# Physics (Ph) Courses (2021-22)

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, and the Analytic Track, which teaches and uses methods of multivariable calculus. Students enrolled in the Practical Track are encouraged to take Ph 8 bc concurrently. Students will be given information helping them to choose a track at the end of fall term.
Instructors: Cheung, Hsieh, Refael, Cissé.

Ph 2 abc.
Waves, Quantum Mechanics, and Statistical Physics.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 1 abc, Ma 1 abc.
An introduction to several areas of physics including applications in modern science and engineering. Topics include discrete and continuous oscillatory systems, wave mechanics, applications in telecommunications and other areas (first term); foundational quantum concepts, the quantum harmonic oscillator, the Hydrogen atom, applications in optical and semiconductor systems (second term); ensembles and statistical systems, thermodynamic laws, applications in energy technology and other areas (third term). Although best taken in sequence, the three terms can be taken independently.
Instructors: Porter, Cheung, Adhikari.

Ph 3.
Introductory Physics Laboratory.
6 units (0-3-3):
first, second, third terms.
Prerequisites: Ph 1 a or instructor's permission.
Introduction to experimental physics and data analysis, with techniques relevant to all fields that deal in quantitative data. Specific physics topics include ion trapping, harmonic motion, mechanical resonance, and precision interferometry. Broader skills covered include introductions to essential electronic equipment used in modern research labs, basic digital data acquisition and analysis, statistical interpretation of quantitative data, professional record keeping and documentation of experimental research, and an introduction to the Mathematica programming language. Only one term may be taken for credit.
Instructors: Black, Libbrecht.

FS/Ph 4.
Freshman Seminar: Astrophysics and Cosmology with Open Data.
6 units (3-0-3):
first term.
Astrophysics and cosmology are in the midst of a golden age of science-rich observations from incredibly powerful telescopes of various kinds. The data from these instruments are often freely available on the web. Anyone can do things like study x-rays from pulsars in our galaxy or gamma rays from distant galaxies using data from Swift and Fermi; discover planets eclipsing nearby stars using data from Kepler; measure the expansion of the universe using supernovae data; study the cosmic microwave background with data from Planck; find gravitational waves from binary black hole mergers using data from LIGO; and study the clustering of galaxies using Hubble data. We will explore some of these data sets and the science than can be extracted from them. A primary goal of this class is to develop skills in scientific computing and visualization-bring your laptop! Not offered 2021-22.

Ph 5.
Analog Electronics for Physicists.
9 units (0-5-4):
first term.
Prerequisites: Ph1abc, Ma1abc, Ma2 taken concurrently.
A fast-paced laboratory course covering the design, construction, and testing of practical analog and interface circuits, with emphasis on applications of operational amplifiers. No prior experience with electronics is required. Basic linear and nonlinear elements and circuits are studied, including amplifiers, filters, oscillators and other signal conditioning circuits. Each week includes a 45 minute lecture/recitation and a 2½ hour laboratory. The course culminates in a two-week project of the student's choosing.
Instructors: Rice, Libbrecht.

Ph 6.
Physics Laboratory.
9 units:
second term.
Prerequisites: Ph 2 a or Ph 12 a, Ma 2, Ph 3, Ph 2 b or Ph 12 b (may be taken concurrently), Ma 3 (may be taken concurrently).
A laboratory introduction to experimental physics and data analysis. Experiments use research-grade equipment and techniques to investigate topics in classical electrodynamics, resonance phenomena, waves, and other physical phenomena. Students develop critical, quantitative evaluations of the relevant physical theories; they work individually and choose which experiments to conduct. Each week includes a 30-minute individual recitation and a 3 hour laboratory.
Instructors: Rice, Politzer.

Ph 7.
Physics Laboratory.
9 units:
third term.
Prerequisites: Ph6, Ph2b or Ph12b, Ph2c or Ph12c taken concurrently.
A laboratory course continuing the study of experimental physics introduced in Physics 6. The course introduces some of the equipment and techniques used in quantum, condensed matter, nuclear, and particle physics. The menu of experiments includes some classics which informed the development of the modern quantum theory, including electron diffraction, the Stern-Gerlach experiment, Compton scattering, and the Mössbauer Effect. The course format follows that of Physics 6: students work individually and choose which experiments to conduct, and each week includes a 30 minute individual recitation and a 3 hour laboratory.
Instructors: Rice, Politzer.

Ph 8 bc.
Experiments in Electromagnetism.
3 units (0-3-0):
second, third terms.
Prerequisites: Ph 1 a.
A two-term sequence of experiments that parallel the material of Ph 1 bc. It includes measuring the force between wires with a homemade analytical balance, measuring properties of a 1,000-volt spark, and building and studying a radio-wave transmitter and receiver. The take-home experiments are constructed from a kit of tools and electronic parts. Measurements are compared to theoretical expectations.
Instructor: Spiropulu.

FS/Ph 9.
Freshman Seminar: The Science of Music.
6 units (2-0-4):
first term.
This course will focus on the physics of sound, how musical instruments make it, and how we hear it, including readings, discussions, demonstrations, and student observations using sound analysis software. In parallel we will consider what differentiates music from other sounds, and its role psychically and culturally. Students will do a final project of their choice and design, with possibilities including a book review, analysis of recordings of actual musical instruments, or instrument construction and analysis. Freshmen only; limited enrollment.
Instructor: Politzer.

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: Spiropulu.

FS/Ph 11 abc.
Freshman Seminar: Beyond Physics.
6 units (2-0-4):
second, third terms of freshman year and first term of sophomore year.
Freshmen are offered the opportunity to enroll in this class by submitting potential solutions to problems posed in the fall term. A small number of solutions will be selected as winners, granting those students permission to register. This course demonstrates how research ideas arise, are evaluated, and tested and how the ideas that survive are developed. Weekly group discussions and one-on-one meetings with faculty allow students to delve into cutting edge scientific research. Ideas from physics are used to think about a huge swath of problems ranging from how to detect life on extrasolar planets to exploring the scientific underpinnings of science fiction in Hollywood films to considering the efficiency of molecular machines. Support for summer research at Caltech between freshman and sophomore years will be automatic for students making satisfactory progress. Graded pass/fail. Freshmen only; limited enrollment.
Instructor: Phillips.

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. Chen, Filippone, Patterson.
Instructor: X.

Ph 20.
Computational Physics Laboratory I.
6 units (0-6-0):
first, second, third terms.
Prerequisites: CS 1 or equivalent.
Introduction to the tools of scientific computing. Use of numerical algorithms and symbolic manipulation packages for solution of physical problems. Python for scientific programming, Mathematica for symbolic manipulation, Unix tools for software development.
Instructors: Mach, Weinstein.

Ph 21.
Computational Physics Laboratory II.
6 units (0-6-0):
first, second, third terms.
Prerequisites: Ph 20 or equivalent experience with programming.
Computational tools for data analysis. Use of python for accessing scientific data from the web. Bayesian techniques. Fourier techniques. Image manipulation with python.
Instructors: Mach, Weinstein.

Ph 22.
Computational Physics Laboratory III.
6 units (0-6-0):
first, second, third terms.
Prerequisites: Ph 20 or equivalent experience with programming and numerical techniques.
Computational tools and numerical techniques. Applications to problems in classical mechanics. Numerical solution of 3-body and N-body systems. Monte Carlo integration.
Instructors: Mach, Weinstein.

Ph 50 ab.
Caltech Physics League.
3 units (1-0-2):
first, second terms.
Prerequisites: Ph 1 abc.
This course serves as a physics club, meeting weekly to discuss and analyze real-world problems in physical sciences. A broad range of topics will be considered, such as energy production, space and atmospheric phenomena, astrophysics, nano-science, and others. Students will use basic physics knowledge to produce simplified (and perhaps speculative) models of complex natural phenomena. In addition to regular assignments, students will also compete in solving challenge problems each quarter with prizes given in recognition of the best solutions. Not offered 2021-22.

Ph 70.
Oral and Written Communication.
6 units (2-0-4):
first, second, 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.
Prerequisites: Ph 7 or instructor's permission.
Advanced preparation for laboratory research. Dual emphasis on practical skills used in modern research groups and historic experiments that illuminate important theoretical concepts. Topics include advanced signal acquisition, conditioning, and data processing, introductions to widely-used optical devices and techniques, laser-frequency stabilization, and classic experiments such as magnetic resonance, optical pumping, and doppler-free spectroscopy. Fundamentals of vacuum engineering, thin-film sample growth, and cryogenics are occasionally offered. Special topics and student-led projects are available on request.
Instructors: Black, Libbrecht.

Ph 78 abc.
Senior Thesis (Experiment).
9 units:
first, second, third terms.
Prerequisites: To register for this course, the student must obtain approval of the chair of the Physics Undergraduate Committee (Ken Libbrecht).
Open only to senior physics majors. Experimental research must be supervised by a faculty member, the student's thesis adviser. Two 15-minute presentations to the Physics Undergraduate Committee are required, one near the end of the first term and one near the end of third term. The written thesis must be completed and distributed to the committee one week before the second presentation. 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 untli 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. Not offered on a pass/fail basis.

Ph 79 abc.
Senior Thesis (Theory).
9 units:
first, second, third terms.
Prerequisites: To register for this course, the student must obtain approval of the chair of the Physics Undergraduate Committee (Ken Libbrecht).
Open only to senior physics majors. Theoretical research must be supervised by a faculty member, the student's thesis adviser. Two 15-minute presentations to the Physics Undergraduate Committee are required, one near the end of the first term and one near the end of third term. The written thesis must be completed and distributed to the committee one week before the second presentation. 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 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. Not offered on a pass/fail basis.

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. Offered in alternate years. Not offered 2021-22.

Ay/Ph 104.
Relativistic Astrophysics.
9 units (3-0-6):
third term.
Prerequisites: Ph 1, Ph 2 ab.
This course is designed primarily for junior and senior undergraduates in astrophysics and physics. It covers the physics of black holes and neutron stars, including accretion, particle acceleration and gravitational waves, as well as their observable consequences: (neutron stars) pulsars, magnetars, X-ray binaries, gamma-ray bursts; (black holes) X-ray transients, tidal disruption and quasars/active galaxies and sources of gravitational waves.
Instructor: Kasliwal.

Ph 105.
Analog Electronics for Physicists.
9 units:
first term.
Prerequisites: Ph1abc, Ma2, or equivalent.
A laboratory course intended for graduate students, it covers the design, construction, and testing of simple, practical analog and interface circuits useful for signal conditioning and experiment control in the laboratory. No prior experience with electronics is required. Students will use operational amplifiers, analog multipliers, diodes, bipolar transistors, and passive circuit elements. Each week includes a 45 minute lecture/recitation and a 2½ hour laboratory. The course culminates in a two-week project of the student's choosing.
Instructors: Rice, Libbrecht.

Ph 106 abc.
Topics in Classical Physics.
9 units (4-0-5):
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. Ph106a will be devoted to mechanics, including Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, central forces, and rigid-body motion. Ph106b will be devoted to fundamentals of electrostatics, magnetostatics, and electrodynamics, including boundary-value problems, multipole expansions, electromagnetic waves, and radiation. It will also cover special relativity. Ph106c will cover advanced topics in electromagnetism and an introduction to classical optics.
Instructors: Fuller, Golwala.

APh/Ph 112 ab.
Noise and Stochastic Resonance.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 12 abc, ACM 95/100 ab and Ph 106 abc, equivalent background, or instructor's permission.
The presence of noise in experimental systems is often regarded as a nuisance since it diminishes the signal to noise ratio thereby obfuscating weak signals or patterns. From a theoretical perspective, noise is also problematic since its influence cannot be elicited from deterministic equations but requires stochastic-based modeling which incorporates various types of noise and correlation functions. In general, extraction of embedded information requires that a threshold be overcome in order to outweigh concealment by noise. However, even below threshold, it has been demonstrated in numerous systems that external forcing coupled with noise can actually boost very weak signatures beyond threshold by a phenomenon known as stochastic resonance. Although it was originally demonstrated in nonlinear systems, more recent studies have revealed this phenomenon can occur in linear systems subject, for example, to color-based noise. Techniques for optimizing stochastic resonance are now revolutionizing modeling and measurement theory in many fields ranging from nonlinear optics and electrical systems to condensed matter physics, neurophysiology, hydrodynamics, climate research and even finance. This course will be conducted in survey and seminar style and is expected to appeal to theorists and experimentalists alike. Review of the current literature will be complimented by background readings and lectures on statistical physics and stochastic processes as needed.
Instructor: Troian.

APh/Ph 115.
Physics of Momentum Transport in Hydrodynamic Systems.
9 units (3-0-6):
second term.
Prerequisites: ACM 95 or equivalent.
Contemporary research in many areas of physics requires some knowledge of the principles governing hydrodynamic phenomena such as nonlinear wave propagation, symmetry breaking in pattern forming systems, phase transitions in fluids, Langevin dynamics, micro- and optofluidic control, and biological transport at low Reynolds number. This course offers students of pure and applied physics a self-contained treatment of the fundamentals of momentum transport in hydrodynamic systems. Mathematical techniques will include formalized dimensional analysis and rescaling, asymptotic analysis to identify dominant force balances, similitude, self-similarity and perturbation analysis for examining unidirectional and Stokes flow, pulsatile flows, capillary phenomena, spreading films, oscillatory flows, and linearly unstable flows leading to pattern formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods will be taught in class as needed. Not offered 2021-2022.
Instructor: Troian.

APh/Ph/Ae 116.
Physics of Thermal and Mass Transport in Hydrodynamic Systems.
9 units (3-0-6):
third term.
Prerequisites: ACM 95 or equivalent and APh/Ph 115 or equivalent.
Contemporary research in many areas of physics requires some knowledge of how momentum transport in fluids couples to diffusive phenomena driven by thermal or concentration gradients. This course will first examine processes driven purely by diffusion and progress toward description of systems governed by steady and unsteady convection-diffusion and reaction-diffusion. Topics will include Fickian dynamics, thermal transfer in Peltier devices, Lifshitz-Slyozov growth during phase separation, thermocouple measurements of oscillatory fields, reaction-diffusion phenomena in biophysical systems, buoyancy driven flows, and boundary layer formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods such as singular perturbation, Sturm-Liouville and Green's function analysis will be taught in class as needed. Not offered 2021-2022.
Instructor: Troian.

Ph/APh/EE/BE 118 ab.
Physics of Measurement.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 127, APh 105, or equivalent, or permission from instructor.
This course explores the fundamental underpinnings of experimental measurements from the perspectives of coupling, responsivity, noise, backaction, and information. Its overarching goal is to enable students to develop intuition about, and to critically evaluate, a diversity of real measurement systems - and to provide a framework for estimating the ultimate and practical limits to information that can be extracted from them. Topics will include physical signal transduction and responsivity, fundamental noise processes, modulation, frequency conversion, synchronous detection, signal-sampling techniques, digitization, signal transforms, spectral analyses, and correlation methods. The first term will cover the essential fundamental underpinnings, while topics in second term will focus their application to high frequency, microwave, and fast time-domain measurements where distributed approaches become imperative. The second term (in alternate years) may focus on topics that include either measurements at the quantum limit, biosensing and biological interfaces, of functional brain imaging. Not offered 2021-22.
Instructor: Roukes.

CS/Ph 120.
Quantum Cryptography.
9 units (3-0-6):
first term.
Prerequisites: Ma 1b, Ph 2b or Ph 12b, CS 21, CS 38 or equivalent recommended (or instructor's permission).
This course is an introduction to quantum cryptography: how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically. The course covers the fundamental ideas of quantum information that form the basis for quantum cryptography, such as entanglement and quantifying quantum knowledge. We will introduce the security definition for quantum key distribution and see protocols and proofs of security for this task. We will also discuss the basics of device-independent quantum cryptography as well as other cryptographic tasks and protocols, such as bit commitment or position-based cryptography. Not offered 2021-2022

Ph 121 abc.
Computational Physics Lab.
6 units (0-6-0):
first, second, third terms.
Many of the recent advances in physics are attributed to progress in computational power. In the advanced computational lab, students will hone their computational skills bu working through projects inspired by junior level classes (such as classical mechanics and E, statistical mechanics, quantum mechanics and quantum many-body physics). This course will primarily be in Python and Mathematica. This course is offered pass/fail.
Instructors: Simmons-Duffin, Refael.

Ph 125 abc.
Quantum Mechanics.
9 units (4-0-5):
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. Chen.
Instructors: Wise, Porter, Y.

Ph 127 ab.
Statistical Physics of Interacting Systems, Phases, and Phase Transitions.
9 units (4-0-5):
first, second terms.
Prerequisites: Ph 12 c or equivalent; quantum mechanics at the level of Ph 125 ab is required for Ph 127 b; may be taken concurrently.
An advanced course in statistical physics that focuses on systems of interacting particles. Part a will cover interacting gases and spin models of magnetism, phase transitions and broken symmetries, classical field theories, and renormalization group approach to collective phenomena. Part b will introduce the path-integral based quantum to classical statistical mechanics mapping, as well as dualities and topological-defects descriptions, with applications to magnets, superfluids, and gauge field theories.
Instructor: Motrunich.

Ph 129 abc.
Mathematical Methods of Physics.
9 units (4-0-5):
first, second terms.
Prerequisites: Ma 2 and Ph 2 abc, or equivalent.
Mathematical methods and their application in physics. First term focuses on group theoretic methods in physics. Second term includes analytic methods such as complex analysis, differential equations, integral equations and transforms, and other applications of real analysis. Third term covers probability and statistics in physics. Each part may be taken independently. Part c not offered 2021-2022. Chen, Chatziioannou.
Instructor: X.

Ph 135.
Introduction to Condensed Matter.
9 units (3-0-6):
first term.
Prerequisites: Ph 125 ab or equivalent or instructor's permission.
This course is an introduction to condensed matter which covers electronic properties of solids, including band structures, and transport. In addition, the course will introduce topological band-structure effects, covering Berry phase, the Thouless pump, and topological insulators. Ph 135 is continued by Ph/APh 223 ab in the winter and spring terms.
Instructor: Refael.

Ph 136 abc.
Applications of Classical Physics.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 106 ab 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. Ph 136a will focus on thermodynamics, statistical mechanics, random processes, and optics. Ph136b will focus on fluid dynamics, MHD, turbulence, and plasma physics. Ph 136c will cover an introduction to general relativity. Offered in alternate years. Not offered 2021-22.

Ph/APh 137 abc.
Atoms and Photons.
9 units (3-0-6):
first, second terms.
Prerequisites: Ph 125 ab or equivalent, or instructor's permission.
This course will provide an introduction to the interaction of atomic systems with photons. The main emphasis is on laying the foundation for understanding current research that utilizes cold atoms and molecules as well as quantized light fields. First term: resonance phenomena, atomic/molecular structure, and the semi-classical interaction of atoms/molecules with static and oscillating electromagnetic fields. Techniques such as laser cooling/trapping, coherent manipulation and control of atomic systems. Second term: quantization of light fields, quantized light matter interaction, open system dynamics, entanglement, master equations, quantum jump formalism. Applications to cavity QED, optical lattices, and Rydberg arrays. Third term [not offered 2021-2022]: Topics in contemporary research. Possible areas include introduction to ultracold atoms, atomic clocks, searches for fundamental symmetry violations, synthetic quantum matter, and solid state quantum optics platforms. The emphasis will be on reading primary and contemporary literature to understand ongoing experiments.
Instructors: Hutzler, Endres.

APh/Ph 138 ab.
Quantum Hardware and Techniques.
9 units (3-0-6):
third term, a and b offered in alternating years.
Prerequisites: Ph 125abc or Ph 127ab or Ph137ab or instructor's permission.
This class covers multiple quantum technology platforms and related theoretical techniques, and will provide students with broad knowledge in quantum science and engineering. It will be split into three-week modules covering: applications of near-term quantum computers, superconducting qubits, trapped atoms and ions, topological quantum matter, solid state quantum bits, tensor-product states.
Instructors: Faraon, Minnich.

Ph 139.
Introduction to Elementary Particle Physics.
9 units (3-0-6):
second term.
Prerequisites: Ph 125 ab or equivalent, or instructor's permission.
This course provides an introduction to particle physics which includes Standard Model, Feynman diagrams, matrix elements, electroweak theory, QCD, gauge theories, the Higgs mechanism, neutrino mixing, astro-particle physics/cosmology, accelerators, experimental techniques, important historical and recent results, physics beyond the Standard Model, and major open questions in the field.
Instructor: Weinstein.

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. The instructor will complete a student evaluation at the end of the term. Graded pass/fail.

Ph 172.
Research in Physics.
Units in accordance with work accomplished:
.
Undergraduate students registering for 6 or more units of Ph 172 must provide a brief written summary of their work, not to exceed 3 pages, to the option rep at the end of the term. Approval of the student's research supervisor and departmental adviser must be obtained before registering. Graded pass/fail.

Ph 177.
Advanced Experimental Physics.
9 units (0-4-5):
second, third terms.
Prerequisites: Ph 6, Ph 106 a, Ph 125 a or equivalents.
A one-term laboratory course which will require students to design, assemble, calibrate, and use an apparatus to conduct a nontrivial experiment involving quantum optics or other current research area of physics. Students will work as part of a small team to reproduce the results of a published research paper. Each team will be guided by an instructor who will meet weekly with the students; the students are each expected to spend an average of 4 hours/week in the laboratory and the remainder for study and design. Enrollment is limited. Permission of the instructors required.
Instructors: Rice, Hutzler.

CNS/Bi/Ph/CS/NB 187.
Neural Computation.
9 units (3-0-6):
third term.
Prerequisites: introductory neuroscience (Bi 150 or equivalent); mathematical methods (Bi 195 or equivalent); scientific programming.
This course aims at a quantitative understanding of how the nervous system computes. The goal is to link phenomena across scales from membrane proteins to cells, circuits, brain systems, and behavior. We will learn how to formulate these connections in terms of mathematical models, how to test these models experimentally, and how to interpret experimental data quantitatively. The concepts will be developed with motivation from some of the fascinating phenomena of animal behavior, such as: aerobatic control of insect flight, precise localization of sounds, sensing of single photons, reliable navigation and homing, rapid decision-making during escape, one-shot learning, and large-capacity recognition memory.
Instructors: Meister, Rutishauser.

Ph 198.
Special Topics in Physics.
Units in accordance with work accomplished:
.
Topics will vary year to year and may include hands-on laboratory work, team projects and a survey of modern physics research.
Instructor: Staff.

Ph 199.
Frontiers of Fundamental Physics.
9 units (3-0-6):
third term.
Prerequisites: Ph 125 ab, Ph 106 ab, or equivalent.
This course will explore the frontiers of research in particle physics and cosmology, focusing on the physics at the Large Hadron Collider. Topics include the Standard Model of particle physics in light of the discovery of the Higgs boson, work towards the characterization and measurements of the new particle's quantum properties, its implications on physics beyond the standard model, and its connection with the standard model of cosmology focusing on the dark matter challenge. The course is geared toward seniors and first-year graduate students who are not in particle physics, although students in particle physics are welcome to attend. Not offered 2021-2022.

Ph 201.
Candidacy Physics Fitness.
9 units (3-0-6):
third term.
The course will review problem solving techniques and physics applications from the undergraduate physics college curriculum. In particular, we will touch on the main topics covered in the written candidacy exam: classical mechanics, electromagnetism, statistical mechanics and quantum physics, optics, basic mathematical methods of physics, and the physical origin of everyday phenomena.
Instructor: Endres.

Ph 203.
Nuclear Physics.
9 units (3-0-6):
third term.
Prerequisites: Ph 125 or equivalent.
An introduction and overview of modern topics in nuclear physics, including models and structure of nucleons, nuclei and nuclear matter, the electroweak interaction of nuclei, and nuclear/neutrino astrophysics. Not offered 2021-2022.
Instructor: Filippone.

Ph 205 abc.
Relativistic Quantum Field Theory.
9 units (3-0-6):
first, second, third terms.
Prerequisites: 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.
Instructors: Kapustin, Zurek, Wise.

Ph/CS 219 abc.
Quantum Computation.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 125 ab 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.
Instructors: Preskill, Kitaev.

Ph/APh 223 ab.
Advanced Condensed-Matter Physics.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 135 or equivalent, or instructor's permission.
Advanced topics in condensed-matter physics, with emphasis on the effects of interactions, symmetry, and topology in many-body systems. Ph/APh 223a covers second quantization, Hartree-Fock theory of the electron gas, Mott insulators and quantum magnetism, spin liquids, bosonization, and the integer and fractional quantum Hall effect. Ph/APh 223b will continue with BCS theory of superconductivity, Ginzburg-Landau theory, elements of unconventional and topological superconductors, theory of superfluidity, Bose-Hubbard model and bosonic Mott insulators, and some aspects of quantum systems with randomness.
Instructor: Alicea.

Ph 229 abc.
Advanced Mathematical Methods of Physics.
9 units (3-0-6):
first, second terms.
Prerequisites: 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. Part c will not be offered in 2021-2022.
Instructors: Ooguri, Kapustin.

Ph 230 abc.
Elementary Particle Theory.
9 units (3-0-6):
first, third terms.
Prerequisites: Ph 205 abc or equivalent.
First term: Standard model, including electroweak and strong interactions, symmetries and symmetry breaking (including the Higgs mechanism), parton model and quark confinement, anomalies. Second and third terms: more on nonperturbative phenomena, including chiral symmetry breaking, instantons, the 1/N expansion, lattice gauge theories, and topological solitons. Other topics include topological field theory, precision electroweak, flavor physics, conformal field theory and the AdS/CFT correspondence, supersymmetry, Grand Unified Theories, and Physics Beyond the Standard Model. Part c will not be offered in 2021-2022.
Instructors: Zurek, Gukov.

Ph 232.
Introduction to Topological Field Theory.
9 units (3-0-6):
first term.
Prerequisites: Ph 205.
Topological field theories are the simplest examples of quantum field theories which, in a sense, are exactly solvable and generally covariant. During the past twenty years they have been the main source of interaction between physics and mathematics. Thus, ideas from gauge theory led to the discovery of new topological invariants for 3-manifolds and 4-manifolds. By now, topological quantum field theory (TQFT) has evolved into a vast subject, and the main goal of this course is to give an accessible introduction to this elegant subject.
Instructor: Gukov.

Ph 235 ab.
Theoretical Cosmology and Astroparticle Physics.
9 units (3-0-6):
first term.
Prerequisites: General Relativity at the level of Ph 236a, and Quantum Field Theory at the level of Ph 205a.
Cosmology in an expanding universe, inflation, big bang nucleosynthesis, baryogenesis, neutrino and nuclear astrophysics. Second term: Cosmological perturbation theory and the cosmic microwave background, structure formation, theories of dark matter. Not offered 2021-2022.
Instructor: Zurek.

Ph 236 abc.
General Relativity.
9 units (3-0-6):
first, second terms.
Prerequisites: 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 and its applications to gravitational waves, black holes, relativistic stars, causal structure of space-time, cosmology and brane worlds. Offered in alternate years. Part c will not be offered in 2021-2022.
Instructors: Chatziioannou, Teukolsky.

Ph 237.
Gravitational Radiation.
9 units (3-0-6):
third term.
Prerequisites: Ph 106 b, Ph 12 b or equivalents.
Special topics in Gravitational-wave Detection. Physics of interferometers, limits of measurement, coherent quantum feedback, noise, data analysis. Chen.
Instructor: Y.

Ph 242 ab.
Physics Seminar.
4 units (2-0-2):
first, second terms.
An introduction to independent research, including training in relevant professional skills and discussion of current Caltech research areas with Caltech faculty, postdocs, and students. One meeting per week plus student projects. Registration restricted to first-year graduate students in physics.
Instructor: Patterson.

Ph 250.
Introduction to String Theory.
9 units (3-0-6):
second term.
Prerequisites: Ph 205 or equivalent.
This year, we offer a lighter version of the course. It will cover a condensed version of the world-sheet formulation, then basic elements of the target space physics, after which we will discuss interesting phenomena/applications, such as T-duality, D-branes, anomalies, building semi-realistic models of particle physics from string compactifications, etc. Not offered 2021-2022.
Instructor: Gukov.

Ph 300.
Thesis Research.
Units in accordance with work accomplished:
.
Ph 300 is elected in place of Ph 172 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.

### Please Note

The online version of the Caltech Catalog is provided as a convenience; however, the printed version is the only authoritative source of information about course offerings, option requirements, graduation requirements, and other important topics.