Department of Physics

The following list reflects the 2006/2007 faculty.

Chairman Bennett Goldberg

Associate Chairmen Karl Ludwig, Steven Ahlen

Faculty

Steven P. Ahlen Associate Chairman; Professor of Physics, College of Arts and Sciences (experimental high-energy physics, experimental astrophysics). BS, MS, University of Illinois; PhD, University of California, Berkeley

Richard Averitt Assistant Professor of Physics, College of Arts and Sciences (condensed matter experiment). BS, University of California, San Diego; MS, PhD, Rice University

Rama Bansil Professor of Physics, College of Arts and Sciences (biological physics, polymer physics); Assistant Professor of Physiology, School of Medicine. BSc, MSc, University of Delhi (India); PhD, University of Rochester

John M. Butler Professor of Physics, College of Arts and Sciences (experimental high-energy physics). BS, University of Notre Dame; PhD, Stanford University

Robert Carey Director of Undergraduate Studies; Associate Professor of Physics, College of Arts and Sciences (experimental high-energy physics). AB, AM, PhD, Harvard University

Antonio Castro Neto Professor of Physics, College of Arts and Sciences (condensed matter theory). BS, MS, State University of Campinas (Brazil); PhD, University of Illinois at Urbana — Champaign

Claudio Chamon Associate Professor of Physics, College of Arts and Sciences (condensed matter theory). BS, PhD, Massachusetts Institute of  Technology

Andrew Cohen Professor of Physics, College of Arts and Sciences (elementary particle theory). BS, Stanford University; PhD, Harvard University

Andrew Duffy Assistant Professor of Physics, College of Arts and Sciences. BS, Mount Allison University; PhD, Queen’s University (Ontario, Canada)

Maged El-Batanouny Professor of Physics, College of Arts and Sciences (surface physics). BS, Cairo University (Egypt); MS, PhD, University of California, Davis

Shyamsunder Erramilli Director of Graduate Studies; Professor of Physics and Biomedical Engineering, College of Arts and Sciences (biological physics). BS, University of Pune (India); MS, Indian Institute of Technology (India); PhD, University of Illinois

Sheldon L. Glashow Arthur G. B. Metcalf Professor of Science, College of Arts and Sciences (elementary particle theory). PhD, Harvard University; Nobel Laureate; DSc (hon.), Yeshiva University; DSc (hon.), Université d’Aix-Marseille II (France)

Bennett B. Goldberg Chairman; Professor of Physics, College of Arts and Sciences (condensed matter experiment). BA, Harvard University; MS, PhD, Brown University

Ulrich Heintz Associate Professor of Physics, College of Arts and Sciences (high-energy physics). Vordiplom in Physics, Universität Tübingen (Germany); PhD, State University of New York at Stony Brook

Mi K. Hong Research Professor of Physics, College of Arts and Sciences (biological physics). BS, Seoul National University (South Korea); PhD, University of Illinois, Urbana — Champaign

Emanuel Katz Assistant Professor of Physics, College of Arts and Sciences (elementary particle theory). BS, PhD, Massachusetts Institute of Technology

Edward T. Kearns Associate Professor, College of Arts and Sciences (particle astrophysics). BS, Massachusetts Institute of Technology; MA, PhD, Harvard University

William Klein Professor of Physics, College of Arts and Sciences (condensed matter theory); Associate Director, Center for Polymer Studies, Graduate School of Arts and Sciences. BA, PhD, Temple University

Paul Krapivsky Research Associate Professor of Physics, College of Arts and Sciences (statistical physics, condensed matter theory). MS, PhD, Moscow Institute of Physics and Technology

Kenneth D. Lane Professor of Physics, College of Arts and Sciences (elementary particle theory). BS, MS, Georgia Institute of Technology; PhD, Johns Hopkins University

Karl F. Ludwig Jr. Associate Chairman; Professor of Physics, College of Arts and Sciences (condensed matter experiment). BA, Cornell University; MS, PhD, Stanford University

James P. Miller Professor of Physics, College of Arts and Sciences (experimental intermediate-energy particle and nuclear physics). BS, MS, PhD, Carnegie Mellon University

Pritiraj Mohanty Associate Professor of Physics, College of Arts and Sciences (condensed matter experiment). BS, Revenshaw College; MSc, Indian Institute of Technology; PhD, University of Maryland

Meenakshi Narain Associate Professor of Physics, College of Arts and Sciences (experimental particle physics). BS, Gorakhpur University; PhD, State University of New York at Stony Brook

So-Young Pi Professor of Physics, College of Arts and Sciences (elementary particle theory). BS, Seoul National University (Korea); PhD, State University of New York at Stony Brook

Anatoli Polkovnikov Assistant Professor of Physics, College of Arts and Sciences (condensed matter physics). BA, MA, St. Petersburg State Technical University, PhD, Yale University

Claudio Rebbi Professor of Physics, College of Arts and Sciences (high-energy theory, computational physics). Director, Center for Computational Science. Laurea in Fisica, PhD, Università degli Studi di Torino (Italy)

Sidney Redner Professor of Physics, College of Arts and Sciences (statistical physics, condensed matter theory). AB, University of California, Berkeley; PhD, Massachusetts Institute of Technology

B. Lee Roberts Professor of Physics, College of Arts and Sciences (experimental intermediate-energy particle physics). BS, University of  Virginia; MS, PhD, College of William and Mary

James W. Rohlf Professor of Physics, College of Arts and Sciences (experimental high-energy physics). BA, BS, University of Minnesota; PhD, California Institute of Technology

Kenneth J. Rothschild Professor of Physics, College of Arts and Sciences (biological physics); Associate Professor of Physiology, School of Medicine. BS, Rensselaer Polytechnic Institute; PhD, Massachusetts Institute of Technology

Anders Sandvik Associate Professor of Physics, College of Arts and Sciences (condensed matter computational physics). MS, Abo Akademi University (Finland); PhD, University of California, Santa Barbara

Martin Schmaltz Assistant Professor of Physics, College of Arts and Sciences (high energy physics). Vordiplom, Gottingen University; MS, PhD, University of California

James Shank Research Professor of Physics, College of Arts and Sciences (high energy). BS, Oakland University; PhD, University of California, Berkeley

William J. Skocpol Faculty Director; Professor of Physics, College of Arts and Sciences (condensed matter experiment). BA, Michigan State University; MA, PhD, Harvard University

Kevin E. Smith Professor of Chemistry, Professor of Physics, College of Arts and Sciences (experimental condensed matter physics); Academic Advisor to the Trustee Scholars. BA, University of Dublin (Ireland); MS, MPhil, PhD, Yale University

H. Eugene Stanley Director, Center for Polymer Studies, Graduate School of Arts and Sciences; University Professor and Professor of Physics, College of Arts and Sciences (condensed matter theory); Professor of Physiology, School of Medicine. BA, Wesleyan University; PhD, Harvard University

James L. Stone Professor of Physics, College of Arts and Sciences (experimental high-energy physics). BS, Ohio University; MS, PhD, University of Michigan

Lawrence R. Sulak Professor of Physics, College of Arts and Sciences (experimental high-energy physics). BS, Carnegie-Mellon University; AM, PhD, Princeton University

Ophelia Tsui Associate Professor of Physics, College of Arts and Sciences (condensed matter experiment). BSc, University of Hong Kong; MSc, PhD, Princeton University

J. Scott Whitaker Associate Dean, Graduate School of Arts and Sciences; Professor of Physics, College of Arts and Sciences (experimental high-energy physics). BA, PhD, University of California, Berkeley

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Affiliated Faculty

Irving Bigio Professor of Physics, College of Arts and Sciences; Professor of Electrical Engineering and Professor of Biomedical Engineering, School of Engineering. BS, MS, PhD, University of Michigan

Kenneth Brecher Professor of Astronomy and Physics (astrophysics), College of Arts and Sciences. BS, PhD, Massachusetts Institute of Technology

Richard Brower Research Professor of Physics, College of Arts and Sciences; Professor of Electrical Engineering, School of Engineering. BA, MA, Harvard University; PhD, University of California, Berkeley

David Campbell Provost; Adjunct Professor of Physics, College of Arts and Sciences. BA, Harvard College; PhD, Cambridge University (England)

Charles DeLisi Professor of Physics; Arthur G. B. Metcalf Professor of Science and Engineering; Director, All University Graduate Program in Bioinformatics, College of Arts and Sciences, College of Engineering. PhD, New York University

Alvaro De Rüjula Professor of Physics, College of Arts and Sciences (elementary particle theory). PhD, Universidad Autónoma de Madrid (Spain)

Evan Evans Professor of Physics, College of Arts and Sciences; Professor of Electrical Engineering, School of Engineering

Roscoe Giles Associate Professor of Physics, College of Arts and Sciences; Deputy Director, Center for Computational Science;  Associate Professor of Electrical Engineering, School of Engineering. BA, University of Chicago; MS, PhD, Stanford University

Dirk Kreimer Professor of Physics and Mathematics, College of Arts and Sciences. PhD, University of Mainz (mathematical physics)

Amit Meller Associate Professor of Physics, College of Arts and Sciences; Associate Professor of Biomedical Engineering, School of Engineering. BS, Tel Aviv University; MS, PhD, Weizmann Institute of Science

Jerome Mertz Associate Professor of Physics, College of Arts and Sciences; Associate Professor of Biomedical Engineering, School of Engineering. BA, Princeton University; PhD, University of Paris VI, University of California, Santa Barbara

Theodore Moustakas Professor of Physics, College of Arts and Sciences; Professor of Electrical Engineering, School of Engineering. BS, MS, Aristotle University (Greece); PhD, Columbia University

Alexander Sergienko Associate Professor of Physics, College of Arts and Sciences; Associate Professor of Engineering. MS, PhD, Moscow State University (Russia)

Anna Swan Associate Professor of Physics, College of Arts and Sciences; Associate Professor of Electrical Engineering, School of Engineering. PhD, Boston University

Malvin C. Teich Professor of Physics, College of Arts and Sciences; Professor of Electrical and Computer Engineering, Biomedical Engineering, School of Engineering. BS, Massachusetts Institute of Technology; PhD, Cornell University

Selim M. Ünlü Professor of Physics, College of Arts and Sciences; Professor of Electrical Engineering, College of Engineering. BSc, Middle East Technical University (Turkey); MS, PhD, University of Illinois, Urbana-Champagne

Emeriti

Edward C. Booth Professor Emeritus of Physics, College of Arts and Sciences (experimental intermediate-energy and nuclear physics). AB, Princeton University; PhD, Johns Hopkins University

Bernard Chasan Professor Emeritus of Physics, College of Arts and Sciences (biophysics). AB, Columbia University; PhD, Cornell University

Robert S. Cohen Director Emeritus, Center for Philosophy and History of Science, Graduate School of Arts and Sciences; Professor Emeritus of Physics and Philosophy, College of Arts and Sciences (history and philosophy of science). BA, Wesleyan University; MS, PhD, Yale University

Ernesto Corinaldesi Professor Emeritus of Physics, College of Arts and Sciences (quantum mechanics). Dott. in Fisica, Università degli Studi di Roma (Italy); PhD, University of Manchester (England)

Dean S. Edmonds Jr. Professor Emeritus of Physics, College of Arts and Sciences (lasers). BS, PhD, Massachusetts Institute of Technology; MA, Princeton University

Wolfgang Franzen Professor Emeritus of Physics and Research Professor, College of Arts and Sciences (atomic physics, surface physics). BS, Haverford College; MA, Columbia University; PhD, University of Pennsylvania

William Hellman Professor Emeritus of Physics, College of Arts and Sciences (elementary particle theory). BS, Brooklyn College; PhD, Syracuse University

Frank Krienen Research Professor Emeritus of Engineering and Applied Physics, Graduate School of Arts and Sciences (experimental high-energy physics, accelerator physics). BS, IR, Universiteit van Amsterdam (Netherlands)

Abner Shimony Professor Emeritus of Philosophy and Physics, College of Arts and Sciences (foundations of physics). BA, PhD, Yale University; AM, University of Chicago; PhD, Princeton University

John J. Stachel Director, Institute of Relativity Studies, Graduate School of Arts and Sciences; Professor Emeritus of Physics, College of Arts and Sciences (general relativity). BS, City University of New York, City College; MS, PhD, Stevens Institute of Technology

Charles R. Willis Professor Emeritus of Physics, College of Arts and Sciences (condensed matter theory, quantum optics). AB, PhD, Syracuse University

George O. Zimmerman Professor Emeritus of Physics, College of Arts and Sciences (low-temperature physics). BS, MS, PhD, Yale University

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The Graduate Program

The Department of Physics offers programs leading to degrees of Master of Arts and Doctor of Philosophy in Physics.  A PhD in Cellular Biophysics is offered in conjunction with the Department of Physiology and the Biophysics Institute of the Medical School. The department also has an academic program for undergraduates leading to the simultaneous awarding of the BA and MA degrees. Details regarding this program are given in the Undergraduate Programs Bulletin.

The ratio of full-time faculty members to graduate students in the department is high, creating an atmosphere that allows graduate students easy and informal access to their professors.

During their first year in the Graduate School of Arts and Sciences, students are encouraged to explore the various research areas and facilities available in the department. They are not obliged to commit themselves firmly to a specific area of research until they have passed their comprehensive examination.

The Department of Physics provides many opportunities for research in various areas of physics. In theoretical physics, research areas include elementary particle physics, condensed-matter physics, statistical physics, econophysics, polymer physics, and cooperative phenomena in biological systems. Research being carried out in experimental areas include condensed-matter physics; surface physics; polymer physics; low-temperature physics; intermediate energy nuclear physics; high-energy physics; astrophysics; and biological physics.

The department is located at 590 Commonwealth Avenue and the Physics Research Building is at 3 Cummington Street. The physics buildings house offices for graduate students, staff, and faculty. They are equipped with atomic, nuclear, low-temperature, high-energy, surface physics, biological physics, and laser Raman spectroscopic laboratories. Instructional laboratories and lecture rooms are also located in these buildings. Major condensed-matter physics and biological physics research laboratories are also located in the Center for Photonics. Research is aided by a precision instrumentation shop, an electronics design facility, and a research computation facility, all of which may be used by graduate students. Research is also carried out at the Bates Linear Accelerator, Brookhaven National Laboratory, Fermi National Accelerator Laboratory, Stanford Linear Accelerator Center, CERN, National Synchrotron Light Source, the Advanced Light Source, Super Kamiokande (Japan), and the Stanford Synchrotron Radiation Laboratory.

An extensive network of computational facilities supports the research activities of the department. There are networked multiprocessor DELL and SGI servers and centralized Sun workstations available to departmental faculty, staff, and students. Additional Unix and Linux servers and workstations, as well as many Windows PC’s, are available to research groups.

For computationally intensive applications, students have access to supercomputing resources supported through the Center for Computational Science and the Office of Information Technology.  At the high end, these currently consist of an IBM BlueGene system with 1024 dual-processor compute nodes and an aggregate peak performance of 5.7 Tflops, IBM p690 servers with 112 processors and a peak capacity of about 600 Gflops, and an IBM p655 server with 48 processors and a peak capacity of about 200 Gflops, as well as an IBM Linux cluster with 52 two processor compute nodes and 24 display nodes. The Departmental Computer Facility supports a wide range of software applications for physics data collection, analysis, simulation, and visualization.

Further information is available from the Department of Physics at 590 Commonwealth Avenue, Boston, MA 02215; 617353-2600; or the Physics Department.


Admissions Tests and Prerequisites Applicants for admission are required to submit the results of the Graduate Record Examination General Test and Subject Test in Physics. They should have completed the equivalent of an undergraduate major in Physics, typically with a grade average of B or higher.

Seminars Seminars, with and without credit, are held in the various major areas of experimental and theoretical physics and astronomy. There is also a departmental colloquium.

MA in Physics

The department has prepared a pamphlet entitled Formal Requirements for Graduate Study in Physics, which lists the requirements for the MA degree in some detail. This pamphlet is available at the Department of Physics.

Advisor A faculty advisor is assigned to the student upon arrival. This advisor is succeeded by a thesis supervisor when the student chooses a thesis subject.

Course Requirements A total of eight courses (32 credits) are required (with grades of B – or higher). Of these, five must be lecture courses numbered between 500 and 850. These lecture courses must include CAS PY 581 Advanced Laboratory, CAS PY 511, 512 Quantum Mechanics, CAS PY 501 Mathematical Physics, CAS PY 521 Electrodynamics, and CAS PY 541 Statistical Physics and Thermodynamics I.

Written Comprehensive Examination and Thesis Requirements To qualify for a master’s degree, a student must either pass the written comprehensive examination, or write a thesis based on research and study in physics.

Examination Option A full description of the written comprehensive examination appears in the outline of the PhD program. A student must initially take this examination in September of the second year. A passing grade qualifies a student for the degree of Master of Arts; however, a pass with distinction is needed to qualify for the PhD degree.

Thesis Option The thesis option is available to those who do not achieve a passing grade in written comprehensive examination. MA thesis work typically is not accompanied by any departmental financial aid. To pursue the thesis option, a student should seek a faculty advisor to supervise the MA dissertation. The scope of the dissertation work is to be determined by the faculty advisor and should: (1) critically evaluate previous research in the candidate’s field; (2) present the results of a scientific investigation in an intelligible and logical manner; (3) apply known or new methods to advance an experimental technique, extend the application of a physical theory, or produce new data or observations.

As the research nears completion, the candidate writes a dissertation describing the results. The faculty advisor consults with the Director of Graduate Studies to appoint an examination committee which consists of four departmental faculty members, including a first and second reader. The committee will examine the candidate’s knowledge of the subject based on an oral defense of the dissertation. The defense consists of a general presentation of the candidate’s research which should last no more than 30 minutes. The candidate may then be questioned on the background, scope, and limits of the research work.

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PhD in Physics

The department has prepared a pamphlet entitled Formal Requirements for Graduate Study in Physics, which lists the requirements for the PhD degree in some detail. This pamphlet is available at the Physics Department.

Admissions Tests and Prerequisites For admissions tests, see above. The candidate must have completed the requirements for the master’s degree or its equivalent in physics.

Course Requirements A total of eight courses (32 credits) beyond those used to fulfill the master’s degree requirements are required (with grades of B – or higher). Of these, five must be lecture courses numbered between 500 and 850.

Up to three nonlecture courses (numbered above 850) may be counted toward the course requirements, but no more than one directed study course and one seminar course may be counted toward the course requirements.

The formal lecture courses must include one semester of CAS PY 581 Advance Laboratory, unless this was taken to fulfill the master’s degree requirements, and two distribution courses for either Category I (elementary particle and mathematical physics) or Category II (biological physics and condensed-matter physics). A student whose research lies within Category I topics must take two courses from among those listed in Category II and vice versa. The courses in each category are listed below.

Category I: Elementary Particle, Computational, and Mathematical Physics CAS PY 502, 551, 561, 621; GRS PY 701, 702, 713, 714, 731, 751, 752, 761, 762, 811

Category II: Biological Physics, Computational, and Condensed-Matter Physics CAS PY 502, 542, 543,621; GRS PY 741, 742, 743, 747, 771, 841, 842. Note: Only one of PY 502 and 621 may be counted towards the distribution requirement.

Students are expected to audit one course each term from the list of 700- and 800-level courses after the completion of formal course requirements. The tuition for such audits is covered by the continuing student fee.

Qualifying Examinations A student is required to demonstrate proficiency in physics on a comprehensive written examination which covers a range of fundamental topics, and a more specialized preliminary oral examination. The written examination must be completed with distinction before a student is eligible to attempt the oral examination. The oral examination involves the presentation of results of a limited-scale research project. In this examination, the candidate is expected to demonstrate both research competency and mastery of the basic underlying knowledge. The detailed requirements for each examination are outlined below. The written and oral examinations together constitute the PhD Qualifying Examination required by the Graduate School of Arts and Sciences. Upon successful completion of both sections, the student is formally advanced to PhD candidacy and may begin a doctoral research project.

Written Comprehensive Examination The Written Comprehensive Examination consists of two sessions that are given twice each year in August/September and January, prior to the beginning of instruction. The examination tests knowledge of five basic areas of physics at approximately the MA degree level in the United States, corresponding to the 500-level physics courses at Boston University. The five basic areas are: (1) classical mechanics, (2) electromagnetic theory, (3) quantum mechanics, (4) modern physics, (5) thermodynamics and statistical mechanics. The possible examination grades are fail, pass, or pass with distinction (high pass). While a “pass” is sufficient to qualify for the master’s degree, a PhD degree candidate must attain a “pass with distinction.”

1. Postbachelor’s Program Postbachelor’s students are expected to take the examination initially no later than September of their second year of study at Boston University. Students not achieving a high pass on the first attempt are expected to retake the examination when it is next offered. Generally only two examination attempts are permitted.

If a high pass is not achieved by the second attempt, a student who has satisfied the appropriate course and language requirements may receive a terminal master’s degree if the comprehensive examination was passed at the master’s level or if a master’s dissertation is completed.

2. Post-master’s Program All post-master’s students are expected to take the examination inititally no later than January of their first year after admission into the program. Students not achieving a high pass on the first attempt are expected to retake the examination when it is next offered. Generally, only two attempts at the examination are permitted.

Oral Qualifying Examination The Oral Qualifying Examination has four purposes: (1) to enable faculty to judge a student’s ability to carry out research at the level required for the completion of a PhD, (2) to allow a student to explore in a preliminary way a research field and a possible thesis topic, (3) to allow a student and faculty member to test a working relationship; and (4) to test the student’s breadth of knowledge, awareness of the literature, and understanding of the relationships of the research to other fields of physics. Successful completion of the oral exam is the crucial first step in beginning a research career in physics.

1. Prerequisites Eligibility for the oral exam requires a pass with distinction in the Written Comprehensive Examination and a passing grade in CAS PY 581 Advanced Laboratory.

2. Deadlines The Oral Qualifying Examination is normally taken within one calendar year of successful completion of the Written Comprehensive Examination. In addition, it must be taken no later than January of the third year after admission for postbachelor’s students, and no later than May of the second year for post-master’s students.

3. Procedures An eligible student seeks a faculty advisor and together they formulate a test project. The precise nature of the project and the degree of faculty supervision should be determined after consultations between the student and the supervising faculty member. An experimental project might consist of a feasibility study, a study of the implications of published experimental results, or an actual experiment. A theoretical project might entail concentrated study on a specific topic, or a theoretical calculation based on newly acquired knowledge. It is strongly recommended, though not required, that the project involve original research. The usual duration of the project is one semester.

When the project is completed, the student undergoes an oral examination which is conducted by a committee of four faculty members, including the faculty supervisor. The committee is proposed by the supervisor and must be approved by the director of graduate studies. The committee should be finalized at least three weeks prior to the scheduled examination date. At least two weeks in advance of the examination, the student must submit a one-page abstract to the examination committee. The examination is open only to members of the Graduate School faculty.

The oral qualifying examination consists of an oral presentation which should last no longer than 45 minutes. After the presentation, the student may be questioned about the details of the presentation, his/her understanding of related fields of physics, the basic physical principles underlying any aspect of this project, and the relevance of the project to a broader context. The questioning may be far-ranging, as befits a qualifying exam. The entire examination will normally last one-and-one-half to two hours.

A student who passes the oral qualifying examination is advanced to PhD candidacy and should proceed with dissertation research.

Residency Requirement, Dissertation Prospectus, Dissertation, and Final Oral Examination See the departmental brochure Formal Requirements for Graduate Study in Physics and the General Requirements for the PhD section on this website.

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PhD in Cellular Biophysics

See requirements under Cellular Biophysics Program on this website .

Courses

CAS PY 501 Mathematical Physics

Boundary value problems with an emphasis on electrostatics; Maxwell equations in vacuum; complex analysis and contour integrals; variational calculus; Sturm-Liouville theory; Fourier and Laplace transforms; group theory; tensors; approximate methods; iterative maps; numerical analysis; nonlinear methods. Ahlen. 4 cr, 1st sem.

CAS PY 502 Computational Physics

Prereq: consent of instructor. Fundamental methods of computational physics and applications; numerical algorithms; linear algebra, differential equations; computer simulation; vectorization, parallelism, and optimization. Examples and projects on scientific applications. Sandvik. 4 cr, 1st sem.

CAS PY 511 Quantum Mechanics I

Prereq: CAS PY 451 and PY 452; coreq: CAS PY 501. General theory of quantum mechanics including the Schrödinger, Heisenberg, and interaction pictures. The path integral formulation. Angular momentum: orbital and spin angular momentum, addition of angular momenta, Wigner-Eckart theorem. Scattering theory: time-independent, partial waves and phase shift, identical particles, time-dependent, and propagators. Lane. 4 cr, 1st sem.

CAS PY 512 Quantum Mechanics II

Prereq: CAS PY 511. Continuation of CAS PY 511. Degenerate and nondegenerate perturbation theory. Second quantization of nonrelativistic systems with applications to scattering, lifetime of excited atomic states, and many-body problems. Relativistic quantum mechanics: Klein-Gordon equation, Dirac equation. Lane. 4 cr, 2nd sem.

Prereq: CAS PY 405. Vector and tensor analysis. Electrostatics, uniqueness, electrostatic energy, capacitance. Boundary value problems, conformal mapping, variable separation, Green’s functions. Multipole expansion, electric polarization, atomic models, anisotropic media. Contour integration and application to frequency-dependent dielectric constant. Dielectrics, electrostatic energy, boundary value problems. Ahlen. 4 cr, 2nd sem.

CAS PY 522 Electromagnetic Theory II

Prereq: CAS PY 521. Continuation of CAS PY 521. Magnetostatics, dipole moment, magnetic materials, boundary value problems. Electromagnetic induction, magnetic energy, Maxwell’s equations. Electromagnetic waves in materials, reflection, refraction. Waveguides. Scattering and diffraction. Special relativity, Lorentz transformation, covariant electrodynamics. Interaction of charges with matter. Radiation, Lienard-Wiechert potential, synchrotron radiation, antennas. Erramilli. 4 cr, 1st sem. To be offered 2007/2008

CAS PY 541 Statistical Mechanics I

Prereq: CAS PY 410. Probability theory. Ensembles. Steepest descent methods. Paramagnetism, ideal gas, Einstein model, adsorption isotherms. Thermodynamics, Maxwell relations, heat capacity. Bose and Fermi gases. Electrons in metals, white dwarf stars, black-body radiation, phonons, Bose-Einstein condensation. Interacting systems, virial expansion, Van der Waals gas. Phase transitions; mean-field theories, spin systems. Redner. 4 cr, 1st sem.

CAS PY 542 Statistical Mechanics II

Prereq: CAS PY 541. Continuation of CAS PY 541; emphasis on non-equilibrium statistical mechanics. Fluctuations: equilibrium fluctuations, instabilities, fluctuation dissipation theories. Elementary kinetic theory: mean free path approach, Boltzmann equation. Stochastic mathematics: probability theory, Markoff processes, Gaussian processes, first-passage processes. Brownian motion: Langevin equations, Fokker-Planck equation. Klein. 4 cr, 1st sem.

CAS PY 543 Introduction to Solid-State Physics

Prereq: CAS PY 406, PY 410, and PY 451. An introduction to crystal structure and defects; crystal binding; reciprocal space and applications: crystal diffraction, Brillouin zones, density of states; lattice vibrations; specific heat; electronic bands and Fermi surfaces; metals, semiconductors and insulators. Simple transport equations. Introduction to magnetism and superconductivity. Smith. 4 cr, 2nd sem.

CAS PY 551 Introduction to Particle Physics

Prereq: CAS PY 451 and PY 452. Fundamental particles and their symmetries. Isospin and flavor. Discrete symmetries. Phenomenology of weak and strong interactions. Introduction to detector techniques. Rohlf. 4 cr, 2nd sem.

CAS PY 561 Introduction to Nuclear Physics

Prereq: CAS PY 511. A general introduction to nuclear physics. Topics covered include an introduction to the nucleus, nuclear forces, theories of nuclear structure, decay and reaction processes, and special topics of interest, such as nuclear energy, origin of nuclei, etc. (Course offered only upon sufficient demand.) Staff. 4 cr, 1st sem.

CAS PY 581 Advanced Laboratory

Prereq: CAS PY 354. Classical experiments in atomic and nuclear physics; development of new experiments; basic research projects. Experiments include magnetic resonance, nuclear decay studies, Zeeman effect, holography, black-body radiation, x-ray diffraction, Mössbauer studies, positron annihilation, and flux quantization. Sulak. 4 cr, 1st sem.

GRS PY 621 Advanced Scientific Computing in Physics

Introduces advanced computational techniques for research problems in physics, with emphasis on computationally intensive applications in a massively parallel supercomputing environment. Corequisite laboratory meets together with CAS CS 512 (or CAS CS 551), CH 455, and ENG EK 521, focusing on algorithms and computational tools with cross-disciplinary application. Rebbi. 4 cr, 2nd sem.

CAS PY 681 Electronics for Scientists

Prereq: CAS PY 212 or PY 252, and CAS MA 124; or consent of instructor. A survey of practical electronics for all science students who wish to gain a working knowledge of electronic instrumentation and, in particular, its construction. Two four-hour laboratory-lecture sessions per week. Staff. 4 cr, 2nd sem.

GRS PY 699 Teaching College Physics I

The goals, contents, and methods of instruction in physics. General teaching-learning issues. Required of all teaching fellows. TBA. 2 cr, 1st & 2nd sem.

GRS PY 701, 702 Advanced Mathematical Physics

Prereq: CAS PY 501 or equivalent. Mathematical structures; algebraic systems, topological spaces, measure theory, and integration. Functional analysis: Banach and Hilbert spaces, linear functionals, operators, and spectral theory. Other applications at discretion of instructor. (Course offered only upon sufficient demand.) Staff. 4 cr, 1st sem. & 2nd sem.

GRS PY 711 Advanced Quantum Theory for Condensed Matter

Prereq: CAS PY 511, PY 512. Scattering and multiple scattering theory. Field quantization, Green’s function, time-ordering, and Wick’s theorem. Perturbation theory and Feynman diagrams. Correlation functions and density matrices. Spontaneous symmetry breaking and Goldstone’s theorem. (Course offered only upon sufficient demand.) Staff. 4 cr, 1st sem.

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GRS PY 713 Quantum Field Theory I

Prereq: CAS PY 511 and PY 512. For particle physics students concurrent enrollment in CAS PY 551 or GRS PY 751 is strongly recommended. Provides an introduction to the techniques of quantum field theory with applications to high-energy and condensed-matter physics. Topics include field equations and quantization of many-body systems; Green function and linear response theory; Smatrix and scattering theory; path integration; perturbation expansions and the Feynman rules; renormalization and effective field theories; expansion and critical exponents. (Course offered only upon sufficient demand.) Staff. 4 cr, 1st sem.

GRS PY 714 Quantum Field Theory II

Prereq: GRS PY 713 and PY 751 or equivalent. A continutation of GRS PY 713 for particle physicists. Topics include relativistic fields; LSZ formalism; the Lorentz group; quantum electrodynamics; nonabelian gauge symmetry; spontaneous symmetry breaking; Goldstone’s theorem; the Higgs mechanism; the Glashow-Weinberg-Salam model. (Course offered only upon sufficient demand.) Staff. 4 cr, 2nd sem.

GRS PY 731 Theory of Relativity

Prereq: CAS PY 521, PY 522, and PY 531, or consent of instructor. Space-times, space-time structures and gravitation. Affine spaces, pseudo-metric spaces and special-relativistic space-time. Manifolds, connections, and curvature. Four-dimensional formulation of Newton’s Theory of Gravitation. Physics in locally special-relativistic space-times. Gravitational field equations. Weak gravitational fields. Schwarzchild solution. Variational principles and initial value problems. Gravitational radiation. Cohen. (Course offered only upon sufficient demand.) 4 cr, 2nd sem.

GRS PY 741 Solid-State Physics I

Prereq: CAS PY 511, PY 512, PY 541, and PY 542, or equivalent. Methods and properties of electron and phonon band structures — local density functional, Green functions (APW and KKR) and phase shift, pseudopotentials, tight binding. Representative systems: covalent, ionic, simple metals, transition metals, transition metal compounds, and correlation gaps. Screening, dielectric function and applications: optical properties and photoemission, excitons, electron-photon interaction, Kohn anomalies, lattice instabilities. Electrons and phonons at surfaces. Transport equations. Polkovnikov. 4 cr, 1st sem.

GRS PY 742 Solid-State Physics II

Prereq: GRS PY 741. Continuation of CAS PY 741; applications of quantum theory to solid-state systems with many-body effects: electron-phonon interaction and the Frölich Hamiltonian, polarons, superconductivity; microscopic theory of magnetism, spin waves, and magnons. Quantum transport theory and the Kubo formula. Scattering theory, localized states, averaging over disorder; Anderson localization. Various topics of current interest: quantum antiferromagnets, charge and spin density waves, heavy fermions, surface physics, quantum Hall effect, metal-insulator transition. Polkovnikov. 4 cr, 2nd sem.

GRS PY 743 Low-Temperature Physics

Prereq: CAS PY 512, PY 542. Superconductivity, superfluidity, and properties of 3He and 4He at low temperatures. Techniques and measurement of physical quantities near absolute zero. (Course offered only upon sufficient demand.) Staff. 4 cr, 1st sem.

GRS PY 744 Polymer Physics

Prereq: CAS PY 541 or GRS CH 653, and consent of instructor. Introduction to polymer physics, focusing on the structure, phase behavior, and dynamics of isolated chains, polymer solutions, and gels. Development of underlying theoretical formalism and comparison with experimental results. Discussion of applications to novel polymeric materials. (Course offered only upon sufficient demand.) Bansil. 4 cr.

GRS PY 747 Advanced Statistical Mechanics

Prereq: CAS PY 501, PY 512, PY 531, and PY 542. Classical and quantum statistical ensembles and their physical interpretations; connection between statistical and thermodynamic quantities. Irreversible process: Boltzmann equation, transport theory, thermal fluctuations, introduction to stochastic process theory. Applications, e.g., imperfect gases, phase transitions, cooperative phenomena, and liquid helium. (Offered alternate years.) Klein. 4 cr, either sem.

GRS PY 751, 752 High-Energy Physics

Prereq: CAS PY 511 and PY 512, or consent of instructor. Yearlong course on phenomenological aspects of modern high-energy physics. Principal topics are the standard model of strong and electro-weak interactions and the physics of electro-weak symmetry breaking. Intended for both theoretical and experimental students and emphasizes current calculational techniques. (Offered alternate years.) Katz. 4 cr, 1st & 2nd sem.

GRS PY 761 Nuclear Physics

Prereq: CAS PY 511 and PY 512. Nuclear properties. Experimental methods of nuclear physics. Electron scattering and nuclear form fractors. Muonic atoms. Symmetries and conservation laws in nuclear physics. Nuclear models. The nucleon-nucleon force and the nuclear forces. Weak interactions and decay. (Course offered only upon sufficient demand.) Staff. 4 cr, 1st sem.

GRS PY 762 Intermediate Energy Physics

Prereq: CAS PY 511 and PY 512; GRS PY 711; GRS PY 761 and consent of instructor. The pion-nucleon system, pion physics, muon physics and weak interactions, photo production of mesons of nucleons and nuclei, exotic atoms, and hypernuclei. Hadron scattering at intermediate and high energies. (Course offered only upon sufficient demand.) Staff. 4 cr, 2nd sem.

GRS PY 771 Biophysics

Prereq: facility with calculus; a BA in Physics, Chemistry, or the equivalent; and consent of instructor. Introduction to biomolecular forces, energy flow, and thermodynamics in biological systems. Hydrophobic interactions and membrane structure. Feedback and control mechanisms; allosteric enzymes. Mechanisms of transport in biological membranes. Emphasis on the physical principles underlying biological structure and function. Rothschild. 4 cr, 2nd sem.

GRS PY 811 Advanced Quantum Field Theory

Prereq: GRS PY 713 and PY 714; GRS PY 731. Covers advanced methods in quantum field theory. Topics include QCD, confinement and chiral symmetry breaking, renormalization group, monopoles and instantons, the U (1) problem. (Course offered only upon sufficient demand.) Staff. 4 cr, 1st sem.

GRS PY 841 Symmetry in Solid-State Physics

Prereq: GRS PY 741, PY 742, or consent of instructor. Theory of finite groups, crystalline point groups, crystal double groups, crystal field theory, selection rules, perturbation theory, Kramer’s theorem, applications to solid-state physics. (Course offered only upon sufficient demand.) El Batanouny. 4 cr, 1st sem.

GRS PY 842 Many-Body Topics in Solid-State Physics

Prereq: GRS PY 741, PY 742, and PY 711, or PY 713, and PY 747. Applications of many-body techniques in classical and quantum mechanics including graphical techniques and Green’s functions. Thermodynamic Green’s functions. Includes normal and superconducting Fermi systems, superfluid Boson systems, quantum magnetism, transport theory, localization. (Course offered only upon sufficient demand.) Staff. 4 cr, 2nd sem.

GRS PY 891, 892 Seminar: Philosophical Foundations of Physics

Prereq: consent of instructor. Logical and historical analysis of concepts and theories of classical and modern physics. Staff. 4 cr, 1st & 2nd sem.

GRS PY 895, 896 Seminar: Special Topics in Theoretical Physics

Prereq: consent of instructor. Theoretical research topics include general relativity, quantum field theory, high energy and particle physics, phase transitions, renormalization group, laser physics, kinetic equations, biophysics, computational physics, and selected topics in mathematical physics. Staff.  Variable cr,1st & 2nd sem.

GRS PY 897, 898 Seminar: Special Topics in Experimental Physics -

Surface physics; intermediate energy nuclear physics experiments; low temperature techniques, liquid and solid helium, and magnetism at low temperatures. Raman effect, gels, and biophysics. High-energy physics experimental techniques. Staff. Variable cr, 1st & 2nd sem.

GRS PY 961 Scholarly Methods in Physics I

Introduction to scholarly methods in physics teaching and research. Reading and reporting scientific literature; ethical obligations in physics teaching and research; priority disputes; online publications and copyright issues; effective reading and writing in physics; discussions about careers in physics. Required of first-semester doctoral students. Staff. 2 cr, 1st sem.

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Directed Research

May be taken as semester or half-semester courses. Hours arranged. Variable cr.

GRS PY 901, 902 Research in Physics

Ahlen, Averitt, Bansil, Bigio, Butler, Carey, Castro Neto, Chamon, Chasan, Cohen, ElBatanouny, Erramilli, Evans, Glashow, Goldberg, Heintz, Katz, Kearns, Klein, Lane, Ludwig, Mertz, Miller, Mohanty, Moustakas, Narain, Pi, Rebbi, Redner, Roberts, Rohlf, Rothschild, Sandvik, Schmaltz, Sergienko, Skocpol, Smith, Stachel, Stanley, Stone, Sulak, Tsui, Ünlü, Whitaker. Variable cr.

GRS PY 907, 908 Research in Physics and Philosophy

Cohen, Stachel. Variable cr.

GRS PY 909, 910 Directed Study in Physics

Ahlen, Averitt, Bansil, Bigio, Butler, Carey, Castro Neto, Chamon, Chasan, Cohen, El-Batanouny, Erramilli, Evans, Glashow, Goldberg, Heintz, Katz, Kearns, Klein, Lane, Ludwig, Mertz, Miller, Mohanty, Moustakas, Pi, Polkovnikov, Rebbi, Redner, Roberts, Rohlf, Rothschild, Sandvik, Schmaltz, Sergienko, Skocpol, Smith, Stachel, Stanley, Stone, Sulak, Tsui, Ünlü, Whitaker. Variable cr.

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31 October 2007
Boston University
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