Physics

Faculty of the Department of Physics

Christopher Stubbs, Professor of Physics and of Astronomy (Chair)
Nima Arkani-Hamed, Professor of Physics, Associate of the Department of Physics (on leave 2007-08 )
Howard C. Berg, Herchel Smith Professor of Physics and Professor of Molecular and Cellular Biology
George Brandenburg, Senior Research Fellow in Physics
Adam E. Cohen, Assistant Professor of Chemistry and Chemical Biology and of Physics
Eugene A. Demler, Professor of Physics
John M. Doyle, Professor of Physics
Gary J. Feldman, Frank B. Baird, Jr. Professor of Science
Melissa Franklin, Mallinckrodt Professor of Physics (Director of Graduate Studies)
Gerald Gabrielse, George Vasmer Leverett Professor of Physics (on leave 2007-08 )
Peter L. Galison, Joseph Pellegrino University Professor
Howard Georgi, Harvard College Professor and Mallinckrodt Professor of Physics (Director of Undergraduate Studies)
Roy J. Glauber, Mallinckrodt Professor of Physics (on leave spring term)
Jene A. Golovchenko, Rumford Professor of Physics and Gordon McKay Professor of Applied Physics
Markus Greiner, Assistant Professor of Physics
Joao Pedro Guimaraes Da Costa, Assistant Professor of Physics
Bertrand I. Halperin, Hollis Professor of Mathematicks and Natural Philosophy
Lene V. Hau, Mallinckrodt Professor of Physics and of Applied Physics (on leave spring term)
Thomas C. Hayes, Lecturer on Physics
Eric J. Heller, Professor of Chemistry and Physics
Jennifer E. Hoffman, Assistant Professor of Physics
Paul Horowitz, Professor of Physics and of Electrical Engineering (on leave 2007-08 )
John Huth, Donner Professor of Science (on leave 2007-08 )
Arthur M. Jaffe, Landon T. Clay Professor of Mathematics and Theoretical Science
Efthimios Kaxiras, Gordon McKay Professor of Applied Physics and Professor of Physics (on leave fall term)
Mikhail D. Lukin, Professor of Physics
Vinothan N. Manoharan, Assistant Professor of Physics and Chemical Engineering
Charles M. Marcus, Professor of Physics
Paul C. Martin, John Hasbrouck Van Vleck Professor of Pure and Applied Physics (on leave fall term)
Eric Mazur, Gordon McKay Professor of Applied Physics and Professor of Physics (on leave spring term)
Masahiro Morii, Professor of Physics
David J. Morin, Lecturer on Physics (Assistant Director of Undergraduate Studies)
Venkatesh Narayanamurti, John A. and Elizabeth S. Armstrong Professor of Engineering and Applied Sciences, Professor of Physics, Dean of the School of Engineering and Applied Sciences
David R. Nelson, Arthur K. Soloman Professor of Biophysics and Professor of Physics and Applied Physics
Peter S. Pershan, Frank B. Baird, Jr. Professor of Science
Mara Prentiss, Mallinckrodt Professor of Physics
Lisa Randall, Professor of Physics (on leave spring term)
Subir Sachdev, Professor of Physics
Aravinthan D. T. Samuel, Associate Professor of Physics
Irwin I. Shapiro, Timken University Professor
Isaac F. Silvera, Thomas D. Cabot Professor of the Natural Sciences (on leave fall term)
Andrew Strominger, Professor of Physics
Cumrun Vafa, Donner Professor of Science
Ronald L. Walsworth, Senior Lecturer on Physics
David A. Weitz, Mallinckrodt Professor of Physics and of Applied Physics
Robert M. Westervelt, Mallinckrodt Professor of Applied Physics and of Physics
Tai T. Wu, Gordon McKay Professor of Applied Physics and Professor of Physics (on leave spring term)
Amir Yacoby, Professor of Physics
Matias Zaldarriaga, Professor of Astronomy and of Physics
Xiaowei Zhuang, Professor of Chemistry and Chemical Biology

Other Faculty Offering Instruction in Physics

James G. Anderson, Philip S. Weld Professor of Atmospheric Chemistry
Gerald Holton, Mallinckrodt Research Professor of Physics and Research Professor of the History of Science
Andrew J. M. Kiruluta, Assistant Professor of Radiology (Medical School)
Charles M. Lieber, Mark Hyman, Jr. Professor of Chemistry
Hongkun Park, Professor of Chemistry and Chemical Biology
Howard A. Stone, Vicky Joseph Professor of Engineering and Applied Mathematics
George M. Whitesides, Woodford L. and Ann A. Flowers University Professor

There are three separate calculus-based sequences of courses covering introductory physics: Physical Sciences 1, 2, and 3 and Physics 11a, 11b, or at the intermediate calculus level, Physics 15a, 15b, 15c. 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.

Physical Sciences 1, 2, and 3 present an introductory treatment of college physics and chemistry in 3 semesters. The courses will be thematically driven, with the themes being related to major societal issues and/or biological systems where appropriate. The Physical Sciences sequence is designed to meet 2 semesters of the physics as well as 1 semester of the chemistry required by all medical schools, and is intended to teach physical concepts in a way that is immediately relevant to students in the life sciences.

Most medical schools also accept the Physics 15 or Physics 11 sequences. Premedical students should inquire at the medical schools to which they expect to apply. Students who do not intend to take advanced courses in the mathematical sciences, and especially those concentrating in biology or biochemistry, may find that the Physical Sciences 1, 2, and 3 sequence covers a broader range of subject matter, and might more appropriately serve their needs than Physics 11a and 11b.

Further details may be found under the individual course headings.

Primarily for Undergraduates

Physical Sciences 1. Chemical Bonding, Energy, and Reactivity: An Introduction to the Physical Sciences
Catalog Number: 2225
James G. Anderson and Efthimios Kaxiras
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Physical Sciences 1 engages the principles of chemistry and physics within major conceptual themes that underpin critical contributions of the physical sciences to societal objectives. In particular, the concepts central to chemical bonding, kinetic theory of molecular motion, thermochemistry, kinetics, equilibria, entropy and free energy, acids and bases, electrochemistry, and nuclear chemistry will be taught in the context of (1) world energy sources, forecasts and constraints, (2) global climate change, and (3) modern materials and technology.
Note: This course is part of an integrated introduction to the physical science intended for students who plan to pursue a concentration in the physical or life sciences and/or satisfy pre-medical requirements in Chemistry. May not be counted toward a degree in addition to the former Chemistry 7. This course, when taken for a letter grade, meets the Core area requirement for Science A. Students interested in Physical Sciences 1 should take the Chemistry Placement Exam.
Prerequisite: A few operations of calculus are developed and used. Fluency in pre-calculus secondary school mathematics is assumed. Students are expected to have AP or honors level high school chemistry, or have completed Life and Physical Sciences A (LPS A) with a satisfactory grade.

Physical Sciences 2. Mechanics, Elasticity, Fluids, and Diffusion
Catalog Number: 6053
Melissa Franklin, Logan Stewart Mccarty, and Howard A. Stone
Half course (fall term). Tu., Th., 9:30–11, plus weekly discussion sections and laboratory sessions to be arranged. EXAM GROUP: 11, 12
An introduction to classical mechanics, with special emphasis on the motion of organisms in fluids, from proteins to planets. Topics covered include: kinematics, Newton’s laws of motion, oscillations, elasticity, random walks, diffusion, and fluids. Examples and problems set questions will be drawn from the life sciences and medicine.
Note: This course, when taken for a letter grade, meets the Core area requirement for Science A.
Prerequisite: Physical Sciences 1 (or Chemistry 7), Mathematics 1b, or the equivalent.

Physical Sciences 3. Electromagnetism, Light, Entropy, and Information
Catalog Number: 5262
George M. Whitesides, Melissa Franklin, Masahiro Morii, and Aravinthan D. T. Samuel
Half course (spring term). Tu., Th., 9:30–11, plus weekly discussion sections and five laboratory sessions to be arranged. EXAM GROUP: 11, 12
This course will examine the two universal driving forces that guide nearly all chemical and biological phenomena: electromagnetism and entropy. Detailed case studies will examine the biological applications of electromagnetic radiation and the role of information in biological systems. Topics covered include: electric and magnetic fields and forces, light, waves, entropy, and information processing in electronic circuits and in biology.
Note: This course is part of an integrated introduction to the physical sciences intended for students who plan to pursue a concentration in the life sciences and/or satisfy pre-medical requirements in Physics. May not ordinarily be taken for credit in addition to Physics 1b, 11b, or 15b. This course, when taken for a letter grade, meets the Core area requirement for Science A.
Prerequisite: Physical Sciences 2 (or Physics 1a or 11a), Mathematics 1b, or equivalent.

Physics 11a. Mechanics
Catalog Number: 3131
Cumrun Vafa
Half course (fall term). Tu., Th., 11:30–1; weekly ninety-minute discussion sections. EXAM GROUP: 13, 14
Physics 11a is the first half of a one-year physics sequence. It introduces classical mechanics, including the laws of conservation of energy, momentum, and angular momentum; translational motion of particles, rigid bodies, and fluids; rotational motion of rigid bodies; and description of waves. 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. This course, when taken for a letter grade, meets the Core area requirement for Science A.

Physics 11b. Electricity, Magnetism, and Waves
Catalog Number: 5472
Charles M. Marcus
Half course (spring term). Tu., Th., 9:30–11. EXAM GROUP: 11, 12
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 a brief introduction to quantum physics.
Note: May not be taken for credit by students who have passed Physics 15b or Physics 15c. This course, when taken for a letter grade, meets the Core area requirement for Science A.
Prerequisite: Physics 11a; Mathematics 21a or 23a.

Physics 15a. Introductory Mechanics and Relativity
Catalog Number: 1984
David J. Morin and Joao Pedro Guimaraes Da Costa
Half course (fall term; repeated spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
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; fluids; special relativity.
Note: This course, when taken for a letter grade, meets the Core area requirement for Science A. Laboratory sessions may be arranged.
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
Jennifer E. Hoffman and Masahiro Morii (fall term), and Subir Sachdev and Ronald L. Walsworth (spring term)
Half course (fall term; repeated spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
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. This course, when taken for a letter grade, meets the Core area requirement for Science A.
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
Markus Greiner (fall term) and Jennifer E. Hoffman (spring term)
Half course (fall term; repeated spring term). Tu., Th., 1:30-3, and three hours per week of conference and laboratory. EXAM GROUP: 15, 16
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. This course, when taken for a letter grade, meets the Core area requirement for Science A.
Prerequisite: Physics 15a, Physics 15b, or written permission of the Head Tutor in Physics. Mathematics preparation at least at the level of Mathematics 21b taken concurrently is required. Some prior knowledge of complex numbers (for example as taught in Mathematics 1b) is helpful. Linear algebra and differential equations are used extensively. Students taking Mathematics 21b concurrently will likely find that some concepts are introduced in Physics 15c before they have seen them in Mathematics 21b. Some students may wish to postpone Physics 15c until they have completed Mathematics 21b.

Physics 16. Mechanics and Special Relativity
Catalog Number: 2019
Howard Georgi
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
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.
Note: This course, when taken for a letter grade, meets the Core area requirement for Science A. Laboratory sessions may be arranged.
Prerequisite: Score of 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 17. Exploratory Physics Lab - (New Course)
Catalog Number: 2930 Enrollment: Limited to 18.
Amir Yacoby and Melissa Franklin
Half course (spring term). W., F., 2–6, includes one-hour weekly tutorial. EXAM GROUP: 7, 8, 9
The exploratory physics lab teaches students how to investigate physical phenomena from an experimental stand point. During the lab, students are required to make hypotheses about the underlying physics behind the phenomena and then experimentally test the validity of their hypotheses. During each experiment the students are required to identify the relevant experimental variables, suggest ways to measure them and implement these ideas in the lab. The lab is set up to enable students to follow their individual creativity and initiative in their experimental endeavor.
Note: Students explore at most three or four phenomena. Topics include mechanics, electromagnetism, buoyancy, surface tension and more. The experiments are chosen to match the student’s background level in physics and math.
Prerequisite: Physics 15a or 16 and preferably concurrent with Physics 15b.

*Physics 90r. Supervised Research
Catalog Number: 2460
David J. Morin and members of the Department
Half course (fall term; repeated spring term). Hours to be arranged.
Note: Primarily for 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 the Physics Department Web page. Course enrollment forms may be obtained from Lyman 233.

*Physics 91r. Supervised Reading Course for Undergraduates
Catalog Number: 1218
David J. Morin 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 Lyman 233 and on the Physics Department’s website. Course enrollment forms may be obtained from Lyman 233.

*Physics 95. Topics in Current Research
Catalog Number: 2806
Eric Mazur
Half course (fall term). M., at 3, W., 7:30–9 pm.
The goal of this tutorial is to guide students from learning physics by subject (E&M, quantum mechanics, etc.) to appreciating physics as an intense, diverse discipline of modern research. Every Wednesday evening a faculty member speaks on his/her area of research, preceded by assigned reading and a lecture designed to introduce students to some of the basic physics, as well as important developments and burning problems at the frontiers of research.
Note: Primarily for junior and senior concentrators.

Cross-listed Courses

[Science A-29. The Nature of Light and Matter]
Science A-39. Time
Science A-49. The Physics of Music and Sound

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 120 (formerly Physics 121). History and Philosophy of Modern Physics
Catalog Number: 0160
Peter L. Galison
Half course (spring term). Tu., Th., at 10. EXAM GROUP: 12
Philosophical questions raised by historical developments in 20th and 21st century physics, and conversely, historical-scientific questions raised by philosophical inquiry. Special and general relativity. Issues in quantum mechanics surrounding causality, determinism, realism, and probabilism. Atomic and thermonuclear weapons. Growth of large-scale experimental high-energy physics. What is meant by "unified" field theories? Is a reductionist theory of nature possible? Rise of string theory and nanosciences. Readings: scientific, historical, and philosophical texts.
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.
Thomas C. Hayes
Half course (fall term; repeated spring term). W., F., 1:30-5. EXAM GROUP: 6, 7, 8, 9
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. Moves quickly from passive circuits, to discrete transistors, then concentrates on operational amplifiers, used to make a variety of circuits including integrators, oscillators, regulators, and filters. The digital half of the course treats analog-digital interfacing, emphasizes the use of microcontrollers and programmable logic devices (PLDs).

Physics 125. Widely Applied Physics
Catalog Number: 6990
John M. Doyle
Half course (spring term). M., W., 12–1:30. EXAM GROUP: 5, 6
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. Example topics: the Big Bang, stars, nuclear reactions, and searches for extra-solar planets; aerodynamics, rockets and spacecraft; materials properties; electronic noise, lasers, and the global positioning system; magnetic resonance imaging, physiology of major organs, and health risks; energy use and production; climate and global change.
Prerequisite: Physics 15a, b, c, and mathematics at the level of Mathematics 21a (which may be taken concurrently). Physics 143a and 181 helpful, but not required.

Physics 136. Physics of Medical Imaging
Catalog Number: 0182
Andrew J. M. Kiruluta (Medical School)
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Presents the physics of modern medical imaging techniques. Explores the physics of diagnostic imaging from a unified electromagnetics’ viewpoint ranging from a simple mapping of radiation attenuation coefficients in X-ray, gamma radiative single photon (SPECT) and double photon (positron) emission tomography (PET), echo measurements in ultrasound, interferometric pulse echo characterization in optical coherence tomography (OCT) to resonance absorption in a nuclear magnetic resonance (NMR) induced inhomogeneously broadened RF absorber.
Prerequisite: Physics 15b or 11b and mathematics preparation at least to the level of Mathematics 21b taken concurrently. Physics 143a and b are recommended but not essential.

Physics 140. Introduction to Biophysics
Catalog Number: 5394
Howard C. Berg and Aravinthan D. T. Samuel
Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
An introduction to the physics and biology of stochastic processes that affect the behavior of cells, biopolymers and biological motors. Elements of probability and statistics, entropic elasticity, the random walk, diffusion, sedimentation and electrophoresis. Applications to sensory physiology, cell motility, stretching and twisting of DNA and the motion of motors along biopolymers.
Note: Given in alternate years. Lectures, problem sets, discussions. May not be taken for credit by students who have taken MCB 140.
Prerequisite: Mathematics at the level of 21a, Physics 15a, b or Physics 11a, b or permission of the instructor. Some familiarity with elementary statistical mechanics helpful.

[Physics 141. The Physics of Sensory Systems in Biology]
Catalog Number: 1284
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Half course (spring term). Hours to be arranged.
Living organisms use sensory systems to inform themselves of the sights, sounds, and smells of their surrounding environments. Sensory systems are physical measuring devices, and are therefore subject to certain limits imposed by physics. Here we will consider the physics of sensory measurement and perception, and study ways that biological systems have solved their underlying physical problems. We will discuss specific cases in vision, olfaction, and hearing from a physicist’s point of view.
Note: Expected to be given in 2008–09.
Prerequisite: Physics 11a,b or 15 a,b,c required. Physics 181 recommended, but not required.

Physics 143a. Quantum Mechanics I
Catalog Number: 1050
John M. Doyle (fall term) and Eugene A. Demler (spring term)
Half course (fall term; repeated spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Introduction to nonrelativistic quantum mechanics: uncertainty relations; Schrödinger equation; Dirac notation; matrix mechanics; one-dimensional problems including particle in box, tunneling, and harmonic oscillator; angular momentum, hydrogen atom, spin, Pauli principle; time-independent perturbation theory; scattering.
Prerequisite: Linear algebra including matrix diagonalization; Physics 15c or written permission of the Head Tutor.

Physics 143b. Quantum Mechanics II
Catalog Number: 0253
Lene V. Hau
Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Advanced topics in quantum mechanics, including quantum statistics, Bose-Einstein condensation, time-dependent problems, interaction of quantum systems with lasers, quantization of the radiation field, emission and absorption of radiation, collision theory, measurement theory, Bell’s inequality, entanglement and quantum teleportation, and introduction to quantum computing.
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 pm, 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
Ganpathy Murthy (University of Kentucky)
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, the role of variational principles, symmetry and conservation laws, Hamilton’s equations, Hamilton-Jacobi theory and phase space dynamics. Applications to celestial mechanics, quantum mechanics, the theory of small oscillations and classical fields, and nonlinear oscillations, including chaotic systems 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
Mikhail D. Lukin
Half course (spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Aimed at advanced undergraduates. Emphasis on the properties and sources of the electromagnetic fields and on the wave aspects of the fields. Course starts with electrostatics and subsequently develops the Maxwell equations. Topics: electrostatics, dielectrics, magnetostatics, electrodynamics, radiation, wave propagation in various media, wave optics, diffraction and interference. A number of applications of electrodynamics and optics 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 175. Quantum Electronics and Modern Optics]
Catalog Number: 9076
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Half course (spring term). Hours to be arranged.
Introduction to quantum electronics (laser physics) and modern optical physics aimed at advanced undergraduates. Review of electromagnetic theory and relevant aspects of quantum mechanics. Wave nature of light. Physics of basic optical elements. Propagation of focused beams, optical resonators, dielectric waveguides. Interaction of light with matter. Lasers. Physics of specific laser systems. Introduction to nonlinear optics. Modern applications.
Note: Expected to be given in 2008–09.
Prerequisite: Physics 15b, 15c, 143a, or permission of the instructor

Physics 181. Statistical Mechanics and Thermodynamics
Catalog Number: 6346
Vinothan N. Manoharan
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Introduction to thermal physics: basic concepts of thermodynamics (energy, heat, work, temperature, and 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 and Ronald L. Walsworth (fall term), and Peter S. Pershan, Isaac Silvera and Robert Westervelt (spring term)
Half course (fall term; repeated spring term). Tu., Th., 1–5. EXAM GROUP: 15, 16, 17, 18
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: 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
Robert M. Westervelt
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
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, and superconductivity.
Note: 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.

Cross-listed Courses

Applied Mathematics 147. Nonlinear Dynamical Systems
[Applied Physics 195. Introduction to Solid State Physics]
Astronomy 145. Topics in Astrophysics
Astronomy 150. Radiative Processes in Astrophysics
Astronomy 191. Astrophysics Laboratory
Astronomy 192. Tools and Techniques of Astronomical Measurements
Chemistry 160. Physical Chemistry
Chemistry 161. Statistical Thermodynamics
Chemistry 163. Frontiers in Biophysics
*Chemistry 165. Experimental Physical Chemistry
Earth and Planetary Sciences 131. Introduction to Physical Oceanography and Climate
Engineering Sciences 120. Introduction to the Mechanics of Solids
Engineering Sciences 123. Introduction to Fluid Mechanics and Transport Processes
Engineering Sciences 154. Electronic Devices and Circuits
Engineering Sciences 173. Electronic and Photonic Devices
Engineering Sciences 181. Engineering Thermodynamics
Engineering Sciences 190. Introduction to Materials Science and Engineering

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., 10–11:30. EXAM GROUP: 3, 4
An introduction to general relativity: Riemannian geometry; the Principle of Equivalence; Einstein’s field equation; the Schwarzchild solution, the Newtonian limit; experimental tests, black holes, the causal structure of spacetime.
Prerequisite: Physics 151 and 153, and Mathematics 21 or equivalents.

Physics 211. General Relativity, Cosmology, and Other Topics
Catalog Number: 0469
Frederik Denef
Half course (spring term). W., F., 2–3:30. EXAM GROUP: 7, 8
Our focus is the classical and quantum theory of black holes. The general Kerr-Newman solution; causal structure; Penrose diagrams; the classical laws of black hole mechanics, experimental evidence; Hawking radiation; the information paradox; de Sitter and black hole entropy.
Note: Auditors should obtain permission of instructor.
Prerequisite: General relativity at level of Physics 210 or equivalent. Physics 253a helpful, but not required.

Physics 218. Modern Dynamical Systems
Catalog Number: 1362
Paul C. Martin
Half course (spring term). Tu., 1–2:30, F., 1:30–3. EXAM GROUP: 6, 7, 15, 16
Classical hamiltonian theory. Integrable systems, nonlinear dynamics, and chaos. Maps, KAM theory, and bifurcations. Mixing and ergodic theory. Dynamics of continuous systems, especially fluids. Stochastic processes.
Prerequisite: Physics 151 and 143a, b or equivalent; Applied Math 201, 202 or equivalent.

Physics 232 (formerly Physics 232a). Advanced Classical Electromagnetism
Catalog Number: 4885
David R. Nelson
Half course (fall term). M., W., F., at 10. EXAM GROUP: 3
Maxwell’s equations in macroscopic media, conservation laws, Green’s functions, time-dependent solutions and radiation, scattering and diffraction, and gauge invariance. Time permitting: Debye-Huckel theory, Lorentz transformations, and radiation from rapidly accelerating charges and negative refractive index materials.
Prerequisite: Physics 153 and Applied Math 105a, 105b, 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 and Ronald Walsworth (fall term), and Peter S. Pershan, Isaac Silvera and Robert Westervelt (spring term)
Half course (fall term; repeated spring term). Tu., Th., 1–5. EXAM GROUP: 15, 16, 17, 18
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: A substantial amount of outside reading may be required.

[Physics 248. Phenomena of Elementary Particle Physics ]
Catalog Number: 5431
----------
Half course (spring term). Hours to be arranged.
An introduction to the phenomena of elementary particle physics. Topics include weak interactions, QCD deep inelastic scattering and nucleon structure functions, heavy quark production and decay and QED.
Note: Expected to be given in 2008–09.
Prerequisite: Some familiarity with relativistic quantum mechanics.

Physics 251a. Advanced Quantum Mechanics I
Catalog Number: 2191
Bertrand I. Halperin
Half course (fall term). M., W., F., at 12. EXAM GROUP: 5
Basic course in nonrelativistic quantum mechanics. Review of wave functions and the Schrödinger 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
Bertrand I. Halperin
Half course (spring term). M., W., F., at 12. EXAM GROUP: 5
Heisenberg picture; time-dependent perturbations; inelastic scattering; degenerate harmonic oscillators; electrons in a uniform magnetic field; quantized radiation field; absorption and emission of radiation; identical particles and second quantization; symmetry principles; Feynman Path integrals.
Prerequisite: Physics 251a.

Physics 253a. Quantum Field Theory I
Catalog Number: 8050
Arthur M. Jaffe
Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
Introduction to relativistic quantum mechanics and quantum field theory. Canonical quantization, scalar and spinor fields, scattering theory, Feynman diagrams, and renormalization.
Prerequisite: Physics 251a,b or equivalents.

Physics 253b. Quantum Field Theory II
Catalog Number: 5250
Arthur M. Jaffe
Half course (spring term). Tu., Th., 2–3:30. EXAM GROUP: 16, 17
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 253c. Quantum Field Theory III
Catalog Number: 4000
Howard Georgi
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
This course explores advanced topics in quantum field theory. Possible topics include semi-classical methods, tunneling in flat and curved spaces, topological defects, lattice gauge theories, conformal field theories in diverse dimensions, large N and string description of gauge theory, the AdS/CFT correspondence, and supersymmetric gauge theories in four dimensions.
Prerequisite: Physics 253b.

[Physics 262. Statistical Physics]
Catalog Number: 1157
Subir Sachdev
Half course (fall term). M., W., F., at 11. EXAM GROUP: 4
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; Bose-Einstein condensation.
Note: Expected to be given in 2008–09. Students may wish to take Applied Physics 284 when this course is bracketed.
Prerequisite: Physics 143a, b and Physics 181 or Engineering Sciences 181.

[Physics 268r. Classical and Quantum Phase Transitions]
Catalog Number: 7951
----------
Half course (spring term). Hours to be arranged.
The theory of phase transitions at zero and non-zero temperatures. Landau theory. Fluctuations and field theory. Renormalization group. Quantum transitions between insulators, superfluids, metals, and magnets. Modern ideas on the description of correlated states by emergent gauge fields.
Note: Expected to be given in 2008–09.
Prerequisite: Physics 262 or equivalent.

Physics 269r. Topics in Statistical Physics and Quantitative Biology
Catalog Number: 6214
David R. Nelson
Half course (spring term). M., W., F., at 11. EXAM GROUP: 4
Introduction to strongly interacting soft condensed matter and biophysical systems. We hope to discuss the theory of flexible polymer chains, single molecule biophysics, motor proteins, gene regulation and the statistical dynamics of mutations, selection and genetic drift.
Prerequisite: Physics 262, Applied Physics 284 or equivalent.

[Physics 270. Mesoscopic Physics and Quantum Information Processing]
Catalog Number: 0788
----------
Half course (spring term). Hours to be arranged.
Introduces the subject of quantum effects in electronic systems, including conductance fluctuations, localization, electron interference, and many-body effects such as the Kondo effect. This year, we will also focus on solid state implementations of quantum information processing systems.
Note: Expected to be given in 2008–09. The reading list focuses primarily on the experimental literature, augmented by recent texts and reviews. The format of the course is a combination of lectures and journal-club-style presentations. A term paper on a topic within mesoscopic condensed matter physics or quantum information will allow for deeper exploration. Given in alternate years.
Prerequisite: Basic familiarity with quantum mechanics and solid state physics at the level of undergraduate courses.

[Physics 271 (formerly Physics 287). Topics in the Physics of Quantum Information]
Catalog Number: 7647
Mikhail D. Lukin
Half course (fall term). Hours to be arranged.
Introduction to physics of quantum information, with emphasis on ideas and experiments ranging from quantum optics to condensed matter physics. Background and theoretical tools introduced. The format is a combination of lectures and class presentations.
Note: Expected to be given in 2008–09.
Prerequisite: Quantum mechanics at the level of introductory graduate courses.

[Physics 283b. Beyond the Standard Model]
Catalog Number: 7153
Nima Arkani-Hamed
Half course (fall term). Hours to be arranged.
Covers current advances in particle physics beyond the Standard Model. Topics could include supersymmetry, the physics of extra dimensions, and connections between particle physics and cosmology.
Note: Expected to be given in 2008–09.

[Physics 284. Strongly Correlated Systems in Atomic and Condensed Matter Physics]
Catalog Number: 4673
Eugene A. Demler and Mikhail D. Lukin
Half course (fall term). Hours to be arranged.
Explores an emerging interface involving strongly correlated systems in atomic and condensed matter physics. Topics include bosonic and fermionic Hubbard models, quantum spin systems, low dimensional systems, non-equilibrium coherent dynamics and system-bath interactions. Special attention to the physics of ultracold atoms. Potential application to quantum information and metrology. Lectures and seminar-like class presentations.
Note: Expected to be given in 2008–09.
Prerequisite: Graduate quantum mechanics or permission of instructors.

[Physics 285a. Modern Atomic and Optical Physics I]
Catalog Number: 8204
Mikhail D. Lukin
Half course (fall term). Hours to be arranged.
Introduction to modern atomic physics. The fundamental concepts and modern experimental techniques will be introduced. Topics will include two-state systems, magnetic resonance, interaction of radiation with atoms, transition probabilities, spontaneous and stimulated emission, dressed atoms, trapping, laser cooling of “two-level” atoms, structure of simple atoms, fundamental symmetries, two-photon excitation, light scattering and selected experiments. The first of a two-term subject sequence that provides the foundations for contemporary research.
Note: Expected to be given in 2008–09.
Prerequisite: One course in quantum mechanics (143a and b, or equivalent).

Physics 285b. Modern Atomic and Optical Physics II
Catalog Number: 4195
Mikhail D. Lukin
Half course (fall term). M., W., 12–1:30. EXAM GROUP: 5, 6
Introduction to quantum optics and modern atomic physics. The basic concepts and theoretical tools will be introduced. Topics will include coherence phenomena, non-classical states of light and matter, atom cooling and trapping and atom optics. The second of a two-term subject sequence that provides the foundations for contemporary research.
Prerequisite: A course in electromagnetic theory (Physics 232a or equivalent); one half-course in intermediate or advanced quantum mechanics.

[Physics 287a. Introduction to String Theory]
Catalog Number: 2012
Andrew Strominger
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 2008–09.
Prerequisite: Physics 253a, b or equivalent.

Physics 287br. Topics in String Theory
Catalog Number: 4555
Andrew Strominger
Half course (fall term). W., F., 2:30–4. EXAM GROUP: 7, 8
A selection of topics from current areas of research on string theory.
Prerequisite: Physics 287a.

[Physics 289r. Eigenvalues of Random Matrices]
Catalog Number: 6400
Arthur M. Jaffe
Half course (spring term). Hours to be arranged.
We study eigenvalues of random matrices from several points of view, including how supersymmetry helps in their understanding. These problems relate to different fields of physics, including random systems and quantum gravity.
Note: Expected to be given in 2008–09.
Prerequisite: Knowledge of quantum theory and of analysis. Knowledge of field theory will be helpful but is not essential.

Cross-listed Courses

Applied Mathematics 201. Physical Mathematics I
Applied Mathematics 202. Physical Mathematics II
[Applied Mathematics 203 (formerly Applied Mathematics 203r). Nonlinear Dynamics and Chaos]
Applied Mathematics 205. Practical Scientific Computing
[Applied Physics 216. Modern 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 298r. Interdisciplinary Chemistry, Engineering and Physics: Seminar
Engineering Sciences 274. Quantum Technology I
Engineering Sciences 275. Nanophotonics
[MCB 212. Topics in Biophysics]

Graduate Courses of Reading and Research

Courses of preliminary reading or experimental research are designated by “a.” Thesis research are designated by “b” and these courses are to be used only when an instructor has agreed to supervise a student’s research for the PhD. 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 301a,301b. Experimental Atomic and Elementary Particle Physics
Catalog Number: 1735,1736
Gerald Gabrielse 1768 (on leave 2007-08 )

*Physics 303a,303b. Sensory and Behavioral Neuroscience
Catalog Number: 1727,1792
Aravinthan D. T. Samuel 4625

*Physics 305a,305b. Experimental High Energy Physics
Catalog Number: 7929,0855
John Huth 3506 (on leave 2007-08 )

*Physics 307a,307b. Atomic/Bio-physics, Quantum Optics
Catalog Number: 7534,3277
Lene V. Hau 2151 (on leave spring term)

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

*Physics 311a,311b. Experimental Atomic, Molecular, and Low-Energy Particle Physics
Catalog Number: 6839,6838
John M. Doyle 3507

*Physics 313a,313b. Experimental Condensed Matter Physics
Catalog Number: 7154,6363
Amir Yacoby 5596

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

*Physics 317a,317b. Topics in Biophysics
Catalog Number: 8345,0990
Xiaowei Zhuang 3991

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

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

*Physics 323a,323b. Nanostructures and Mesoscopic Physics
Catalog Number: 3629,9079
Charles M. Marcus 2890

*Physics 327a,327b. Topics in Condensed Matter Physics
Catalog Number: 5969,6524
David R. Nelson 5066

*Physics 329a,329b. Condensed Matter and Statistical Theory
Catalog Number: 6198,6373
Bertrand I. Halperin 4755

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

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

*Physics 337a,337b. Topics in Experimental High Energy Physics
Catalog Number: 1809,6368
Masahiro Morii 3798

*Physics 339a,339b. Condensed Matter and Atomic Physics
Catalog Number: 5096,6843
Subir Sachdev 5252

*Physics 341a,341b. Topics in Experimental Atomic and Condensed Matter Physics
Catalog Number: 1990,6602
Markus Greiner 5344

*Physics 343a,343b. Observational Cosmology and Experimental Gravitation
Catalog Number: 4253,6881
Christopher Stubbs 4856

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

*Physics 347a,347b. Topics in Quantum Optics
Catalog Number: 8010,1627
Mikhail D. Lukin 3990

*Physics 351a,351b. Experimental Soft Condensed Matter and Materials Physics
Catalog Number: 6533,5661
Vinothan N. Manoharan 5251

*Physics 353a,353b. Topics in Statistical Physics
Catalog Number: 3721,5287
Paul C. Martin 2103 (on leave fall term)

*Physics 355a,355b. Theory of Elementary Particles
Catalog Number: 1213,7654
Roy J. Glauber 2113 (on leave spring term)

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

*Physics 359a,359b. Topics in Condensed Matter Physics
Catalog Number: 8238,7560
Eugene A. Demler 3847

*Physics 363a,363b. Topics in Condensed Matter Theory
Catalog Number: 2957,2958
Efthimios Kaxiras 3050 (on leave fall term)

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

*Physics 367a,367b. Experimental Astrophysics
Catalog Number: 1075,1274
Paul Horowitz 3537 (on leave 2007-08 )

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

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

*Physics 373a,373b. Historical and Philosophical Approaches to Modern and Contemporary Physics
Catalog Number: 6140,6143
Peter L. Galison 3239

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

*Physics 379a,379b. Topics in Elementary Particle Research and String Theory
Catalog Number: 7523,7524
Andrew Strominger 3700

*Physics 381a,381b. Experimental Condensed Matter Physics
Catalog Number: 1281,2355
Jennifer E. Hoffman 4888

*Physics 383a,383b. Low Temperature Physics of Quantum Fluids and Solids; Ultra High Pressure Physics
Catalog Number: 3851,4395
Isaac F. Silvera 7468 (on leave fall term)

*Physics 385a,385b. Topics in Biophysics
Catalog Number: 5901,5902
Howard C. Berg 1377

*Physics 387a,387b. Applied Photonics
Catalog Number: 5772,5774
Eric Mazur 7952 (on leave spring term)

*Physics 389a,389b. Topics in Field Theory: The Standard Model and Beyond
Catalog Number: 4393,2571
Lisa Randall 4255 (on leave spring term)

*Physics 391a,391b. Experimental Atomic Physics, Biophysics, and Soft Matter Physics
Catalog Number: 1006,2753
Ronald L. Walsworth 2263

*Physics 393a,393b. Topics in Elementary Particle Theory
Catalog Number: 6051,6218
Howard Georgi 4754

*Physics 395a,395b. Topics in Elementary Particle Theory
Catalog Number: 9844,9408
Nima Arkani-Hamed 3886 (on leave 2007-08 )

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