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Chair: John R. Thorstensen

*Professors C. G. Fesen, R. A. Fesen, M. Gleiser, M. K. Hudson, J. W. LaBelle, W. E. Lawrence, J. R. Thorstensen, G. A. Wegner, M. N. Wybourne; Associate Professors M. P. Blencowe, R. R. Caldwell, B. C. Chaboyer, K. A. Lynch, R. Onofrio, A. J. Rimberg, B. N. Rogers, Y-A. J. Soh, L. Viola; Assistant Professor R. M. Millan; Adjunct Professors M. F. Kimmitt, R. A. Naumann, R. A. Treumann; Adjunct Assistant Professors A. J. Brizard, C. G. Levey; Research Professors P. Crane, R. E. Denton, J. G. Lyon, D. C. Montgomery; Research Assistant Professors J. H. Brownell, M. Chu, B. T. Kress, H-R Mueller , T. P. Smith; Visiting Research Instructor M. W. Chevalier; Visiting Professor A. Weiss; Visiting Associate Professor Y. J. Brown; Visiting Assistant Professor P. M. Haines.*

The following courses are especially recommended for students not majoring in one of the sciences: Physics 1 and Astronomy 1, 2/3, and 4.

Prerequisite: Mathematics 3, 8, 13, and 23; Physics 13 and 14. Students with advanced placement may substitute Physics 15 and 16 for Physics 13 and 14.

Students completing a major in physics are required to take a minimum of eight courses in physics, including Physics 19, 24, 41, 42, 43, 44, and two electives including the culminating experience. Students taking Physics 15 and 16 may substitute a third elective for Physics 19. The major requires one upper-level laboratory course; Physics 47, Physics 48, Physics 49, Physics 76 or Astronomy 61. Elective courses are Physics 47, Physics 48, Physics 49, Astronomy 15 or 25, and all physics and astronomy courses numbered in the sixties, seventies and nineties. Courses numbered in the forties may be taken in any order. Chemistry 72 may be substituted for Physics 42. Students planning graduate study in physics or another science, are encouraged to take Physics 66, 76, 91 and other advanced courses in physics and astronomy. Graduate courses in physics and astronomy are open to qualified undergraduates. Students should consult the Chair or the Major Adviser about additional courses in mathematics and other science departments.

Students are required to complete a culminating activity in the major. For the physics major this requirement may be satisfied by receiving credit for one of the following courses: Physics 68, Plasma Physics I; Physics 72, Particle Physics I; Physics 73, Solid State Physics; Physics 74, Space Plasma Physics; Physics 76, Methods of Experimental Physics; Physics 82, Special Topics Seminar; Astronomy 74, Astrophysics; Astronomy 75, High Energy Astrophysics; Astronomy 81, Special Topics in Astronomy; Physics 87, Undergraduate Research. The culminating experience is included in, not in addition to, the eight courses required for the major.

All major programs require an average GPA of 2.0 in all courses counted toward the major, including prerequisites.

A typical program is outlined below. In addition to these courses, a physics major may be completed with almost any Dartmouth Plan attendance pattern, provided that at least one summer and one fall term are spent on campus.

*Year Fall Winter Spring*

First Mathematics 3 Mathematics 8 (Mathematics 13)

Physics 13 Physics 14

Subsequently (Mathematics 13) Mathematics 23

Physics 19 Physics 24 Physics 44

It is desirable that those students who plan to complete more than the minimal major in physics take Physics 13 and 14 in the first year, and Physics 19 and 24 in the sophomore year. Students taking Physics 13 in the fall must have AP credit for Math 3. Those beginning Physics in their sophomore year, however, can easily complete at least the minimal major.

A modified physics major may be desirable for students interested in such careers as engineering physics, geophysics, biophysics, chemical physics, medicine, and health professions. The prerequisites for the modified major are the same as those for the physics major. The modified major consists of ten additional courses, of which at least six must be in the Department of Physics and Astronomy. Courses selected in other sciences should form a unified whole with the physics courses, and should draw on and relate to a physics background. It is also possible to modify the physics major with courses outside the science division, subject to these same general guidelines. A written rationale explaining the intellectual coherence of the proposed program of courses, approved by the Chair, is required in all cases. Interested students are urged to consult the Chair.

The Department of Engineering Sciences and the Department of Physics and Astronomy offer a major in Engineering Physics. This major features a 5/5 split in courses, unlike a modified major which requires six courses from one field and four from the other.

The prerequisite courses for the Engineering Physics major are Mathematics 3, 8, 13, 23; Physics 13, 14; Chemistry 5; and Computer Science 5 or Engineering Sciences 20.

The engineering physics major is a ten-course program consisting of three engineering sciences core courses (Engineering Sciences 22, 23, 24); three physics core courses (Physics 19, 24, 43 [Students taking Physics 15 and 16 may substitute a third elective for Physics 19]); and four electives, two from each department. Two electives must be selected from the following list: Engineering Sciences 25, 33, 34; Physics 42, 68, 91; Physics 73 or Engineering Sciences 131; Physics 66 or Engineering Sciences 120; Physics 44 or Engineering Sciences 140. The other two electives may be courses from the engineering sciences department (numbered above 20, excluding Engineering Sciences 80 and 87) or courses from the physics and astronomy department that fulfill the straight physics major.

A culminating experience is required in the major. This can be taken instead of one of the electives above. The culminating experience may be: a project or a thesis, Engineering Sciences 86, 88 or 190 (Engineering Sciences 190 must be taken as part of the two-course design sequence Engineering Sciences 190/290); or advanced engineering sciences courses such as 63, 76, 91, 92 or any graduate course available for AB credit, or Physics 68, 72, 73, 74, 76, 82, 87, including the senior honors thesis option.

All major programs require an average GPA of 2.0 in all courses counted toward the major, including prerequisites.

For more information contact Professor Mary Hudson (Physics and Astronomy) or Professor William Lotko or Christopher Levey (Engineering Sciences).

Prerequisite: Math 3, 8, 13 and 23; Physics 13 and 14. Students with advanced placement may substitute Physics 15 and 16 for Physics 13 and 14.

Students completing a major in astronomy are required to take a minimum of eight courses in physics and astronomy, including: Astronomy 15, 25, 61, Physics 19, 24, one elective from Astronomy 74, 75, 81 and two electives from Physics 41, 43, 44, 74. Students taking Physics 15 and 16 may substitute a third elective for Physics 19. In addition to the minimum course requirements for an astronomy major, it is recommended that students interested in pursuing a graduate degree in astronomy or astrophysics should take the following courses: Physics 41, 42, 43 and 44. Students interested in observational astronomy should take Physics 48 (Electronics: Introduction to Linear and Digital Circuits) while those interested in theory should take Engineering Sciences 20 (Introduction to Computer Science with Applications in Engineering). Graduate courses in physics and astronomy are open to qualified undergraduates. Students are required to complete a culminating activity in the major. For the astronomy major this requirement may be satisfied by receiving credit for one of the following courses: Astronomy 74, Astrophysics; Astronomy 75, High Energy Astrophysics; Astronomy 81, Special Topics in Astronomy; or Astronomy 87, Undergraduate Research in Astronomy. The culminating experience is included in, not in addition to, the eight courses required for the major.

All major programs require an average GPA of 2.0 in all courses counted toward the major, including prerequisites.

There are seven introductory astronomy courses intended for students with different mathematical and scientific backgrounds and interests:

Elementary courses for students with little or no science or mathematics background: Astronomy 1 (winter), 2 (summer, winter), 3 (summer, winter), and 4 (spring). Note that Astronomy 2 and 3 differ only in that Astronomy 3 includes a laboratory. Astronomy 1, 2/3, and 4 overlap very little in subject matter; any combination of these courses may be taken in any order.

Introductory course for students with some knowledge of calculus and physics: Astronomy 15 (spring).

Introductory courses for advanced physics students, who need not have previous background in astronomy: Astronomy 61 (fall), Astronomy 74 (winter).

Students desiring observing experience at the observatory on Kitt Peak, Arizona, which Dartmouth operates with the University of Michigan, Ohio State University, Columbia University and Ohio University should plan to take Astronomy 81 and/or 87.

*Physics Minor.*

Prerequisite: Mathematics 3, 8, 13, 23, or equivalents; Physics 13 and 14 (or 3 and 4, or 15 and 16).

Four courses are required in addition to the prerequisites. One of these must be Physics 19 except that students taking Physics 15 and 16 may substitute another elective for Physics 19. The other three must be chosen from physics courses numbered 24 and above, and/or astronomy courses numbered 15 and above, at least one of which must be numbered above 40.

*Astronomy Minor.*

Prerequisites: Mathematics 3 and 8 or equivalents; Physics 13 and 14 (or 3 and 4, or 15 and 16).

Four courses are required in addition to the prerequisites. One of these must be Astronomy 15. The other three are Astronomy 25, 61, and 81. Any physics or astronomy course numbered 20 or above may be substituted for one of these three.

Note that Astronomy 25 has Physics 14 as prerequisite.

The minor in Materials Science is sponsored by faculty in Chemistry, Physics and Engineering with an interest in interdisciplinary education and research in materials science .

The first-year program for a student who has received advanced placement in mathematics and qualifies for Physics 15-16 might be as follows:

*Fall Winter Spring*

Mathematics 8 Mathematics 13 Mathematics 23

Physics 15 Physics 16 Physics 24

HONORS PROGRAM IN PHYSICS OR ASTRONOMY

An honors student carries out a program of independent work in physics or astronomy under the supervision of a member of the faculty. This independent work is usually done in the student's senior year, and it may be experimental, theoretical, or observational. A written report on the completed work is required.

Any major meeting the college requirements (pages XXX) is eligible for admission to the departmental Honors Program. To enter the program eligible students should obtain the permission of the Department and of the faculty member who is to supervise the work. This is generally done before the beginning of the senior year. Early consultation with the Department is encouraged.

All departmental Honors are considered individually and awarded by a vote of the faculty. To be considered for *High Honors* the student must defend an Honors Thesis based upon the independent work before a faculty committee. Students with an average in the major of 3.75 or higher who do not complete an honors thesis may be considered for *Honors,* as distinct from High Honors, provided they have completed three courses beyond the minimum number required for the major from among the list of courses numbered 60 or higher. One of the courses must be Physics 76, Physics 82, Astronomy 81 or Physics 87.

All Honors students must meet the minimum requirements of the regular major, and, ordinarily, should take physics, astronomy, and mathematics courses beyond those requirements. Special programs may be worked out for eligible students who wish to include extensive work in a field related to physics or astronomy.

Physics and astronomy courses offered for graduate credit are those numbered 61 or higher. The Department of Physics and Astronomy will allow graduate credit for any course offered by the Departments of Biochemistry, Biological Sciences, Chemistry, Earth Sciences, Engineering Sciences, or Mathematics that receives graduate credit from that department.

The general requirements for the master's degree are given on page XXX of this bulletin. These requirements, together with the specific requirements of the Department of Physics and Astronomy indicated below, normally allow completion of the degree in two years. It is expected that graduate students who have not completed the equivalent of the Dartmouth physics major program will do so in their first year of graduate study.

Special requirements:

1. Degree credit for eight graduate courses, exclusive of teaching courses. Two of the eight courses may be Graduate Research. At least six of the eight courses should be in physics and astronomy.

2. Credit for at least one term of Supervised Undergraduate Teaching (Physics 257).

3. Completion of a culminating experience chosen from the following options:

a. Completion of a satisfactory thesis, which must be defended before the M.S. Thesis Committee in a public forum.

b. Significant co-authorship of a publication submitted to a refereed journal or refereed conference proceedings, defended publicly.

c. Passing the Ph.D. qualifying examination.

A student will be admitted to Ph.D. candidacy upon:

1. Physics students: Receiving credit for six out of the following eight core courses: Physics 76, 91, 100, 101, 103-106.

Astronomy students: Receiving credit for any four of the eight core courses (Physics 76, 91, 100, 101, 103-106) and any four of Astronomy 115-118 and Physics 114.

2. Passing the departmental qualifying examination.

3. Presenting a thesis proposal and successfully defending it before an appointed Ph.D. thesis committee, for certification.

4. Passing a departmental review of the student's course record and preliminary research progress.

5. Receiving credit for at least two terms of Supervised Undergraduate Teaching (Physics 257) and Physics 256.

Students must achieve thesis proposal certification by the end of the fall term of their fourth year, in order to remain in good standing. Students who successfully complete these requirements will be admitted to Ph.D. candidacy by the Department.

The candidate will receive the Ph.D. degree upon

1. Receiving degree credit for at least twelve graduate courses, exclusive of teaching courses. Two of the twelve courses may be Graduate Research, both of which must be completed no later than the second summer in residence.

2. Receiving credit for at least two terms of Supervised Undergraduate Teaching (Physics 257) and Physics 256.

3. Completing a dissertation of substantial significance and publishable quality.

4. Successfully defending the dissertation before the Ph.D. Thesis Committee in a public forum.

It is expected that most students will receive the Ph.D. degree by the end of the fifth year of graduate study.

08S: 12 Offered in alternate years

An introduction to the evolution of physical theories and models of natural phenomena from ancient Greece to modern times. Topics include Pre-Socratic and Aristotelian natural philosophy; the scientific revolutions of Copernicus, Kepler, Galileo, and Newton, and the birth of mechanics; electromagnetism, thermodynamics, and the physics of light in the nineteenth century; the emergence of quantum mechanics and relativity theory; modern particle physics and the search for unification; the interface of particle physics and cosmology; and physics and its contexts (other sciences, worldviews, technologies, the Cold War). Students will carry out five biweekly laboratory experiments illustrating major discoveries. Supplemental course fee required. *Dist: SLA.* Gleiser, Kremer.

06F: 12 07X: 11 07F: 12; Laboratory: Arrange

The fundamental laws and phenomena of mechanics, heat, wave motion, and sound, including relativistic concepts.

The sequence Physics 3-4 is designed primarily for students who do not intend to take Physics 19. One laboratory period per week. Supplemental course fee required.

Prerequisite: Mathematics 3. *Dist: SLA.* Thorstensen (fall).

07W, 07S, 08W, 08S: 12; Laboratory: Arrange

The fundamental laws and phenomena of electricity, magnetism, and light, including quantum mechanical concepts; atomic and nuclear physics. One laboratory period per week. Supplemental course fee required.

Prerequisite: Physics 3. *Dist: SLA.* C. Fesen.

*Consult special listings*

06F, 07W, 07F, 08W: 10; Laboratory: Arrange

The fundamental laws of mechanics. Reference frames. Harmonic and gravitational motion. Thermodynamics and kinetic theory. Physics 13, 14, and 19 are designed as a three-term sequence for students majoring in a physical science. One laboratory period per week. Supplemental course fee required.

Prerequisite: Mathematics 3 and 8 (at least concurrently). *Dist: SLA.* LaBelle (fall), Millan (winter).

07W, 07S, 08W, 08S: 10; Laboratory: Arrange

The fundamental laws of electricity and magnetism. Maxwell's equations. Waves. Electrical and magnetic properties of bulk matter. Circuit theory. Optics. One laboratory period per week. Supplemental course fee required.

Prerequisite: Physics 13 and Mathematics 8, or permission of the instructor. *Dist: SLA.* Caldwell (winter), LaBelle (spring).

06F, 07F: 10; Laboratory: Arrange

Physics 15, 16 and 24 are an alternative sequence to Physics 13, 14, 19 and 24 for students whose substantial background in physics and mathematics enables them to study the material in more depth than is possible in regular sections, and who are willing to devote correspondingly more work to the course. Admission criteria are described in the *First Year*, available from the First-year Office.

Dynamics of particles and rigid bodies. Gravitation. Oscillations and waves. Fluids. Kinetic theory and thermodynamics. One laboratory period per week. Supplemental course fee required.

Prerequisite: Mathematics 8 or 9 concurrently, and permission of the instructor. *Dist: SLA.* Rogers.

07W, 08W: 10; Laboratory: Arrange

Electric and magnetic fields of charges and currents. Electromagnetic induction. Dielectric and magnetic materials. Circuit theory. Maxwell's equations, electromagnetic waves and optics..Special relativity. One laboratory period per week. Supplemental course fee required.

Prerequisite: Physics 15 and Mathematics 13 or 14 concurrently, or permission of the instructor. *Dist: SLA.* Smith.

06F, 07F: 9; Laboratory: Arrange

The general theme of this course is the wave-particle duality of radiation and matter, with an introduction to special relativity. Classical wave phenomena in mechanical and electromagnetic systems including beats, interference, diffraction and polarization. Quantum aspects of electromagnetic radiation include the photoelectric effect, Compton scattering and pair production and annihilation. Quantum aspects of matter include DeBroglie waves, electron diffraction, and the spectrum of the hydrogen atom. The Schr√δdinger equation is introduced in one spatial dimension. Supplemental course fee required.

Prerequisite: Physics 14 and Mathematics 13, or permission of the instructor. *Dist: SCI*. Blencowe.

07W, 07S, 08W, 08S: 10

The theme of this course is the application of the principles of physics to the structure of matter on various scales. The Schr√δdinger equation is discussed in three spatial dimensions, with emphasis on the description of hydrogenic wavefunctions. Spin and the Pauli exclusion principle. Applications may include many-electron atoms, molecules, solids, nuclei and elementary particles.

Prerequisite: Physics 19, or Physics 16, or permission of the instructor. *Dist: SCI*. Viola (winter), Lawrence (spring).

07W, 08W: 10

The differential and integral laws of electric and magnetic fields in vector form. Potential theory and boundary value problems. Maxwell's equations, the wave equation and plane waves.

Prerequisite: Physics 24 and Mathematics 23 or permission of the instructor. *Dist: SCI.* Rimberg.

07X: 10A

Detailed solutions of the Schr√δdinger equation for a variety of systems including bound states and scattering states in one and three dimensions. Matrix representations of spin and orbital angular momenta. Applications to atomic, molecular and nuclear problems are emphasized.

Prerequisite: Physics 24 and Mathematics 23, or permission of the instructor. *Dist: SCI.*

06F, 07F: 9

Kinetic theory of gases. Boltzmann's Principle. Boltzmann, Bose-Einstein and Fermi-Dirac statistics. The statistical approach to thermodynamics. Applications to radiation, atoms, molecules, and condensed matter.

Prerequisite: Physics 24 or permission of the instructor. *Dist: SCI.* Smith.

07S, 08S: 11

The fundamental principles of mechanics. Lagrangian form of the equations of motion. Central force motion, collisions and scattering, dynamics of rigid bodies, vibrations, normal modes, and waves. Nonlinear dynamics and chaos.

Prerequisite: Physics 24 and Mathematics 23, or permission of the instructor. *Dist: SCI.* Blencowe.

06F, 07F: 11

This course covers geometrical, physical, and modern optics topics including the propagation, reflection, dispersion, and refraction of radiant energy; polarization, interference, and diffraction in optical systems; the basics of coherence theory, lasers, quantum optics, and holography. Applications of optical and laser science will be discussed. Lectures and laboratory work.

Prerequisites: Physics 14 or 16 and Mathematics 13, or permission. *Dist: SLA.* Rimberg.

07W, 08W: 11

Principles of operation of semiconductor diodes, bipolar and field-effect transistors, and their application in rectifier, amplifier, waveshaping, and logic circuits. Basic active-circuit theory. DC biasing and small-signal models. Introduction to integrated circuits: the operational amplifier and comparator. Emphasis on breadth of coverage of low-frequency linear and digital networks. Laboratory exercises permit 'hands-on' experience in the analysis and design of simple electronic circuits. The course is designed for two populations: a) those desiring a single course in basic electronics, and b) those desiring the fundamentals necessary for further study of active circuits and systems.

Prerequisite: Physics 14 or 16 and Engineering Sciences 22, or equivalent background in basic circuit theory. *Dist: TAS.* Sullivan.

*Not offered in the period from 06F through 08S.*

An introduction to experimental physics designed to complement the theoretical framework covered in Physics 41-44. Students work independently on experiments drawn from classical mechanics, electromagnetism, statistical physics, and atomic physics. Weekly seminars cover such topics as experimental design, data and error analysis, signal recovery, and computer methods. Supplemental course fee required.

Prerequisite: Physics 24 or permission of the instructor. *Dist: SLA*.

07S: 10

Classical electromagnetic radiation and relativistic electrodynamics. Topics include: electromagnetism and relativity; Maxwell stress-tensor; electromagnetic wave propagation in free space and media; radiation by charged particles; scattering; diffraction; basic elements of general relativity.

Prerequisite: Physics 41 or Engineering Sciences 23 and Physics 44. *Dist: SCI.* Lawrence.

07W, 08W: 11

The physics of ionized gases with emphasis on the theory of waves and instabilities. Includes introduction to magnetohydrodynamics and kinetic theory of plasmas.

Prerequisite: Physics 41 or Engineering Sciences 23. *Dist: SCI.* Lynch.

06F, 07F: 2

Survey of a number of mathematical methods of importance in Engineering and Physical Sciences. Topics include integration and differentiation of multivariable functions, complex variable theory, generalized functions, Fourier and Laplace transforms, directed toward applications in such areas as fluid mechanics, electromagnetics, wave and diffusion phenomena, linear systems, and signal theory.

Prerequisite: Mathematics 33 or Engineering Sciences 22, Engineering Sciences 23, or the equivalent. *Dist: QDS.* Osterberg.

07S: 10A Offered in alternate years

Characterization of elementary particles and their interactions according to the standard model; leptons, quarks, gauge bosons, and the Higgs mechanism. Composite particles and their interactions. Methods of production and measurement of particles. Particle lifetimes and cross sections.

Prerequisite: Physics 42. *Dist: SCI.* Onofrio*.*

06F, 07F: 12

The physics of condensed matter, primarily solids with periodic order. Theory and measurement of electronic, optical, magnetic, and thermal properties of solids. Lattice structures, symmetries, and bonding energies. The reciprocal lattice and the Brillouin Zone. Bloch's Theorem. Electron energy band structure and the Fermi surface, phonon mode dispersion, and other elementary excitations.

Prerequisite: Physics 42, Physics 43 recommended. *Dist: SCI.* Lawrence.

08S: Arrange Offered in alternate years

Plasma processes in the solar system. The solar cycle, solar flares, solar wind outflow and interaction with distinct types of planetary magnetospheres. Plasma waves, particle acceleration and generation of escaping electromagnetic radiation. Magnetosphere-ionosphere coupling, and ionospheric interaction with the neutral atmosphere.

Prerequisites: Physics 66 or 68, or permission of the instructor. *Dist: SCI.* Hudson.

08W: 12 Offered in alternate years

Overview of basic ideas in classical and quantum computation. Concepts and physical realizations of quantum bits (qubits). Topics in quantum computation may include the Deutsch-Jozsa, quantum Fourier transform, Shor factorization and Grover search algorithms. Topics in quantum communication include quantum key distribution schemes and quantum teleportation. Issues relating to the foundations and interpretations of quantum mechanics will be revisited throughout the course.

Prerequisites: Physics 19 or Mathematics 22 or 23. *Dist: QDS.*

07S, 08S: 2A

Experiments emphasizing modern techniques and topics in physical measurements. Experiments will cover areas including condensed matter, particle and plasma physics, and such practical laboratory techniques as noise suppression, digital data acquisition, and operation of standard laboratory equipment. Supplemental course fee required.

Prerequisite: Physics 24. *Dist: SLA.* Rimberg.

All terms: Arrange

Advanced study in physics or astrophysics. Students will read and report orally on significant journal articles and write a paper summarizing their library research.

All terms: Arrange

All terms: Arrange

Intensive individual work on an experimental or theoretical problem in physics or astronomy under the guidance of a staff member.

Prerequisite: permission of the Chair.

07W, 08W: 2A

Formalism of quantum mechanics, operator methods and transformation theory. Measurement theory and uncertainty relations. Position and momentum representation. The harmonic oscillator and ladder operators. Introduction to path integrals. Perturbation methods: WKB, time-independent and time-dependent perturbation theory. Interaction of matter and radiation and selection rules. Symmetries and conservation laws.

Prerequisites: Physics 42. *Dist: SCI.* Viola.

07W: 11 Offered alternate years

An introduction to the study of the early universe, focusing on the interaction of nuclear and particle physics and cosmology, the so-called inner-space outer-space connection. After an investigation of the Robertson-Walker metric and its application to the Big Bang model, the course will address the following topics; thermodynamics in an expanding universe; nucleosynthesis (synthesis of light nuclei) and baryogenesis (origin of excess matter over antimatter); inflationary models of cosmology; primordial phase transitions; introduction to quantum cosmology.

Prerequisites: Physics 41-44, and Astronomy 25 (recommended). *Dist: SCI. Gleiser.*

06F, 07F: 11

Concepts and methods used in the treatment of linear equations with emphasis on matrix operations, differential equations, and eigenvalue problems will be developed following a brief review of analytic function theory. Topics include the Fourier integral, finite and infinite dimensional vector spaces, boundary value problems, eigenfunction expansions, Green's functions, transform techniques for partial differential equations, and series solution of ordinary differential equations. Properties and uses of orthogonal polynomials and such special functions as the hypergeometric, Bessel, Legendre, and gamma functions are discussed. Applications in engineering and physics are emphasized.

Prerequisite: one of Engineering Sciences 92, Mathematics 43, or Mathematics 33 with permission of instructor, or the equivalent. Haines.

06F, 07F: 10A

Lagrangian and Hamiltonian formulation of mechanics, canonical transformations, relativistic mechanics, and continuum mechanics.

Prerequisite: Physics 44. Lynch.

08S: 10 Offered in alternate years

Time-dependent and time-independent perturbation theory, and the variational method. Identical particles, the two-electron system, the Helium atom, many particle systems, and the Hartree-Fock approximation. Scattering theory, bound and resonance states, atom-electron scattering, and Coulomb scattering. Interaction of radiation with matter. The Dirac equation and introduction to second quantization.

Prerequisite: Physics 91, 100, and 101.

07S, 08S: 11

Ensemble theory in classical and quantum mechanics with selected applications. Statistical interpretation of thermodynamics. The approach to equilibrium. Transport processes.

Prerequisite: Physics 71. Onofrio.

07W, 08W: 2A

Potential theory of electrostatics, magnetostatics, and steady currents. Maxwell's equations, gauge transformations, and conservation laws.

Prerequisite: Physics 41. Rogers.

07S: 10A Offered in alternate years

Solutions of the homogeneous and inhomogeneous wave equations, retarded potentials, covariant formulation. Radiation, radiation reaction, and dynamics of charged particles. Scattering and dispersion.

Prerequisite: Physics 66 and 105. Caldwell.

08W: 11 Offered in alternate years

Spontaneous symmetry breaking and the Higgs mechanism. The Weinberg-Salam model. Path integral quantization of scalar fields and functional formalism. The effective action and the effective potential. Divergences and renormalization of field theories. Finite temperature field theory. Symmetry restoration at high temperatures.

Prerequisite: Physics 101 and 103.

Offered as needed

Theory of fluid motion. Kinematics of flow fields. Viscous and ideal flows. Shear flows, hydrodynamic stability, transition, and turbulence. Gas dynamics and shocks. Boundary layers. Rotating fluids, geophysical flows. Thermal convection and conduction. Waves.

Prerequisite: Physics 101, or permission of the instructor.

Offered as needed

Second quantization and quantum field theory applied to many-particle systems at finite temperatures. Perturbation theory, Feynman diagrams and self-consistent theories. Selected topics include quasiparticle and collective excitations, broken symmetries and phase transitions.

Prerequisite: Physics 103.

07S: 12

Continuation of Physics 100 with emphasis on variational calculus, integral equations, and asymptotic and perturbation methods for integrals and differential equations. Selected topics include functional differentiation, Hamilton's principle, Rayleigh-Ritz method, Fredholm and Volterra equations, integral transforms, Schmidt-Hilbert theory, asymptotic series, methods of steepest descent and stationary phase, boundary layer theory, WKB methods, and multiple-scale theory.

Prerequisite: Physics 100, or equivalent. The staff.

07F: Arrange Offered as needed

Statistical mechanics and kinetic theory of plasmas. Transport and thermal relaxation phenomena. Microscopic foundations of a fluid description. Waves and instabilities, linear and nonlinear. Emission, absorption, and scattering of electromagnetic radiation.

Prerequisite: Physics 68, and preferably Physics 106, or permission of the instructor.

07W: Arrange Offered in alternate years

Microscopic theory of electron energy bands in solids; vibrational magnetic and electronic elementary excitations. Applications to classical and quantum transport, magnetism, and superconductivity.

Prerequisite: Physics 73 and 91, or permission of the instructor. Physics 103 recommended. Soh.

08S: Arrange

Structures on manifolds; spacetime structure. Einstein's field equations and their classic solutions. Models of stellar equilibrium and collapse. Gravitational waves. Relativistic cosmologies.

Prerequisite: Permission of the instructor.

Offered as needed

Hydrodynamics of an electrically-conducting fluid. Magnetic confinement fusion devices. Magnetohydrodynamic processes of interest in the solar-terrestrial environment and in astrophysics. Nonlinear MHD phenomena and turbulence.

Prerequisite: Physics 68, and preferably Physics 108, or permission of the instructor.

08S: Arrange Offered in alternate years

An introduction to some of the active research areas on quantum information science, from a physics perspective. While the final choice and balance will be adjusted to actual demand and interest, special emphasis will be devoted to: Quantum algorithms for efficient search, factoring, and quantum simulation; theory and applications of entanglement; methods for quantum control and error correction; physical implementations of quantum information processing.

Prerequisites: Physics 42 and 75, or Physics 91.

07S, 09S: Arrange Offered in alternate years

Theory and techniques used in contemporary plasma physics computational research, especially non-linear plasma simulations, fluid, particle and hybrid. Also linear dispersion codes and data analysis. Significant emphasis on numerical projects.

Prerequisites: Physics 68 or Engineering Sciences 91 (both recommended) or equivalent, or permission of instructor. Denton.

All terms: Arrange

Study and discussion in a current area of physics or astronomy.

All terms: Arrange

Advanced treatment of topics in physics and in astronomy.

07F: Arrange

The physical principles and engineering applications of optics, with an emphasis on optical systems. Geometric optics: ray tracing, first-order analysis, imaging, radiometry. Wave optics: polarization, interference, diffraction, Fourier optics. Sources and detectors. Fiber optic systems.

Prerequisite: Engineering Sciences 50 or Physics 41, and Engineering Sciences 23 and 92 or equivalent. Testorf.

07W: Arrange

Light has now taken its place beside electricity as a medium for information technology and for engineering and scientific instrumentation. Applications for light include telecommunications and computers, as well as instrumentation for materials science, biomedical, mechanical and chemical engineering. The principles and characteristics of lasers, detectors, lenses, fibers and modulators will be presented, and their application to specific optical systems introduced. The course will be taught in an interdisciplinary way, with applications chosen from each field of engineering. Students will choose design projects in their field of interest.

Prerequisite: Engineering Sciences 23 or Physics 41. Garmire.

08W: Arrange

Elementary physics (classical and quantum) is applied to create models for the behavior of semiconductor devices. The distribution of electron energy, the gap between energy bands, and the mechanisms of current flow are derived. The pn junction and its variations, bipolar junction transistor, junction field effect transistor, and MOSFET devices are studied. Other devices studied are chosen from among opto-electronic and heterojunction devices.

Prerequisite: Engineering Sciences 24 and 32 or equivalents. Garmire.

All terms: Arrange

Advanced graduate students may elect a program of independent reading.

07S, 08S: 2A

This survey course discusses both the physical principles and practical applications of the more common modern methods of materials characterization. It covers techniques of both microstructural analysis (OM, SEM, TEM, electron diffraction, XRD), and microchemical characterization (EDS, XPS, AES, SIMS, NMR, RBS and Raman spectroscopy), together with various scanning probe microscopy techniques (AFM, STM, EFM and MFM). Emphasis is placed on both the information that can be obtained together with the limitations of each technique. The course has a substantial laboratory component, including a project involving written and oral reports, and requires a term paper.

Prerequisite: Engineering Sciences 24 or permission. I. Baker.

All terms: Arrange

Part time (one credit) thesis research under the guidance of a staff member. Open to candidates for the M.S. degree and Ph.D. students before admission to candidacy.

All terms: Arrange

Part time (two credits) thesis research under the guidance of a staff member. Open to candidates for the M.S. degree and Ph.D. students before admission to candidacy.

All terms: Arrange

Full time (three credits) thesis research under the guidance of a staff member. Open to candidates for the M.S. degree and Ph.D. students before admission to candidacy.

06F, 07F: Arrange

Course designed for incoming graduate students who will serve as graduate teaching assistants in the department. The course will provide students with resources and experiences directly relevant to typical teaching assistant duties, including public speaking, lab supervision, teacher/student relations and grading.

Required of entering Ph.D. students. This course is not open for credit to undergraduates. Millan.

All terms: Arrange

Tutoring, laboratory teaching, student evaluation, and leading recitation classes, under the supervision of a faculty member.

Prerequisite: Physics 256.

All terms: Arrange

Part time (one credit) thesis research under the guidance of a staff member. Open to candidates for the Ph.D. degree.

All terms: Arrange

Part time (two credits) thesis research under the guidance of a staff member. Open to candidates for the Ph.D. degree.

All terms: Arrange

Full time (three credits) thesis research under the guidance of a staff member. Open to candidates for the Ph.D. degree.

07W, 08W: 11

An introduction to the study of the nine major planets and their natural satellites, together with asteroids and comets. Topics to be discussed include formation and evolution of the early solar system, Terrestrial and Jovian planetary surfaces and atmospheres, comparative planetology, and the collision of planetary bodies. Course material will include results from recent planetary spacecraft missions. Labs include making observations with telescopes. No prerequisite. Supplemental course fee required. *Dist: SLA.* R. Fesen.

06F: 11 07X: 10 07F: 11

A survey of contemporary knowledge of the nature and the evolution of stars, galaxies and the universe. Topics include stellar evolution, the origin of the elements, the deaths of stars, black holes, the structure of our Galaxy, other galaxies, dark matter, the expanding universe and the big bang. Physical processes underlying these phenomena are discussed. Starting in the 2001-2002 academic year, no student may receive credit for both Astronomy 2 and Astronomy 3. Identical to Astronomy 3, but without the observing laboratory. *Dist. SCI*. Wegner (fall).

06F: 11 07X: 10 07F: 11

A survey of contemporary knowledge of the nature and the evolution of stars, galaxies and the universe. Topics include stellar evolution, the origin of the elements, the deaths of stars, black holes, the structure of our Galaxy, other galaxies, dark matter, the expanding universe and the big bang. Physical processes underlying these phenomena are discussed. Students will make observations with radio and optical telescopes. Supplemental course fee required. Starting in the 2001-2002 academic year, no student may receive credit for both Astronomy 2 and Astronomy 3. Identical to Astronomy 2, but with an observing laboratory. *Dist. SLA.* Wegner (fall).

07S: 12 Offered in alternate years

A survey of the development of theories of the cosmos from ancient to modern times in an historical sequence, commencing with ancient attitudes and progressing to modern concepts. Topics discussed include the Ptolemaic and Copernican theories, the emergence of an observational basis of astronomy through the works of Kepler and Galileo. Newton's synthesis, relativity theory and its application to modern cosmologies. Supplemental course fee required. *Dist: SCI.* R. Fesen*.*

*Consult special listings*

07S, 08S: 10A

An introduction to astronomy and astrophysics for science majors and others with some background in physics, providing an observational and theoretical background for more advanced topics in astrophysics. Topics include basic properties of stars as derived from observations, stellar evolution, black holes, transfer of energy by electromagnetic radiation, the interstellar gas and the Milky Way galaxy. Students will make observations with the telescope.

Prerequisite: an introductory physics course (or permission of instructor) and Mathematics 3. *Dist: SCI.* Thorstensen.

07W, 08W: 10A

This is a course in physical cosmology. The first half builds the Universe from the bottom up, focusing on galaxies. Topics include galaxy classification dynamics, clustering, dark matter, and evidence for the large scale homogeneity. The second half builds the Universe from the top down, developing the Big Bang cosmology. Topics include FRW equation classical cosmological tests, nucleosynthesis, and cosmic microwave background.

Prerequisite: Physics 14 or permission of the instructor. *Dist: SCI.* Chaboyer.

07F: Arrange Offered in alternate years

The fundamental techniques of observational astronomy. Topics include detectors, photometry, spectroscopy, data acquisition and analysis.

Prerequisite: Astronomy 2, 3 or 15. *Dist: SLA.* Wegner.

07W: 12 Offered in alternate years

A study of modern astrophysics for the advanced physics undergraduate or graduate student who may or may not have previous background in astronomy. The overall theme of the course is the creation of the elements-from the big bang to the current epoch. Physical processes in stellar interiors, stellar evolution, and nucleosynthesis will be emphasized. Starting in the 2003-2004 academic year, no student may receive credit for both Astronomy 74 and Astronomy 115.

Prerequisite: Physics 43 and Astronomy 2, 3 or 15, or permission of instructor. *Dist: SCI*. Chaboyer.

08S: 12 Offered in alternate years

The physics and observations of black holes, neutron stars, white dwarfs, supernova remnants, and extragalactic objects through x-ray, gamma-ray, and cosmic rays.

Prerequisites: Physics 19 and Astronomy 25 or the equivalent, or permission of the instructor. *Dist: SCI*.

All Terms: Arrange

Advanced study of a topic in observational astronomy, culminating in a one- to two-week observing session at the observatory in Arizona.

All terms: Arrange

Intensive individual work on an observational or theoretical problem in astronomy or cosmology under the guidance of a staff member.

Prerequisite: permission of the Chair.

07W: 12 Offered in alternate years

A study of the physical processes in stellar interiors, stellar evolution, and nucleosynthesis. Topics to be covered include big bang nucleosynthesis, the equations of stellar structure, equations of state, opacities, nuclear reactions, energy transport in stars, polytrope models, stellar models, the evolution of stars, and supernovae. Starting in the 2003-2004 academic year, no student may receive credit for both Astronomy 74 and Astronomy 115.

Prerequisite: Permission of instructor. Chaboyer.

07S: Arrange

The structure of galaxies and the dynamics of stellar systems. Topics include application of the Boltzmann transport equation to stellar systems, star cluster models, spiral structure, stellar populations, and the classification of galaxies. Active galaxies and their physical processes.

Prerequisite: Permission of the instructor. Wegner.

07W: Arrange

Structure, dynamics, and energy balance of the interstellar medium. Topics covered include high-energy particle and radiation interactions with interstellar gas, H II regions, shocks, molecular clouds, star forming regions, stellar mass loss nebulae and bubbles, and supernova remnants.

Prerequisite: Astronomy 74, or permission of the instructor. R. Fesen.

08W: Arrange

The observational determination of the structure of the universe. Determination of the astronomical distance scale, Hubble's law, and measurements of the space distribution and peculiar motions of galaxies. Statistical treatment of the data. Quasars and gravitational lenses, nucleosynthesis and the cosmic microwave background. Comparison with cosmological models and theories of galaxy formation.

Prerequisite: Astronomy 74, or permission of the instructor. Wegner.

All terms: Arrange

Advanced treatment of topics in astronomy.