2000-01 Bulletin Entry for:

Objectives

A typical scenario for a physical explanation of a given situation is this: a small collection of basic physical principles relevant to the situation is used to create a mathematical model of it; computations are carried out using the model, leading to predictions that are checked experimentally; if there is agreement, the physical situation is deemed to have been explained. The objective of the program in physics is to make it possible for students to execute such a scenario for a wide range of physical situations. To that end, students are required to attain a firm grasp of the basic principles of classical physics and familiarity with those of quantum physics, to learn how to decide which principles are relevant to a given situation and how to construct the appropriate mathematical model, to develop the mathematical skills necessary to carry out the computations that generate predictions, and to strengthen the experimental skills used in exploring new phenomena and in carrying out the verification step of the typical scenario.

The ability to execute the typical scenario of physical explanation is useful not only to research physicists, but also to scientists in many other fields, especially interdisciplinary ones, such as environmental science; it is also useful to engineers, to members of the medical profession, and to architects. For that reason, the physics program has made special arrangements to integrate a physics concentration with study preparing for a career in any of the areas mentioned above.

The graduate program in physics is designed to equip students with a broad understanding of major fields of physics and to train them to carry out independent, original research. This objective is to be attained by formal course work and supervised research projects. As the number of students who are accepted is limited, a close contact between students and faculty is maintained, permitting close supervision and guidance of each student.

Advanced degrees will be granted upon evidence of the student's knowledge, understanding, and proficiency in classical and modern physics. The satisfactory completion of advanced courses will constitute partial fulfillment of these requirements. Research upon which theses may be based, with residence at Brandeis, may be carried out in the following areas:

1. Theoretical Physics

Quantum theory of fields; elementary particle physics; relativity; supergravity; string theory; quantum statistical mechanics; quantum theory of the solid state; critical phenomena and phase transitions; computational neuroscience.

2. Experimental Physics

High energy experimental physics; solid-state physics; surface physics; liquid-crystal physics; light scattering; positron physics; radio astronomy; and biophysical magnetic resonance.

How to Become an Undergraduate Concentrator

Since the sequence in which physics courses should be taken is tightly structured, and in most cases requires at least three years to complete, students contemplating a concentration in physics should consult the physics advising coordinator at the first opportunity. For most students either such consultation should take place before enrolling in courses at the beginning of the first year, or PHYS 11a and 19a should be part of the first semester program.

How to Be Admitted to the Graduate Program

The general requirements for admission to the Graduate School apply to candidates for admission to the graduate area in physics. Admission to advanced courses in physics will be granted following a conference with the student at entrance.

Faculty

Experimental high-energy physics.

Experimental high-energy physics.

Experimental low-energy positron physics.

Condensed matter theory. Electronic structure of solids and disordered systems.

Quantum theory of fields. Elementary particles. Gravitation. Supergravity. Strings.

Physics of liquid crystals and macromolecules.

Quantum field theory. Strings. Elementary particles. Supergravity.

Statistical physics.

Experimental solid-state physics.

Experimental high-energy physics.

Theoretical condensed matter physics.

Educational software.

Liquid crystals. Colloids. Polymers.

Mathematical physics.

Theoretical astrophysics. Radio astronomy.

Elementary particle theory. Quantum theory of fields. String theory.

History and philosophy of science. Quantum theory of measurements.

Computational neuroscience.

Radio astronomy. Cosmology.

Experimental high-energy physics.

Requirements for the Undergraduate Concentrations

The requirement for the concentration in physics leading to the degree of Bachelor of Arts is the equivalent of 11 semester courses in physics and two semester courses in mathematics. There must be the equivalent of at least three semesters in laboratory courses (PHYS 19a and 19b together count as one semester, as do PHYS 18a and 18b). One must also take PHYS 30b. Mathematics and physics courses numbered under 10 may not be used to fulfill the physics concentration requirement. A student not intending to pursue graduate study in physics may be permitted to substitute two advanced courses in other fields to meet physics concentration requirements, subject to the approval of the advising coordinator. A student with a concentration in physics and an interest in biophysics may want to take courses in biophysics, biology, biochemistry, chemistry, or neuroscience. With departmental approval, a student may use such courses to satisfy part of the physics concentration requirements.

To satisfy the requirements for the concentration in physics leading to the degree of Bachelor of Science, students must successfully complete the 11 physics courses required for the B.A. in physics and six additional courses. Two of the additional six courses should be chosen from the following: PHYS 25b, 32b, 33a, 40a, 45a, 100a, 104a, 110a. Another two courses must be selected from the following: NBIO 136b, CHEM 41a, 41b, any MATH course numbered 27 or higher (excluding courses used to fulfill the math requirement below), any COSI course numbered 21 or higher, or any other course approved by the physics department that is either listed or cross-listed in other departments within the School of Science. The final two courses must be chosen from one of the following pairs of courses: MATH 15a and MATH 20a, or MATH 21a and MATH 21b, or any two MATH courses numbered higher than 21.

A student may be admitted to a special four-year B.A./M.A. program upon recommendation of the department and the Graduate School by May 1 preceding the senior year. The student must successfully complete at least 38 courses. All the regular requirements for the M.A. degree in physics must be met: successful completion of six graduate courses in physics numbered 160 or above, and satisfactory performance on the qualifying examination. No more than two of the graduate level courses may be counted towards concentration requirements. Grades of B- or better are required in the six courses numbered 160 or above. The qualifying examination includes the final examinations in PHYS 161a (formerly 101a), 161b (formerly 101b), 162a (formerly 102a), and 162b (formerly 102b), and two oral examinations on all of physics through the first-year graduate level. The department will recommend admission to this program only if the student's record indicates that the student can successfully complete the requirements. Consultation with the physics advising coordinator before March 1 of the sophomore year is highly recommended for a student contemplating this program.

Requirements for the Undergraduate Minor

Six semester courses in physics at the level of PHYS 10 or above, not including PHYS 18a,b or PHYS 19a,b.

Special Notes Relating to Undergraduates

There are several natural tracks through the undergraduate physics courses. The first is: Year 1--PHYS 11a,b, 19a,b, MATH 10a,b; Year 2--PHYS 20a,b, 29a,b, MATH 21a,b or PHYS 110a; Year 3--PHYS 30a,b; Year 4--PHYS 40a, 100a.

The second, a premedical track, is: Year 1--PHYS 11a,b, 19a,b, MATH 10a,b; Year 2--PHYS 20a,b, 29a,b, CHEM 11a,b, 18a,b; Year 3--BIBC 22a, BIOL 22a, 18a,b, CHEM 25a,b, 29a,b; Year 4--PHYS 30a,b.

Students are encouraged to construct other tracks that might better suit their needs in consultation with their advisors.

A student intending to pursue graduate work in physics will normally add to the tracks above PHYS 25b, 100a, and 104a or graduate courses dealing with previously treated subjects at a more advanced level, such as PHYS 161a,b (formerly 101a,b), and 162a,b (formerly 102a,b). Normally only two or three of the five courses PHYS 25b, 32b, 33a, 45a, and 104a will be offered in a given year; the others will normally be offered in the following year. Undergraduates are not permitted to enroll in physics courses numbered above 160 without the explicit approval of their appropriate concentration advisors.

A student who has attained a grade of 4 or 5 on the Advanced Placement Examination Physics B may obtain credit for PHYS 10a,b; a student who has attained a grade of 4 or 5 on the Advanced Placement Examination C may obtain credit for PHYS 11a,b. A student who claims either of these advanced placement credits may not take any of the following courses for credit: PHYS 9b, PHYS 10a,b, PHYS 11a,b, PHYS 15a,b.

In order to be a candidate for a degree with distinction in physics, one must take a departmentally approved honors program of either PHYS 99d or two semester courses in physics numbered above 160, and one must obtain honor grades. Students should have their honors programs approved by the departmental honors advisor before the beginning of the senior year.

Requirements for Advanced Degrees

Normally, first-year graduate students will elect courses from the 100 series, with at least four courses numbered above 160. To obtain credit toward residence for a graduate course taken at Brandeis, a student must achieve a final grade of B- or better in that course. Students may obtain credit for advanced courses taken at another institution provided their level corresponds to the level of graduate courses at Brandeis and that an honor grade in those courses was obtained. To place out of PHYS 161a or b or 162a or b, a student must pass an exemption exam before the end of the second week of the course.

Requirements for the Degree of Master of Arts

One year in residence as a full-time student. No transfer residence credit will be allowed toward the fulfullment of the master's requirements.

Six semester-courses in physics numbered above 160. A thesis on an approved topic may be accepted in place of a semester-course.

There is no foreign language requirement for advanced degrees in physics.

Satisfactory performance in the qualifying examination is required. The final examinations in PHYS 161a, 161b, 162a, and 162b serve as the written part of the qualifying examination. To qualify, each of these courses must be passed with a grade of B or better. An oral examination passed at the end of the first year completes the qualifying process.

Requirements for the Degree of Doctor of Philosophy

All of the requirements for the master's degree and the following:

The minimum residence requirement is three years. A student may obtain up to one year's residence credit toward the Ph.D. requirements for graduate studies taken at another institution.

At least two graduate courses in the list below must be taken during the first four terms: PHYS 163a, 167b, 168b, 169b, 200a, 202a, 204a. Note, however, that not all of the above courses will necessarily be given each year. PHYS 202a (Quantum Mechanics III) is strongly recommended for all students. A total of at least nine semester courses in physics numbered above 160 is required for the doctoral degree.

Advanced examinations will be in topics partitioned in the several areas of research interest of the faculty. Faculty members working in each general area will function as a committee for this purpose and provide information about their work through informal discussions and seminars. The advanced examination requirement consists of a written paper and an oral examination. While no original research by the student is required, it is hoped that a proposal for a possible thesis topic will emerge. It is generally expected that the candidates will take the advanced examination in the field they wish to pursue for the Ph.D. thesis by the middle of the fourth term.

After passing the advanced examination, the student begins work with an advisor who guides his or her research program. The advisor should be a member of the Brandeis faculty but in special circumstances may be a physicist associated with another research institution. The graduate committee of the physics faculty will appoint a dissertation committee to supervise the student's research. The student's dissertation advisor will be the chair of the dissertation committee.

The doctoral dissertation must represent research of a standard acceptable to the faculty committee appointed for each Ph.D. candidate. The Final Oral Examination, or defense, is an examination in which the student will be asked questions pertaining to the dissertation research.

Courses of Instruction

(1-99) Primarily for Undergraduate Students

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Elementary physical ideas will be used to discuss the life and death of stars, the structure of the galaxies, and the large-scale features and evolution of the universe. Usually offered every year.

Mr. Wardle

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Philosophical questions related to modern developments in physics will be discussed. An explanation of quantum mechanics and relativity will be presented so that their interesting features can be understood. Usually offered in odd years.

Mr. Schweber

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Focuses on specific scientific and technological issues encountered in economic development. The scientific material needed to understand different approaches will be analyzed using simple mathematics as an essential tool. Usually offered every year.

Mr. Lange

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Analyzes some of the public safety issues involved in assessing risk and making technological decisions. The case history method will be used. Usually offered in even years.

Mr. Goldstein

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Introduces students to the laws, concepts, and phenomena of physics. Lecture and laboratory are well integrated to explore selected topics of general interest. Usually offered every year.

Mr. Wellenstein

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Introduces students in the life sciences to the laws and concepts of mechanics and thermodynamics. Usually offered every year.

Mr. Fraden

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Introduces students in the life sciences to the phenomena and concepts of acoustics, electricity and magnetism, optics, and modern physics. Usually offered every year.

Mr. Fraden

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Newtonian mechanics. Kinetic theory and thermodynamics. Usually offered every year.

Mr. Canter

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Elementary electromagnetism presented from a modern point of view. Special relativity. Usually offered every year.

Mr. Canter

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Advanced version of PHYS 11a for students with good preparation in physics and mathematics. Newtonian mechanics. Kinetic theory and thermodynamics. Usually offered every year.

Mr. Pendleton

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Advanced version of PHYS 11b for students with good preparation in physics and mathematics. Elementary electromagnetism presented from a modern point of view. Special relativity. Usually offered every year.

Mr. Pendleton

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10a. One two-and-a-half hour laboratory per week. One, one-hour lecture per week. Usually offered every year.

Mr. Wardle

Laboratory course consisting of basic physics experiments designed to accompany PHYS 10b. One two-and-a-half hour laboratory per week. One, one-hour lecture per week. Usually offered every year.

Mr. Wellenstein

Laboratory course designed to accompany PHYS 11a. Introductory statistics and data analysis including use of microcomputers and basic experiments in mechanics. One afternoon or evening of laboratory per week. One, one-and-a-half hour lecture per week. Usually offered every year.

Mr. Jensen

Laboratory course designed to accompany PHYS 11b. Basic experiments in electricity, magnetism, and optics. Basic electrical measurements. Determination of several fundamental physical constants. One afternoon or evening of laboratory per week. One, one-and-a-half hour lecture per week. Usually offered every year.

Mr. Heller

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A broad survey of the phenomena and ideas underlying modern physics--kinetic theory, radiation, the Bohr atom, nuclei and radioactivity, relativity, elementary particles, solids, and the foundations of quantum mechanics. Usually offered every year.

Mr. Meyer

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Free and forced oscillations of simple systems. Oscillations with many degrees of freedom. Standing and traveling waves. Wave packets and Fourier analysis. Polarization, interference, and diffraction. Usually offered every year.

Mr. Wang

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Application of basic physical principles to the study of stars, galaxies, quasars, and the large-scale structure of the universe. Usually offered in even years.

Mr. Roberts

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Introductory laboratory in analog electronics. Topics to be covered are DC circuits; AC circuits, complex impedance analysis; diodes, transistors; and amplifiers. Usually offered every year.

Mr. Kirsch

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Introductory laboratory in digital electronics. Topics to be covered are Boolean algebra, combinational logic; sequential logic, flip-flops, counters; digital-analog conversion; and microprocessors. The last half of the semester will be spent on individual design projects. Usually offered every year.

Mr. Meyer

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The fundamentals of electromagnetic theory. Includes electrostatics, magnetostatics, electric and magnetic circuits, and Maxwell's equations. Usually offered every year.

Mr. Roberts

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Introduction to quantum mechanics: atomic models, Schrödinger equation, angular momentum, hydrogen atom. Multielectron atoms and interaction of atoms with the electromagnetic field. Usually offered every year.

Mr. Blocker

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Study of microprocessor design and use as controller for other devices. Topics include architecture of microcomputers, interfacing, digital control, analog control, and software development. Usually offered in odd years.

Mr. Kirsch

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Geometric optics, wave optics, optical signal processing, and integrated optics. Usually offered in even years.

Mr. Bensinger

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Thermodynamics and statistical mechanics. The thermal properties of matter. Usually offered every year.

Mr. Lange

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An introductory course on the theory and applications of signal analysis and processing. Usually offered in odd years.

Mr. Canter

Tutorial for students studying advanced material not covered in regular courses. Usually offered every year.

Staff

Tutorial for students studying advanced material not covered in regular courses. Usually offered every year.

Staff

Open to exceptional students who wish to study an area of physics not covered in the standard curriculum. Usually offered every year.

Staff

Open to exceptional students who wish to study an area of physics not covered in the standard curriculum. Usually offered every year.

Staff

Research assignments and preparation of a report under the direction of an instructor. Usually offered every year.

Staff

(100-199) For Both Undergraduate and Graduate Students

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Lagrangian dynamics, Hamiltonian mechanics, planetary motion, general theory of small vibrations. Introduction to continuum mechanics. Usually offered every year.

Ms. Chakraborty

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The formal description of periodic systems. The vibrational and electronic properties of solids. Band structure and the Fermi surface. The transport and optical properties of solids. Usually offered in even years.

Ms. Chakraborty

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Complex variables; Fourier and Laplace transforms; special functions; partial differential equations. Usually offered every year.

Mr. Kondev

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A review of physics from the most elementary topics to those treated in other first-year graduate courses. The environment of an oral qualifying examination is reproduced in the tutorial. Usually offered every year.

Mr. Meyer

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Continuation of PHYS 113a. Usually offered every year.

Mr. Canter

(Formerly PHYS 115a)

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Advanced introduction to the theory of nonlinear dynamical systems, bifurcations, chaotic behaviors, and fractal patterns. Concepts and analysis are illustrated by examples from physics, chemistry, and biology. The course will be complemented by a significant number of computer labs. Usually offered in even years.

Mr. Wang

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Electrostatics, magnetostatics, boundary value problems. Usually offered every year.

Mr. Schnitzer

(Formerly PHYS 101b)

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Maxwell's equations. Quasi-stationary phenomena. Radiation. Usually offered every year.

Mr. Schnitzer

(Formerly 102a)

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Nonrelativistic quantum theory and its application to simple systems; spin systems and the harmonic oscillator. Feynman diagram visualization of time-dependent perturbation theory. Usually offered every year.

Mr. Grisaru

(Formerly 102b)

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The hydrogen atom. Systems of identical particles. Coupling of angular momenta. Scattering theory. Semiclassical analysis of interaction of atomic systems and electromagnetic waves. Usually offered every year.

Mr. Grisaru

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The thermal properties of matter. Derivation of thermodynamics from statistical physics. Statistical theory of fluctuations. Usually offered in odd years.

Ms. Chakraborty

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The phenomenology of elementary particles and the strong, weak, and electromagnetic interactions. Properties of particles, kinematics of scattering and decay, phase space, quark model, unitary symmetries, and conservation laws. Usually offered in even years.

Mr. Blocker

(Formerly PHYS 108b)

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Bremsstrahlung, synchrotron radiation, inverse Compton scattering. Extended and compact radio sources, jets, superluminal motion. Quasars and active galactic nuclei, IR to X-ray continua, spectral line formation. Black holes and accretion disks. Usually offered irregularly as demand requires; consult department.

Staff

(Formerly PHYS 109b)

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Electronics laboratory for graduate students. Usually offered every year.

Mr. Kirsch

(200 and above) Primarily for Graduate Students

Introduction to current research and problems in gravitational physics. Physical and mathematical background are provided as needed, but emphasis is on recent literature. Usually offered in even years.

Mr. Deser

Nonrelativistic field theory and relativistic quantum mechanics. Graphical version of time-dependent perturbation theory. Application of group theory to quantum mechanics. Usually offered every year.

Mr. Schweber

Topics in condensed matter theory. Usually offered in odd years.

Mr. Kondev

Analysis of important recent developments in particle physics. Usually offered every year.

Mr. Schnitzer

A continuation of PHYS 210a. Usually offered every year.

Mr. Schnitzer

Supervised preparation for the advanced examination. Usually offered every year.

Staff

Supervised preparation for the advanced examination. Usually offered every year.

Staff

Advanced topics and current research in astrophysics are discussed. Usually offered every year.

Mr. Wardle

A continuation of PHYS 301a. Usually offered every year.

Mr. Wardle

Seminar covers latest advances in elementary particle physics. Includes student presentations and invited speakers. Usually offered every year.

Mr. Kirsch

A continuation of PHYS 302a. Usually offered every year.

Mr. Blocker

Seminar covers latest developments in atomic, solid-state, and surface physics as studied using positron techniques. Includes student presentations and invited speakers. Usually offered every year.

Mr. Canter

A continuation of PHYS 303a. Usually offered every year.

Mr. Canter

Analysis and discussion of recent important developments in solid-state physics. Usually offered every year.

Ms. Chakraborty

A continuation of PHYS 304a. Usually offered every year.

Ms. Chakraborty

Recent advances in the physics of liquid crystals and related systems such as microemulsions, colloidal suspensions, and polymer solutions. Usually offered every year.

Mr. Meyer

A continuation of PHYS 305a. Usually offered every year.

Mr. Fraden

An advanced graduate seminar course on current theoretical issues dealing with the dynamics and information processing of neural systems. Usually offered every year.

Mr. Wang

Usually offered every year.

Ms. Chakraborty

Specific sections for individual faculty members as requested.

Staff

Specific sections for individual faculty members as requested.

Staff

Specific sections for individual faculty members as requested.

Staff

Ms. Chakraborty and Mr. Kondev

Mr. Deser

Specific sections for individual faculty members as requested.

Staff

Specific sections for individual faculty members as requested.

Staff

Staff

Specific sections for individual faculty members as requested.

Staff

Specific sections for individual faculty members as requested.

Staff

Staff

Cross-Listed Courses

Seminar in Biophysical Research