, and the spectra of relativistic open and closed strings. The course will conclude with an exploration of D-branes, T-duality, or string thermodynamics, depending on student interest. Instructor: Schulz.

Ph 135 ab. Applications of Quantum Mechanics. 9 units (3-0-6); first, second terms. Prerequisite: Ph 125 abc or equivalent. Applications of quantum mechanics to topics in contemporary physics. Elementary particle physics and neutrino physics will be offered first, second terms, respectively. Terms may be taken separately. Instructors: Hughes, Frey, McKeown, Vogel.

Ph 136 abc. Applications of Classical Physics. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 106 abc or equivalent. Applications of classical physics to topics of interest in contemporary “macroscopic’’ physics. Continuum physics and classical field theory; elasticity and hydrodynamics; plasma physics; magnetohydrodynamics; thermodynamics and statistical mechanics; gravitation theory, including general relativity and cosmology; modern optics. Content will vary from year to year, depending on the instructor. An attempt will be made to organize the material so that the terms may be taken independently. Not offered 2005–06.

Ph 171. Reading and Independent Study. Units in accordance with work accomplished. Occasionally, advanced work involving reading, special problems, or independent study is carried out under the supervision of an instructor. Approval of the instructor and of the student’s departmental adviser must be obtained before registering. Graded pass/fail.

Ph 172. Research in Experimental Physics. Units in accordance with work accomplished. Approval of the student’s research supervisor and department adviser must be obtained before registering. Graded pass/fail.

Ph 173. Research in Theoretical Physics. Units in accordance with work accomplished. Approval of the student’s research supervisor and departmental adviser must be obtained before registering. Graded pass/fail.

CNS/Bi/BE/Ph 178. Evolution and Biocomplexity. 9 units (3-0-6). For course description, see Computation and Neural Systems.

CNS/Bi/Ph/CS 187. Neural Computation. 9 units (3-0-6). For course description, see Computation and Neural Systems.

Ph 199. Major Open Questions in Physics. 9 units (3-0-6); third term. Prerequisites: Ph 125 abc, Ph 106 abc. This course will examine several open questions in modern physics. Topics will include the following: What is the expansion history of the universe? What are dark matter and dark energy? Where does mass come from? Why is the universe made of matter rather than antimatter? Is nature supersymmetric? Is there a quantum theory of gravity that can describe the universe? Why is there a spectrum of fermion masses? How heavy are neutrinos, and what was their role in the formation of the universe? Where do ultrahigh-energy cosmic rays come from? What can we learn from the detection of gravitational waves? Instructor: Weinstein.

Ph 205 abc. Relativistic Quantum Mechanics. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 125. Topics: the Dirac equation, second quantization, quantum electrodynamics, scattering theory, Feynman diagrams, non-Abelian gauge theories, Higgs symmetry-breaking, the Weinberg-Salam model, and renormalization. Instructor: Kapustin.

Ph 210. Theoretical Quantum Chromodynamics. 9 units (3-0-6); third term. Prerequisite: Ph 205 ab. Applications of quantum field theory to quantum chromodynamics, including operator product expansion, twist expansion and applications to deep inelastic scattering and Drell-Yan; effective field theories, including chiral perturbation theory, heavy quark effective theory, and soft collinear effective theory; large Nc; introduction to lattice chromodynamics. Applications to strong interaction phenomenology and weak decays. Instructor: Ramsey-Musolf.

Ph/CS 219 abc. Quantum Computation. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 129 abc or equivalent. The theory of quantum information and quantum computation. Overview of classical information theory, compression of quantum information, transmission of quantum information through noisy channels, quantum error-correcting codes, quantum cryptography and teleportation. Overview of classical complexity theory, quantum complexity, efficient quantum algorithms, fault-tolerant quantum computation, physical implementations of quantum computation. Instructor: Preskill.

Ph/Ay 221 abc. Cosmology and Particle Astrophysics. 9 units (3-0-6); first, second, third terms. Prerequisites: Ph 106 and Ph 125, or equivalents. An introduction to current research in cosmology and particle astrophysics. First term will focus on basics of the Friedman-Robertson-Walker metric, aspects of physical cosmology, and gravitational lensing. Second term will include the early universe and particle astrophysics (e.g., inflation, phase transitions, neutrino astrophysics, particle dark matter, and baryogenesis). Third term will focus on cosmological perturbation theory, structure formation, and the cosmic microwave background. Not offered 2005–06.

Ph/APh 223 abc. Advanced Condensed-Matter Physics. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 125 or equivalent, or instructor’s permission. Advanced topics in condensed-matter physics, emphasizing the application of formal quantum field theory and group theory methods to many-body systems. Selected topics may include path integral and canonical formalisms, Green’s function techniques and Feynman diagrams, Fermi liquid theory, symmetry breaking, Landau-Ginzburg theory of phase transitions, critical phenomena and renormalization group theory, group theory and its applications, field theory for interacting bosons and superfluidity, superconductivity, topological field theory, and strongly correlated electronic systems. Instructor: Yeh.

Ph 225 abc. Advanced Quantum Mechanics. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 125 or equivalent. Advanced theory of quantum mechanics, focusing on formal methods and applications in different fields of physics. Topics will include selections from atomic and molecular physics, quantum optics, quantum information, condensed-matter physics, and nuclear and particle physics, with specific content depending on the instructors. Emphasis will be placed on subject matter directly relevant to research in condensed-matter physics, quantum optics, and atomic physics. Instructors: Yeh, Mabuchi.

Ph 229 abc. Advanced Mathematical Methods of Physics. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 129 abc or equivalent. Advanced topics in geometry and topology that are widely used in modern theoretical physics. Emphasis will be on understanding and applications more than on rigor and proofs. First term will cover basic concepts in topology and manifold theory. Second term will include Riemannian geometry, fiber bundles, characteristic classes, and index theorems. Third term will include anomalies in gauge-field theories and the theory of Riemann surfaces, with emphasis on applications to string theory. Instructor: Kapustin.

Ph 230 abc. Elementary Particle Theory. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 205 abc or equivalent. Advanced methods in quantum field theory. First term: introduction to supersymmetry, including the minimal supersymmetric extension of the standard model, supersymmetric grand unified theories, extended supersymmetry, supergravity, and supersymmetric theories in higher dimensions. Second and third terms: nonperturbative phenomena in non-Abelian gauge field theories, including quark confinement, chiral symmetry breaking, anomalies, instantons, the 1/N expansion, lattice gauge theories, and topological solitons. Not offered 2005–06.

Ph 231 abc. Elementary Particle Physics. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 125 or equivalent. An introduction to elementary particle physics, stressing experimental phenomena and their theoretical interpretations. The standard model and its confrontation with experiment will be covered. Current notions for particle physics beyond the standard model will be explored, along with possible experimental signatures. Experimental techniques will also be discussed, including an introduction to accelerator physics. Instructor: Porter.

Ph 235 abc. Introduction to Supersymmetry and String Theory. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 205. First term: introduction to supersymmetry. After explaining the basic concepts of supersymmetry, the emphasis will be on formulating and analyzing the minimal supersymmetric extension of the standard model and supersymmetric grand unified theories. There will also be brief introductions to supersymmetric theories in higher dimensions, theories with extended supersymmetry, and supergravity. Second term: introduction to superstring theory. Topics to be discussed include relativistic strings and their quantization, perturbative string theory, low energy effective supergravity theories, p-brane solutions and p-brane world volume theories, compactification of extra dimensions, M theory and F theory, dualities relating various superstring and M theory configurations, problems and prospects. Instructor: Schwarz.

Ph 236 abc. Relativity. 9 units (3-0-6); first, second, third terms. Prerequisite: a mastery of special relativity at the level of Goldstein’s Classical Mechanics, or of Jackson’s Classical Electrodynamics. A systematic exposition of Einstein’s general theory of relativity, with emphasis on applications to astrophysical and cosmological problems. In 2005–06, offered first and second terms. Instructors: Thorne, Lindblom.

Ph 237 ab. Gravitational Waves. 9 units (3-0-6); second, third terms. Prerequisite: Ph 106. The theory of gravitational waves: their generation, propagation, and interaction with detectors. Astrophysical sources of gravitational waves: the Big Bang, early-universe phenomena, binary stars, black holes, supernovae, and neutron stars. Gravitational-wave detectors: their design, noise, data analysis, and underlying physics, with emphasis on LIGO and LISA but also detectors based on resonant masses, doppler tracking of spacecraft, pulsar timing, and the polarization of the cosmic microwave background. Not offered 2005–06.

Ph 242 ab. Physics Seminar. 3 units (2-0-1); first, second terms. Topics in physics emphasizing current research at Caltech. One two-hour meeting per week. Speakers will be chosen from both faculty and students. Registration restricted to first-year graduate students in physics; exceptions only with permission of instructor. Graded pass/fail. Instructor: Stone.

Ph 250. Introduction to String Theory. 9 units (3-0-6); first, second, third terms. Prerequisite: Ph 205 or equivalent. The first two terms will focus largely on the bosonic string. Topics covered will include conformal invariance and construction of string scattering amplitudes, the origins of gauge interactions and gravity from string theory, T-duality, and D-branes. The third term will cover perturbative aspects of superstrings, supergravity, various BPS branes, and string dualities. Not offered 2005–06.

Ph 300. Thesis Research. Units in accordance with work accomplished. Ph 300 is elected in place of Ph 172 or Ph 173 when the student has progressed to the point where research leads directly toward the thesis for the degree of Doctor of Philosophy. Approval of the student’s research supervisor and department adviser or registration representative must be obtained before registering. Graded pass/fail.