# Physics (Ph) Undergraduate Courses (2019-20)

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, Alicea.

Ph 2 abc.
Waves, Quantum Mechanics, and Statistical Physics.
9 units (3-0-6):
first, second, third terms.
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, Filippone.

Ph 3.
Introductory Physics Laboratory.
6 units (0-3-3):
first, second, third terms.
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 2019-20.

Ph 5.
Analog Electronics for Physicists.
9 units (0-5-4):
first term.
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.
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.
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.
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.
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.
Instructors: Chen, Filippone, Simmons-Duffin.

Ph 20.
Computational Physics Laboratory I.
6 units (0-6-0):
first, second, third terms.
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):
second, third terms.
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):
second, third terms.
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.
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.
Instructors: Refael, Patterson.

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.
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.
9 units:
first, second, third terms.
Open only to senior physics majors. This 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 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. 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 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. Offered in alternate years. Not offered 2019-20.

Ay/Ph 104.
Relativistic Astrophysics.
9 units (3-0-6):
third term.
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: Instructor: Kasliwal.

Ph 105.
Analog Electronics for Physicists.
9 units:
first term.
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.

Ph 106 abc.
Topics in Classical Physics.
9 units (4-0-5):
first, second, third terms.
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: Weinstein, Golwala, Hutzler.

APh/Ph 115.
Physics of Momentum Transport in Hydrodynamic Systems.
12 units (3-0-9):
second term.
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.
Instructor: Troian.

APh/Ph/Ae 116.
Physics of Thermal and Mass Transport in Hydrodynamic Systems.
12 units (3-0-9):
third term.
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.
Instructor: Troian.

Ph/APh/EE/BE 118 abc.
Physics of Measurement.
9 units (3-0-6):
first, third terms.
This course focuses on exploring the fundamental underpinnings of experimental measurements from the perspectives of responsivity, noise, backaction, and information. Its overarching goal is to enable students to critically evaluate real measurement systems, and to determine the ultimate fundamental 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 correlations. The first term will cover the essential fundamental underpinnings, while topics in second term will include examples from optical methods, high-frequency and fast temporal measurements, biological interfaces, signal transduction, biosensing, and measurements at the quantum limit. Part c not offered in 2019-20.
Instructor: Roukes.

CS/Ph 120.
Quantum Cryptography.
9 units (3-0-6):
first term.
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.
Instructor: Vidick.

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, Motrunich.

Ph 125 abc.
Quantum Mechanics.
9 units (4-0-5):
first, second, third terms.
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.
Instructor: Wise.

Ph 127 abc.
Statistical Physics.
9 units (4-0-5):
first, second, third terms.
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.
Instructors: Motrunich, Brandao.

Ph 129 abc.
Mathematical Methods of Physics.
9 units (4-0-5):
first, second, third terms.
Mathematical methods and their application in physics. First term covers probability and statistics in physics. Second term focuses on group theoretic methods in physics. Third term includes analytic and numerical methods for solving differential equations, integral equations, and transforms, and other applications of real analysis. The three terms can be taken independently.
Instructors: Porter, Chen, Oguri.

Ph 135.
Introduction to Condensed Matter.
9 units (3-0-6):
first term.
This course is an introduction to condensed matter which covers electronic properties of solids, including band structures, transport, and optical properties. Ph 135 a is continued by Ph 223 ab in second and third terms.
Instructor: Refael.

Ph 136 abc.
Applications of Classical Physics.
9 units (3-0-6):
first, second, third terms.
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 2019-20.

Ph/APh 137 abc.
Atoms and Photons.
9 units (3-0-6):
first, second terms.
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 19-20]: 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):
second and third terms.
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: Chen, Endres, Faraon, Hsieh, Minnich, Painter.

Ph 139.
Introduction to High Energy Physics.
9 units (3-0-6):
third term.
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: Patterson.

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.
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):
first term.
Programming will be required. This course investigates computation by neurons. Of primary concern are models of neural computation and their neurological substrate, as well as the physics of collective computation. Thus, neurobiology is used as a motivating factor to introduce the relevant algorithms. Topics include rate-code neural networks, their differential equations, and equivalent circuits; stochastic models and their energy functions; associative memory; supervised and unsupervised learning; development; spike-based computing; single-cell computation; error and noise tolerance. Not offered 2019-20.
Instructor: Perona.

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.
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 2019-20.