Physics

Faculty of the Department of Physics

Gerald Gabrielse, Professor of Physics (Chair )
Howard C. Berg, Professor of Molecular and Cellular Biology and Professor of Physics (on leave 2000-01)
George W. Brandenburg, Senior Research Fellow in Physics; Director of the High Energy Physics Laboratory
Sidney Coleman, Donner Professor of Science
John M. Doyle, Professor of Physics (on leave spring term)
Henry Ehrenreich, Clowes Research Professor of Science (on leave spring term)
Gary J. Feldman, Frank B. Baird, Jr. Professor of Science
Daniel S. Fisher, Professor of Physics and Professor of Applied Physics (on leave spring term)
Andrew Foland, Assistant Professor of Physics
Melissa Franklin, Professor of Physics
Peter L. Galison, Harvard College Professor and the Mallinckrodt Professor of the History of Science and of Physics
Howard Georgi, Mallinckrodt Professor of Physics (on leave spring term)
Roy J. Glauber, Mallinckrodt Professor of Physics
Jene A. Golovchenko, Gordon McKay Professor of Applied Physics and Professor of Physics
Bertrand I. Halperin, Hollis Professor of Mathematicks and Natural Philosophy
Lene V. Hau, Gordon McKay Professor of Applied Physics and Professor of Physics
Thomas C. Hayes, Lecturer on Physics
Eric J. Heller, Professor of Chemistry and Physics
Paul Horowitz, Professor of Physics and Professor of Electrical Engineering (on leave fall term)
John Huth, Professor of Physics
Arthur M. Jaffe, Landon T. Clay Professor of Mathematics and Theoretical Science
Efthimios Kaxiras, Gordon McKay Professor of Applied Physics and Professor of Physics
Leo Kouwenhoven, Visiting Professor of Physics, Visiting Scholar in Physics (Technial University Delft)
Margaret E. Law, Senior Lecturer on Physics (Director of Undergraduate Studies)
Juan Maldacena, Professor of Physics (on leave 2000-01)
Charles M. Marcus, Professor of Physics (Director of Graduate Studies)
Paul C. Martin, John H. Van Vleck Professor of Pure and Applied Physics
Eric Mazur, Harvard College Professor, Gordon McKay Professor of Applied Physics and Professor of Physics
Masahiro Morii, Assistant Professor of Physics
David Joseph Morin, Lecturer on Physics
Venkatesh Narayanamurti, John A. and Elizabeth S. Armstrong Professor of Engineering and Applied Sciences and Professor of Physics
David R. Nelson, Mallinckrodt Professor of Physics and Professor of Applied Physics (on leave 2000-01)
Costas D. Papaliolios, Professor of Physics, Emeritus
Peter S. Pershan, Gordon McKay Professor of Applied Physics and Professor of Physics
Mara Prentiss, Professor of Physics
William H. Press, Professor of Astronomy and of Physics, Fellow of Pforzheimer House (on leave fall term)
Subir Sachdev, Visiting Professor of Physics (Yale University)
Irwin I. Shapiro, Timken University Professor
Isaac F. Silvera, Thomas D. Cabot Professor of the Natural Sciences
Andrew Strominger, Professor of Physics (on leave spring term)
Michael Tinkham, Rumford Professor of Physics and Gordon McKay Professor of Applied Physics (on leave spring term)
Cumrun Vafa, Professor of Physics
Steven Weinberg, Morris Loeb Visiting Professor of Physics (University of Texas, Austin)
David A. Weitz, Gordon McKay Professor of Applied Physics and Professor of Physics
Robert M. Westervelt, Gordon McKay Professor of Applied Physics and Professor of Physics
Tai T. Wu, Gordon McKay Professor of Applied Physics and Professor of Physics (on leave spring term)

Other Faculty Offering Instruction in Physics

Sheldon L. Glashow, Higgins Professor of Physics, Emeritus
Gerald Holton, Mallinckrodt Professor of Physics and Professor of the History of Science, Emeritus

The Physics Department offers three separate sequences of introductory courses: Physics 1a and 1b at the introductory calculus level and Physics 11a, 11b or Physics 15a, 15b, 15c at the intermediate calculus background. Students with strong preparation may also enter the 15 sequence by taking Physics 16 instead of Physics 15a. Each of the three sequences is designed to be a self-contained treatment of classical physics.

Students who expect to concentrate in physics or one of the other sciences in which physics plays a major role will usually take the Physics 15 sequence followed by Physics 143a,b. Students with excellent high-school preparation may begin the Physics 15 sequence taking Physics 16 instead of Physics 15a. Physics 16 is a course in mechanics and special relativity specifically designed for students who have done well in a high-school advanced placement course.

Students who do not plan to continue in physics and have sufficient mathematical skills may wish to take the one year Physics 11 sequence. Physics 11a and 11b offer, in two semesters, classical physics at a level comparable to the longer Physics 15 sequence, but covering fewer topics.

Physics 1a and 1b present a self-contained treatment of classical and modern physics in one year, but at a lower mathematical level than the Physics 11 sequence. Physics 1a and 1b are designed to meet the requirements of all medical schools. Most medical schools will also accept the Physics 15 or Physics 11 sequences. Some prefer that more than two half courses in physics be taken. Premedical students should inquire at the medical schools to which they expect to apply.

Students who do not intend to devote more than one year to the study of physics, and especially those not concentrating in a physical science or mathematics, will probably find that Physics 1a and 1b, with their broader range of subject matter, will more appropriately serve their needs than Physics 11a and 11b.

Further details may be found under the individual course headings.

Primarily for Undergraduates

Physics 1a. Principles of Physics: Mechanics
Catalog Number: 7422
Eric Mazur and Cumrun Vafa
Half course (fall term). Tu., Th., 8:30–10, plus twice weekly conference sections and six laboratory sessions to be arranged. EXAM GROUP: 11
An introduction to classical mechanics: kinematics, Newton’s laws of motion, conservation laws, oscillations, and thermodynamics as understood from the kinetic theory of particles. Brief applications of these ideas to elasticity and fluids as helpful preparation for the MCAT exams are included.
Note: Not designed as an introductory course for physics concentrators; those students should take Physics 15a or 16. Students who have taken Mathematics 21a or the equivalent and desire a one-year survey course may wish to take Physics 11a and 11b in order to make full use of their mathematical background. Physics 1a may not ordinarily be taken for credit in addition to Physics 11a, 15a, 16, or Science A-15.
Prerequisite: Mathematics 1b or the equivalent. Students with a lower level of mathematical preparation should consult the instructor.

Physics 1b. Principles of Physics: Electricity, Waves, Nuclear Physics
Catalog Number: 7483
Cumrun Vafa and Eric Mazur
Half course (spring term). Tu., Th., 8:30–10, plus twice weekly conference sections and five laboratory sessions to be arranged. EXAM GROUP: 10, 11
A continuation of Physics 1a: electricity and magnetism, direct-current and alternating-current circuits, sound and light, radioactivity and nuclear physics.
Note: May not ordinarily be taken for credit in addition to Physics 11b or 15b.
Prerequisite: Physics 1a and Mathematics 1b, or the equivalent.

Physics 11a. Mechanics
Catalog Number: 3131
Melissa Franklin and David A. Weitz
Half course (fall term). Lectures, Tu., Th., 11:30–1; weekly ninety-minute discussion sections. EXAM GROUP: 13
Physics 11a is the first half of a one-year physics sequence. It provides an introduction to classical mechanics, including the laws of conservation of energy, momentum, and angular momentum; the translational motion of particles, rigid bodies, and fluids; the rotational motion of rigid bodies; the general description of waves and optics. Physics 11a may be taken by students who have taken or who are concurrently taking Mathematics 21a or 23a or Applied Mathematics 21a. Calculus is used routinely but the emphasis is placed on the basic concepts.
Note: Physics 11a may not be taken for credit by students who have passed Physics 15a or 16.

Physics 11b. Electricity, Magnetism, and Waves
Catalog Number: 5472
David A. Weitz and Melissa Franklin
Half course (spring term). Lectures, Tu., Th., 10–11:30, weekly ninety-minute discussion sections, and one three-hour laboratory session every two weeks. EXAM GROUP: 12, 13
Physics 11b is the second half of a one-year physics sequence. It covers the basic phenomena of electricity and magnetism, elements of circuits with selected applications, Maxwell’s equations, electromagnetic waves and optics, and a brief introduction to quantum physics.
Note: May not be taken for credit by students who have passed Physics 15b or Physics 15c.
Prerequisite: Physics 11a; Mathematics 21a or 23a.

Physics 15a. Introductory Mechanics and Relativity
Catalog Number: 1984
David Morin (fall term) and George W. Brandenburg (spring term)
Half course (fall term; repeated spring term). Tu., Th., 10–11:30, and a weekly two-hour discussion section. EXAM GROUP: 13
Newtonian mechanics and special relativity. Topics include vectors; kinematics in three dimensions; Newton’s laws; force, work, power; conservative forces, potential energy; momentum, collisions; rotational motion, angular momentum, torque; static equilibrium, oscillations, simple harmonic motions; gravitation, planetary motion; special relativity.
Prerequisite: Mathematics preparation at least at the level of Mathematics 1b concurrently is required. However, some elementary ideas from multivariable calculus may be used and students are encouraged to take Mathematics 21a concurrently.

Physics 15b. Introductory Electromagnetism
Catalog Number: 2701
Daniel S. Fisher (fall term), Mara Prentiss (spring term), and assistants
Half course (fall term; repeated spring term). Fall: Tu., Th., 11:30–1; Spring: Tu., Th., 10–11:30;and a weekly two-hour discussion section and three-hour laboratory session every two weeks. EXAM GROUP: Fall: 14; Spring: 12, 13
Electricity and magnetism at the level of Purcell’s book. Covers all topics in Purcell including Maxwell’s equations in differential form and electric and magnetic fields in materials.
Note: Laboratory “zap” electronics lab in a toolbox—students work on the labs in their dorm rooms—afternoon and evening help labs are scheduled. Laboratories will be under the supervision of Thomas C. Hayes.
Prerequisite: Physics 15a, Physics 16, or written permission of the Head Tutor in Physics. Mathematics preparation at least at the level of Mathematics 21a taken concurrently is required. Vector calculus, div, grad and curl are used extensively—in principle, this is taught in the course. Students taking Mathematics 21a concurrently will likely find that some concepts are introduced in Physics 15b before they have seen them in Mathematics 21a. Some students may wish to postpone Physics 15b until they have completed Mathematics 21a.

Physics 15c. Wave Phenomena
Catalog Number: 8676
Costas D. Papaliolios (fall term), Andrew Foland (spring term) and Masahiro Morii (spring term)
Half course (fall term; repeated spring term). Tu., Th., 1–2:30, and three hours per week of conference and laboratory. EXAM GROUP: 15
Forced oscillation and resonance; coupled oscillators and normal modes; Fourier series; Electromagnetic waves, radiation, longitudinal oscillations, sound; traveling waves; signals, wave packets and group velocity; two- and three-dimensional waves; polarization; geometrical and physical optics; interference and diffraction. Optional topics: Water waves, holography, x-ray crystallography. Solitons.
Note: Laboratory: Continuation of “zap” plus additional labs. Laboratories will be under the supervision of Thomas C. Hayes.
Prerequisite: Physics 15b and mathematics preparation at the level of Mathematics 21b taken concurrently. Some prior knowledge of complex numbers (for example as taught in Mathematics 1b) is helpful. Multivariable calculus is used in the treatment of the wave equation, but plays a much less central role than in Physics 15b.

Physics 16. Mechanics and Special Relativity
Catalog Number: 2019
Howard Georgi
Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 13
Newtonian mechanics and special relativity for students with good preparation in physics and mathematics at the level of the advanced placement curriculum. Topics include an introduction to Lagrangian mechanics, Noether’s theorem, special relativity, collisions and scattering, rotational motion, angular momentum, torque, the moment of inertia tensor, oscillators damped and driven, gravitation, planetary motion, and an introduction to cosmology.
Prerequisite: Score of 4 or 5 on the mechanics section of the Physics C Advanced Placement exam, or equivalent. Mathematics preparation at least at the level of Mathematics 21a taken concurrently is required. Thorough knowledge of calculus of one variable and vectors plus some mathematical sophistication. The mathematical level will be significantly higher than that of Physics 15a.

*Physics 90r. Supervised Research
Catalog Number: 2460
Margaret E. Law and members of the Department
Half course (fall term; repeated spring term). Hours to be arranged. .
Note: Ordinarily open to selected concentrators in Physics, or in Chemistry and Physics, who have obtained honor grades in Physics 15 and a number of intermediate-level courses. The student must be accepted by some member of the faculty doing research in the student’s field of interest. The form of the research depends on the student’s interest and experience, the nature of the particular field of physics, and facilities and support available. Students wishing to write a senior thesis can do so by arranging for a sponsor and enrolling in this course. A list of possible faculty sponsors and their fields is available in Lyman 233 and on Physics Department web page.Course enrollment forms may be obtained from Lyman 233.

*Physics 91r. Supervised Reading Course for Undergraduates
Catalog Number: 1218
Margaret E. Law and members of the Department
Half course (fall term; repeated spring term). Hours to be arranged.
Note: Open to selected concentrators in Physics, Chemistry and Physics, and other fields who wish to do supervised reading and studying of special topics in physics. Ordinarily such topics do not include those covered in a regular course of the Department. Honor grades in Physics 15 and a number of intermediate-level courses are ordinarily required. The student must be accepted by a member of the faculty. A list of possible faculty sponsors and their fields is available in Jefferson 365.

*Physics 95 (formerly Physics 99). Topics in Current Research
Catalog Number: 2806
Isaac F. Silvera
Half course (fall term). M., 3–4, W., 7:30–9 p.m. EXAM GROUP: 8
The goal of this physics tutorial is to guide students in the transition from learning physics by subject (e.g., electricity and magnetism, quantum mechanics, etc.) to appreciating physics as an intense, diverse discipline of modern research. Examples from experimental and theoretical, high and low energy physics are presented. Every Wednesday evening, a physics faculty member speaks on his/her area of research. Each presentation is preceded by assigned reading and a lecture designed to introduce students to some of the basic physics of the area discussed, as well as to important developments and burning problems being addressed at the frontiers of research.
Note: Intended mainly for junior and senior concentrators.

[*Physics 98r. Tutorial ]
Catalog Number: 3033 Enrollment: Limited.
Howard Georgi and members of the Department
Half course (fall term). Hours to be arranged.
Small group tutorial, ordinarily limited to Physics or Chemistry and Physics concentrators. Supervised individual projects and class presentations required. Topics for 1999-2000 to be announced. Past topics have included Relativity, Optical Instrumentation, and Foundations of Quantum Mechanics.
Note: Expected to be given in 2001–02. May be repeated for course credit with permission from the Head Tutor. Only one tutorial may count for concentration credit.
Prerequisite: Introductory physics and math at least through the level of Physics 15b and Math 21b. The detailed prerequisites will vary with the subject of the tutorial.

Cross-listed Courses

Astronomy 45. Introduction to Astrophysics
Science A-29. The Nature of Light and Matter

For Undergraduates and Graduates

Certain physics courses are offered in several other departments. See especially the offerings of the Division of Engineering and Applied Sciences.
Physics 121. History and Philosophy of 20th-Century Physics
Catalog Number: 0160
Peter L. Galison
Half course (spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
An introduction to the history and philosophy of physics for students with a strong undergraduate background in science. Topics include relativity, quantum theory, weapons development, and modern ideas about unification.
Note: May not be taken for credit by students who have taken History of Science 120.
Prerequisite: An introductory course in college physics, preferably at the level of Physics 15c.

Physics 123. Laboratory Electronics
Catalog Number: 0864 Enrollment: Limited to 22 students per section.
Thomas C. Hayes (fall and spring) and Paul Horowitz (spring term)
Half course (fall term; repeated spring term). Section I, Tu., Th., 1:30–5; Section II, W., F., 1:30–5. All students must attend first course meeting on 2/1 at 1:30 in Science Center 206. EXAM GROUP: 6
A lab-intensive introduction to electronic circuit design. Develops circuit intuition and debugging skills through daily hands-on lab exercises, each preceded by class discussion with minimal use of mathematics and physics. The treatment moves quickly from passive circuits, through design with discrete transistors, then concentrates on the application of integrated operational amplifiers to make a variety of circuits including integrators, oscillators, regulators, and filters. The digital half of the course emphasizes the use of programmable logic devices, microprocessors, and microcontrollers, while treating issues that arise in interfacing both analog and digital devices to a computer. Provides an overview of radio and television, digital audio, signal averaging, and construction techniques.
Note: Both sections must report to the first course meeting.

Physics 125. Widely Applied Physics
Catalog Number: 6990
Leo Kouwenhoven (Technial University Delft)
Half course (spring term). W., F., 2–3:30. EXAM GROUP: 7, 8
Applies elementary physics to real things and practical situations. Emphasis is on developing physical intuition and the ability to do order-of-magnitude calculations. New physical concepts are introduced as necessary. Materials: materials engineering, structure of the Earth, mountains, bridges, buildings. Nuclear physics: reactions, cross-sections, origin of the elements in the Big Bang and stars, reactors. Flight: aerodynamics, aircraft, rockets, spacecraft, fluid flow. Energy use and production: the automobile, fossil, nuclear, solar, and wind power. Communications: transistor, signal and noise, radar, radio astronomy. Biological physics: radiation, health risks. Climate and global change.
Note: Physics 143a and 181 are very helpful, but not required.
Prerequisite: Physics 15a,b,c, and mathematics at the level of Mathematics 21a (which may be taken concurrently).

Physics 143a. Quantum Mechanics I
Catalog Number: 1050
Mara Prentiss (fall term) and Daniel S. Fisher (spring term)
Half course (fall term; repeated spring term). Tu., Th., 10–11:30. EXAM GROUP: Fall: 13; Spring: 12, 13
Introduction to nonrelativistic quantum mechanics: uncertainty relations; Schrödinger equation; one-dimensional problems including particle in box, tunneling, and harmonic oscillator; angular momentum, hydrogen atom, spin, Pauli principle; time-independent perturbation theory.
Prerequisite: Physics 15c or written permission of the Head Tutor.

Physics 143b. Quantum Mechanics II
Catalog Number: 0253
Gary J. Feldman
Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Further techniques and applications of quantum mechanics, including approximation methods for time-dependent problems, several and many-particle systems, interaction of quantum systems with radiation and external fields, variational methods, collision theory, and measurement theory.
Prerequisite: Physics 143a.

Physics 145. Elementary Particle Physics
Catalog Number: 6057
Gary J. Feldman
Half course (spring term). Lecture meets M.,W., (F.,) at 10; seminars and sections Tu., Th., 7:30–9 p.m. as needed. EXAM GROUP: 3
Introduction to elementary particle physics. Emphasis is on concepts and phenomenology rather than on a detailed calculational development of theories. Starts with the discovery of the electron in 1897, ends with the theoretical motivation for the Higg’s boson, and attempts to cover everything important in between. Taught partly in seminar mode, with each student presenting a classic paper of the field.
Prerequisite: Physics 143a. Physics 143b or equivalent is useful.

Physics 151. Mechanics
Catalog Number: 2068
Arthur M. Jaffe
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Fundamental ideas of classical mechanics including contact with modern work and applications. Topics include Lagrange’s equations; action principles, Hamilton’s equations; symmetry and conservation laws, Hamilton-Jacobi theory and phase space dynamics. Applications to celestial mechanics, quantum mechanics, rigid body motion, the theory of small oscillations and classical fields, and nonlinear oscillations, including chaotic systems will be presented.
Note: May not be taken for credit in addition to Engineering Sciences 125.
Prerequisite: Physics 15a,b or written permission of the Head Tutor; Mathematics 21a,b or equivalent.

Physics 153. Electrodynamics
Catalog Number: 0264
Arthur M. Jaffe
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Aimed at advanced undergraduates. Emphasis on the properties and sources of the field vectors and on the wave aspect of the electromagnetic fields. Course starts with electrostatics and subsequently develops the Maxwell equations. Topics: electrostatics, dielectrics, magnetostatics, electrodynamics, wave propagation in various media, reflection and refraction, radiation, antennas and interference. In addition, a number of applications of electrodynamics in ‘modern physics’ are discussed.
Prerequisite: Physics 15 a,b, and c, or written permission of the Head Tutor; Mathematics 21a,b or equivalent.

Physics 181. Statistical Mechanics and Thermodynamics
Catalog Number: 6346
Robert M. Westervelt
Half course (spring term). M., W., F., at 11. EXAM GROUP: 4
Introduction to thermal physics: basic concepts of thermodynamics (energy, heat, work, temperature, entropy), classical and quantum ensembles and their origins, and distribution functions. Applications include Debye’s theory of solids, Planck’s theory of black body radiation, classical and quantum gases, magnetism and phase transitions.
Note: May not be taken for credit in addition to Engineering Sciences 181.
Prerequisite: Physics 143a or equivalent.

Physics 191r. Advanced Laboratory
Catalog Number: 7711 Enrollment: Together with Physics 247r, limited to a total of 24 students.
Peter S. Pershan (fall and spring term), Robert M. Westervelt (fall term), and Isaac F. Silvera (spring term)
Half course (fall term; repeated spring term). Tu., Th., 1–5. EXAM GROUP: 15, 16, 17
Students carry out three experimental projects selected from those available representing condensed matter, atomic, nuclear, and particle physics. Included are nuclear magnetic resonance, microwave spectroscopy, optical pumping, scattering of laser light, neutron activation of radioactive isotopes, Compton scattering of gamma rays, the relativistic mass of the electron, recoil free gamma-ray resonance, the lifetime of the muon, studies of superfluid helium, positron annihilation superconducting transitions, the quantum Hall effect, and properties of semiconductors. The facilities of the laboratory include several computers that are used extensively in the laboratory.
Note: The course cooperates with Applied Physics 191; experiments from that course may be chosen when available. A substantial amount of outside reading is expected.
Prerequisite: Physics 15. Physics 143a is recommended.

[Physics 195. Introduction to Solid State Physics]
Catalog Number: 2978
Henry Ehrenreich
Half course (fall term). Hours to be arranged. EXAM GROUP: 12, 13
Fundamental physical properties of crystalline solids discussed in terms of the basic principles of classical and quantum physics. Crystal structure, lattice vibrations, specific heat, energy band theory of metals and semiconductors and insulators, electrical transport in metals and semiconductors, optical and magnetic properties, superconductivity.
Note: Expected to be given in 2001–02. Designed as a first course in solid state physics for students with knowledge of elementary quantum mechanics (Physics 143a). Some knowledge of statistical physics (Physics 181) is also helpful, but not a formal prerequisite. Students who propose to take Applied Physics 295a in the spring term, and who have not previously taken a formal course in solid state physics, are strongly advised to take this course first. It is suggested that students may wish to take Applied Physics 195 when this course is bracketed.

[Physics 197. Computational Physics Methods and Applications]
Catalog Number: 8653
Efthimios Kaxiras
Half course (spring term). Hours to be arranged.
This course develops computational approaches for understanding physical systems, and illustrates the applications of such approaches to specific problems. The methods to be covered include: numerical differentiation and integration, solution of ordinary and partial differential equation, eigensystems, and stochastic approaches like Monte Carlo and genetic algorithms for statistical sampling and optimization of multi-variable systems. The emphasis is on developing the ability to handle both simple and complex physical systems which are analytically intractable. Examples will be drawn from several diverse fields of physics. Familiarity with a programming language (Like Fortran or C) is assumed.
Note: Expected to be given in 2001–02. May not be taken for credit by students who have taken Applied Physics 197.
Prerequisite: Background in mathematics at the level of Applied Mathematics 105b, which may be taken concurrently.

Cross-listed Courses

Applied Physics 195. Introduction to Solid State Physics
Astronomy 145. Topics in Astrophysics
Astronomy 150 (formerly Astronomy 205). Radiative Processes in Astrophysics
Astronomy 191. Astrophysics Laboratory
[Astronomy 192. Astronomical Measurements]
Chemistry 160. Physical Chemistry
Chemistry 161. Statistical Thermodynamics
[Earth and Planetary Sciences 106. Introduction to Planetary Physics]
Engineering Sciences 120. Introduction to the Mechanics of Solids
Engineering Sciences 123. Introduction to Fluid Mechanics
Engineering Sciences 154. Introduction to Electronic Circuits
Engineering Sciences 181. Thermodynamics
Engineering Sciences 190. Introduction to Materials Science

Primarily for Graduates

The courses primarily for graduates are open to undergraduates provided they have passed the prerequisites with a grade of C or higher; in each case, special permission by the instructor is needed. In cases where students do not have the listed prerequisites, the written approval of the Head Tutor is required.
Physics 210. General Theory of Relativity
Catalog Number: 4840
Andrew Strominger
Half course (fall term). W., F., 1–2:30. EXAM GROUP: 6, 7
An introduction to general relativity: Riemannian geometry; the Principle of Equivalence; Einstein’s field equations; the Newtonian limit; gravitational radiation; experimental tests; Penrose diagrams; black holes.
Prerequisite: Physics 151 and 153, and Mathematics 21 or equivalents.

[Physics 211. General Relativity, Cosmology, and Other Topics]
Catalog Number: 0469
Andrew Strominger
Half course (spring term). Hours to be arranged.
The focus will be the classical and quantum theory of black holes. Schwarzchild and Kerr-Newman solutions; causal structure; Penrose diagrams; the classical laws of black hole mechanics, experimental evidence; Hawking radiation; the information paradox; black hole entropy.
Note: Expected to be given in 2001–02. Physics 253a helpful but not required. Auditors should obtain permission of instructor. It is suggested that students may wish to take Astronomy 211 when this course is bracketed.
Prerequisite: General relativity at level of Physics 210 or equivalent.

[Physics 218. Modern Dynamical Systems]
Catalog Number: 1362
Arthur M. Jaffe
Half course (spring term). Hours to be arranged.
Introduction to modern topics in dynamical systems and classical Hamiltonian theory, including nonlinear systems and chaos. Modern topics include iterated maps, Poincare maps, nonlinear resonance theory, KAM theory, structure of phase space, mixing and entropy production, bifurcation theory, homoclinic tangles, Smale horseshoes, fractal repellors and numerical methods.
Note: Expected to be given in 2001–02.
Prerequisite: Physics 151 and 143a,b or equivalent; Applied Math 201,202 or equivalent.

Physics 231 (formerly Physics 232a). Electrodynamics I
Catalog Number: 4885
Paul C. Martin
Half course (spring term). M., W., F., at 10. EXAM GROUP: 3
This course will concentrate on the properties of static fields, electromagnetic waves generated by prescribed charges and currents (including synchroton radiation), and scattering. The formation of Maxwell’s equations as a relativistically covariant field theory (in which the transition to quantum electrodynamics is most natural) will also be presented along with applications where the convariant description is convenient. Some elementary magnetohydrodynamics will also be discussed.
Note: Physics 231 is being offered as a complement to Physics 232, which concentrates on the interactions of radiation with atoms and condensed matter. Neither course has the other as a prerequisite and both may be taken for credit.
Prerequisite: Physics 153 and Applied Mathematics 105a,105b, or equivalent.

Physics 232 (formerly Physics 232b). Advanced Electrodynamics
Catalog Number: 7246
Jene A. Golovchenko
Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 12, 13
Electrodynamical phenomena that are relevant to low-energy experimental physics will be discussed. Topics to be covered will include the interaction of electromagnetic radiation with atoms, molecules and condensed matter, scattering from-non-relativistic charged particles and currents, diffraction phenomena, linear and non-linear optical phenomena, microwave and optical waveguides, propagation in periodic media, including the dynamic theory of x-ray diffraction and photonic crystals.
Prerequisite: Physics 153 and Applied Mathematics 105a and 105b, or equivalent.

Physics 245. Relativistic Quantum Mechanics with Applications
Catalog Number: 3551
John Huth
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Basic techniques of relativistic quantum mechanics and field theory, including Feynman diagrams, with applications. Emphasis is given to the basic concepts of quantum field theory and their applications in the phenomenology of elementary particle physics. Applications covered include QED, weak interactions, and an introduction to the standard electroweak model.
Prerequisite: Two semesters of quantum mechanics, e.g., Physics 143a,b or equivalent.

Physics 247r. Laboratory Course in Contemporary Physics
Catalog Number: 8665 Enrollment: Together with Physics 191r, limited to a total of 24 students.
Peter S. Pershan (fall and spring), Masahiro Morii (fall term), Costas D. Papaliolios (spring term), Isaac F. Silvera (spring term), and Robert M. Westervelt (fall term)
Half course (fall term; repeated spring term). Tu., Th., 1–5. EXAM GROUP: 15, 16, 17
Three experimental projects are selected representing condensed matter, atomic, nuclear, and particle physics. Examples: experiments on NMR, microwave spectroscopy, optical pumping, scattering of laser light, neutron activation, Compton scattering of gamma rays, relativistic mass of the electron, recoil-free gamma-ray resonance, lifetime of the muon, superfluid helium, superconducting transitions, and properties of semiconductors.
Note: The course cooperates with Applied Physics 210r. A substantial amount of outside reading may be required.

[Physics 248. Phenomena of Elementary Particle Physics ]
Catalog Number: 5431
Melissa Franklin
Half course (spring term). Hours to be arranged.
A systematic introduction to the phenomena of elementary particle interactions. Topics: symmetries, hadron spectroscopy, deep inelastic scattering and structure functions, QCD, heavy quark production and decay, CP violation, symmetry breaking, Higg’s mechanism, and others.
Note: Expected to be given in 2001–02.
Prerequisite: Physics 245 or equivalent.

Physics 251a. Advanced Quantum Mechanics I
Catalog Number: 2191
Charles M. Marcus
Half course (fall term). M., W., F., at 12. EXAM GROUP: 5
Basic course in nonrelativistic quantum mechanics. Review of wave functions and the Schrodinger Equation; Hilbert space; the WKB approximation; central forces and angular momentum; scattering; electron spin; measurement theory; the density matrix; time-independent perturbation theory.
Prerequisite: Physics 143a,b or equivalent, or permission of instructor.

Physics 251b. Advanced Quantum Mechanics II
Catalog Number: 2689
Charles M. Marcus
Half course (spring term). M., W., F., at 12. EXAM GROUP: 5
Time-dependent perturbatons; quantized radiation field; absorption and emission of radiation; identical particles and second quantization; symmetry groups.
Prerequisite: Physics 251a.

Physics 253a. Quantum Field Theory
Catalog Number: 8050
Sidney Coleman
Half course (fall term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
Introduction to relativistic quantum mechanics and quantum field theory. Canonical quantization, scalar and spinor fields, scattering theory, Feynman diagrams, renormalization.
Prerequisite: Physics 251a,b or equivalents.

Physics 253b. Quantum Field Theory
Catalog Number: 5250
Sidney Coleman
Half course (spring term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
A continuation of Physics 253a. Vector fields, gauge invariance, functional integration, quantum electrodynamics, spontaneous symmetry breakdown, and an introduction to the standard model.
Prerequisite: Physics 253a.

Physics 262. Statistical Physics
Catalog Number: 1157
Efthimios Kaxiras
Half course (fall term). M., W., F., at 3. EXAM GROUP: 8
Basic principles of statistical physics and thermodynamics, with applications including: the equilibrium properties of classical and quantum gases; phase diagrams, phase transitions and critical points, as illustrated by the gas-liquid transition and simple magnetic models; fluctuations about equilibrium, and the response to time-dependent perturbations.
Note: It is suggested that students may wish to take Applied Physics 284 when this course is bracketed.
Prerequisite: Ordinarily, Physics 143a,b and Physics 181 or Engineering Sciences 181.

Physics 264. Group Theory with Application to Particle Physics
Catalog Number: 5317
Andrew Cohen
Half course (spring term). M., W., F., at 11. EXAM GROUP: 4
Introduces the theory of Lie groups and their representations. Emphasizes compact groups and applications to particle physics.
Prerequisite: Physics 143a and 143b or equivalent.

[Physics 266. Topics in Bose-Einstein Condensation and Superfluidity]
Catalog Number: 0104
Isaac F. Silvera
Half course (spring term). Hours to be arranged.
This special topics course will present a deep treatment of Bose-Einstein condensation and superfluidity in fluids of identical bosons. Both the homogeneous systems such as superfluid helium and the inhomogeneous systems such as the alkali gases and spin-polarized hydrogen will be considered in three and two dimensions. The material will be balanced between theory and experiment. Degenerate Fermion systems will also be discussed.
Note: Expected to be given in 2001–02.
Prerequisite: Quantum mechanics and statistical mechanics.

Physics 268r. Theory of Many-Particle Systems
Catalog Number: 7951
Subir Sachdev (Yale University)
Half course (spring term). M., W., 1–2:30. EXAM GROUP: 6, 7
An introduction to the modern theory of phase transitions presented using examples drawn from quantum many-body systems. Physics of the quantum lsing model, magnetically ordered and spin-gap states of antiferromagnets, the superfluid-insulator transition, and phases of Fermi liquids. Bosonization methods in one dimension. Other topics drawn from current research depending on student interest.
Prerequisite: Physics 262 or equivalent.

[Physics 270. Experiments and Ideas in Mesoscopic Physics]
Catalog Number: 0788
Charles M. Marcus
Half course (spring term). Hours to be arranged.
This special topics course introduces the subject of mesoscopic quantum effects in small electronicsystems, including conductance fluctuations, localization, electron interference, and persistance currents in metals and semiconductors. More or less attention will be given to specialized topics such as hybrid superconducting systems, magnetic and Kondo systems, clean (ballistic) systems,dynamical effects, and the high magnetic field regime, depending on the interests of participants. The reading list will focus primarily on the experimental literature, augmented by recent texts and reviews. The format of the course will be a combination of lectures and journal-club-style presentations.
Note: Expected to be given in 2001–02.
Prerequisite: Basic familiarity with quantum mechanics and solid state physics at the level of undergraduate courses.

Physics 283. The Standard Model
Catalog Number: 3620
Nima Arkani-Hamed (University of California, Berkeley)
Half course (spring term). W., F., 2:30–4. EXAM GROUP: 7, 8
Theory and phenomenology of the Standard Model of particle physics. SU(2)xU(1)xSU(3) gauge theory of the electroweak and strong interactions. Neutral currents, W and Z, charm, bottom and top, and electroweak symmetry breaking. Additional topics in advanced quantum field theory including some or all of the following: including effective field theory; effective chiral theories; heavy quark effective theory; supersymmetry; and unified gauge theories.
Prerequisite: Physics 253a,b or equivalent.

Physics 285. Non-Relativistic Quantum Electrodynamics
Catalog Number: 3264
Roy J. Glauber
Half course (fall term). W., F., 1–2:30. EXAM GROUP: 6, 7
Quantum theory of interactions of light with various atomic systems. Coherence and statistical optics. Statistics of more general boson and fermion systems.
Prerequisite: A course in electromagnetic theory (Physics 232 or equivalent); one half course in intermediate or advanced quantum mechanics.

[Physics 287a. Introduction to String Theory]
Catalog Number: 2012
Juan Maldacena
Half course (fall term). Hours to be arranged.
Introduction to the perturbative formulation of string theories and eleven-dimensional supergravity. Basic examples of compactifications and solitonic solutions and their role in strong-weak coupling dualites in string theory.
Note: Expected to be given in 2001–02. Expected to be ommitted in 2000-01.
Prerequisite: Physics 253a,b or equivalent.

[Physics 287br (formerly Physics 287b). Topics in String Theory]
Catalog Number: 4555
Andrew Strominger
Half course (spring term). Hours to be arranged.
A selection of topics from current areas of research on string theory.
Note: Expected to be given in 2001–02.
Prerequisite: Physics 287a.

[Physics 289r. Supersymmetry and Invarients]
Catalog Number: 6400
Arthur M. Jaffe
Half course (spring term). Hours to be arranged.
Introduction to supersymmetry and constructive quantum field theory, with emphasis on applications to geometric problems.
Note: Expected to be given in 2001–02.
Prerequisite: Basic knowledge of quantum mechanics, analysis, and geometry.

Cross-listed Courses

Applied Mathematics 201. Complex Function Theory with Applications
Applied Mathematics 202. Partial Differential and Integral Equations
[Applied Mathematics 203. Topics in Applied Mathematics]
Applied Mathematics 205. Practical Scientific Computing
Applied Physics 216 (formerly Applied Physics 216r). Optics and Quantum Electronics
[Applied Physics 284. Statistical Thermodynamics]
Applied Physics 295a. Introduction to Quantum Theory of Solids
Applied Physics 295b. Quantum Theory of Solids
Applied Physics 296r. Superconductivity
[Applied Physics 298r. Materials Chemistry and Physics: Seminar]
*Astronomy 204. Galactic and Extragalactic Dynamics
Astronomy 206. Stellar Physics
Astronomy 208. The Physics of the Interstellar Medium
[MCB 212. Topics in Biophysics]

Graduate Courses of Reading and Research

Odd numbers designate courses of preliminary reading or experimental research. Even numbers designate thesis research and are to be used only when an instructor has agreed to supervise a student’s research for the doctorate. Reading and Research courses largely concerned with physics are offered under the sponsorship of several other departments, particularly Astronomy, Chemistry, and Earth and Planetary Sciences; and of the Division of Engineering and Applied Sciences (Applied Mathematics, Applied Physics, Computer Science, and Engineering Sciences).
*Physics 301,302. Experimental Atomic and Elementary Particle Physics
Catalog Number: 1735,1736
Gerald Gabrielse 1768

*Physics 305,306. Experimental High Energy Physics
Catalog Number: 7929,0855
John Huth 3506

*Physics 307,308. Experimental Atomic Physics, Bose-Einstein Condensation, & Quantum Optics
Catalog Number: 7534,3277
Lene V. Hau 2151

*Physics 309,310. Topics in Elementary Particle Theory
Catalog Number: 4556,4561
Cumrun Vafa 2069

*Physics 311,312. Experimental Atomic, Molecular, and Low-Energy Particle Physics
Catalog Number: 6839,6838
John M. Doyle 3507 (on leave spring term)

*Physics 313,314. Topics in String Theory, Quantum Gravity and Field Theory
Catalog Number: 9411,5350
Juan Maldacena 3697 (on leave 2000-01)

*Physics 315,316. Topics in Theoretical Atomic, Molecular, and Optical Physics
Catalog Number: 7387,8871
Eric J. Heller 1074

*Physics 319,320. Topics in Experimental High Energy Physics
Catalog Number: 4520,4521
Melissa Franklin 2500

*Physics 321,322. Experimental Soft Condensed Matter Physics
Catalog Number: 9963,7098
David A. Weitz 2497

*Physics 323. Nanostructures and Mesoscopic Physics
Catalog Number: 3629
Charles M. Marcus 2890

*Physics 324. Nanostructures and Mesoscopic Physics
Catalog Number: 9079
Charles M. Marcus 2890

*Physics 325,326. Electronic Theory of Condensed Matter
Catalog Number: 2946,2952
Henry Ehrenreich 2411 (on leave spring term)

*Physics 327,328. Topics in Condensed Matter Physics
Catalog Number: 5969,6524
David R. Nelson 5066 (on leave 2000-01)

*Physics 329,330. Solid State and Statistical Theory
Catalog Number: 6198,6373
Bertrand I. Halperin 4755

*Physics 331. Topics in Experimental High Energy Physics
Catalog Number: 2727
Andrew Foland 3335

*Physics 332. Topics in Experimental High Energy Physics
Catalog Number: 2820
Andrew Foland 3335

*Physics 333,334. Experimental Atomic Physics
Catalog Number: 2902,2904
Mara Prentiss 2741

*Physics 335,336. Topics in the History and Philosophy of Physics
Catalog Number: 6697,4276
Gerald Holton 1883

*Physics 337. Topics in Experimental High Energy Physics
Catalog Number: 1809
Masahiro Morii 3798

*Physics 338. Topics in Experimental High Energy Physics
Catalog Number: 6368
Masahiro Morii 3798

*Physics 339,340. Theory and Elementary Particles
Catalog Number: 3676,5962
Sheldon L. Glashow 2123

*Physics 341,342. Topics in Elementary Particles
Catalog Number: 1990,6602
Sidney Coleman 2111

*Physics 345,346. Experimental Gravitation: Radio and Radar Astronomy
Catalog Number: 5067,5072
Irwin I. Shapiro 7660

*Physics 351,352. Experimental Low Energy Physics
Catalog Number: 1134,1129
Costas D. Papaliolios 2970

*Physics 353,354. Topics in Statistical Physics
Catalog Number: 3721,5287
Paul C. Martin 2103

*Physics 355,356. Theory of Elementary Particles
Catalog Number: 1213,7654
Roy J. Glauber 2113

*Physics 357,358. Experimental Condensed Matter Physics
Catalog Number: 4430,5227
Robert M. Westervelt 6148

*Physics 361,362. Topics in Condensed Matter and Statistical Physics
Catalog Number: 3750,4793
Daniel S. Fisher 2600 (on leave spring term)

*Physics 363,364. Topics in Condensed Matter Theory
Catalog Number: 2957,2958
Efthimios Kaxiras 3050

*Physics 365,366. Topics in Mathematical Physics
Catalog Number: 5170,1567
Arthur M. Jaffe 2095

*Physics 367,368. Experimental Astrophysics
Catalog Number: 1075,1274
Paul Horowitz 3537 (on leave fall term)

*Physics 369,370. Experimental Condensed Matter: Synchrotron Radiation Studies
Catalog Number: 1538,1539
Peter S. Pershan 1105

*Physics 371,372. Topics in Experimental High Energy Physics
Catalog Number: 2519,6461
Gary J. Feldman 2599

*Physics 373,374. Topics in the History and Philosophy of Modern Physics
Catalog Number: 6140,6143
Peter L. Galison 3239

*Physics 375,376. Superconductivity and Mesoscopic Physics
Catalog Number: 1228,7663
Michael Tinkham 2131 (on leave spring term)

*Physics 377,378. Theoretical High Energy Physics
Catalog Number: 1436,2007
Tai T. Wu 1051 (on leave spring term)

*Physics 379,380. Topics in Elementary Particle Research and String Theory
Catalog Number: 7523,7524
Andrew Strominger 3700 (on leave spring term) (on leave spring term)

*Physics 383,384. Low Temperature Physics of Quantum Fluids and Solids; Ultra High Pressure Physics
Catalog Number: 3851,4395
Isaac F. Silvera 7468

*Physics 385,386. Topics in Biophysics
Catalog Number: 5901,5902
Howard C. Berg 1377 (on leave 2000-01)

*Physics 387,388. Topics in Quantum Optics and Molecular Physics
Catalog Number: 5772,5774
Eric Mazur 7952

*Physics 391,392. Gravitation Theory and Astrophysical Applications
Catalog Number: 6119,6293
William H. Press 4693 (on leave fall term)

*Physics 393,394. Topics in Elementary Particle Theory
Catalog Number: 6051,6218
Howard Georgi 4754 (on leave spring term)

*Physics 397,398. Experimental Condensed Matter Physics
Catalog Number: 7355,7356
Jene A. Golovchenko 1986