Department of Physics and Astronomy

J. CHRISTOPHER CLEMENS, *Chair*

*Professors*

Bruce W. Carney (32) Optical Observational Astrophysics

Gerald N. Cecil (47) Experimental Astrophysics

Arthur E. Champagne (51) Experimental Nuclear Physics and Astrophysics

Thomas B. Clegg (5) Nuclear Physics, Polarization Phenomena

J. Christopher Clemens (64) Observational Astronomy, Astrophysics, Astronomical Instrumentation

Louise A. Dolan (49) Theoretical Particle Physics, Quantum Gravity

Jonathan Engel (57) Theoretical Nuclear Physics

Charles R. Evans (48) Gravity, Relativity, Theoretical Astrophysics

Christian G. Iliadis (61) Experimental Nuclear Astrophysics

Hugon J. Karwowski (37) Experimental Nuclear Physics and Astrophysics

Dmitri V. Khveshchenko (1) Theoretical Physics

Jianping Lu (56) Condensed Matter Theory, Nanotechnology, Medical Physics

Laurie E. McNeil (36) Experimental Condensed Matter and Materials Physics

Y. Jack Ng (30) Theoretical Particle Physics, Gravitation

Lu-Chang Qin (27) Materials Science, Nanotechnology

Daniel E. Reichart (13) Gamma Ray Bursts, Early Universe, Interstellar Extinction, Galaxy Clusters

Richard Superfine (55) Experimental Studies of Interfaces, Biophysics

Frank Tsui (59) Experimental Condensed Matter and Materials Physics

Sean Washburn (50) Experimental Condensed Matter and Materials Physics

John Wilkerson, (12) Experimental Neutrino Physics and Fundamental Symmetries

Yue Wu (54) Nuclear Magnetic Resonance, Electron Spin Resonance in Solids

Otto E. Zhou (62) Materials Science, Nanotechnology

*Associate Professors*

Reyco Henning (11) Neutrino Physics, Particle Astrophysics

Sheila Kannappan (14) Observational Extragalactic Astronomy

Rene Lopez (25) Experimental Condensed Matter Physics

Laura Mersini (19) Theoretical Cosmology

*Assistant Professors*

Rosa Tamara Branca, NMR Imaging

Joaquin Drut, Theory of Strongly Interacting Systems

Adrienne Erickcek, Theoretical Astrophysics and Cosmology

Fabian Heitsch (26), Computational Astrophysics

Nicholas Law, Astrophysics

Amy Oldenburg, Biophotonics and Biomechanics

*Lecturers*

Alice Churukian, UNC-BEST, Physics Education Research

Duane Deardorff, Lab Director, Physics Education Research

David Smith, Physics Education Research

*Research Professors*

Michael R. Falvo, Biophysics, Nanomechanics

Alfred Kleinhammes, Condensed Matter Physics, Materials Science

Pabbitra Sen, Theoretical Condensed Matter Physics

Russell M. Taylor II, Nanotechnology, Computer Imaging

*Research Associate Professors*

Nalin R. Parikh (58) Solid State Physics, Materials Science

*Research Assistant Professors*

Cao Guohua, Medical Physics

David B Hill, Biophysics

E. Timothy O'Brien, Physics Related to Biology, Light Microscopy, Biological Sample Preparation

Kwan Skinner, Materials Physics

*Adjunct Professors*

Marcus Berg, Theoretical Astrophysics and Cosmology

Sha X. Chang, Medical Physics

Richard T. Hammond, General Relativity, Gravity, Optics

David Radford, Nuclear Physics

Ryan M. Rohm, Quantum Field Theory, Theoretical Particle Physics

Jie Tang, Materials Physics, Nanomaterials

*Adjunct Associate Professor*

Anton Tonchev, Nuclear Physics

*Adjunct Assistant Professors*

Yueh Lee, Medical Physics

*Professors Emeriti*

C. Victor Briscoe

Sang-Il Choi

Wayne Christiansen

Kian S. Dy

John Hernandez

William M. Hooke

Paul S. Hubbard

Horst Kessemeier

Edward J. Ludwig

J. Ross Macdonald

James Rose

Larry Rowan

Dietrich Schroeer

Stephen M. Shafroth

Lawrence M. Slifkin

William J. Thompson

James W. York Jr.

The Department of Physics and Astronomy offers graduate work leading to the degrees of master of science and doctor of philosophy.

The active fields of research are biophysics, medical physics, condensed-matter physics, materials physics, nanotechnology, nuclear physics, neutrino physics and nuclear astrophysics, quantum field theory, theoretical particle physics, general relativity and gravitation, extragalactic and stellar astronomy, and astrophysics. Students can also work in the UNC–Chapel Hill biophysics program, or they can study under any advisor so long as the research project is supervised by a committee that contains a majority of UNC–Chapel Hill Physics and Astronomy faculty. The graduate courses are designed to give students a broad foundation and to introduce them to the special fields in which the research interests of the department lie.

The general regulations of The Graduate School govern the work for the degrees of master of science and doctor of philosophy. To begin a graduate program in physics or astrophysics, the student should have completed most of the requirements for the degree of bachelor of science with a major in physics at the University, or their equivalent elsewhere. The minimum prerequisite for graduate study consists of the basic undergraduate courses PHYS 116, 117, 128, 128L, 301, 321, 341, 521, 311, and 312, together with MATH 232, 233, and 528.

The M.S. degree in physics may be taken with or without thesis. However, even if a thesis is not submitted, a student must work with a research group for at least one semester, in order to learn the research techniques in a field of physics or astronomy. If the research is theoretical, the student must also gain experimental experience for at least one semester. A minor is not required for the M.S. degree, but one may be chosen in accord with the regular graduate requirements for this option. The equivalent of one semester teaching experience is required of all M.S. degree candidates. The M.S. astrophysics track must include ASTR 701 and a minimum of six hours from ASTR 519, 702, 703 or 704.

The requirements for a Ph.D. in physics are (a) successful completion of the following core courses in the department, or completion of their equivalents elsewhere as an undergraduate or graduate student: 701, 711, 712, 741, 721, and 722; (b) passing the Ph.D. written examination based on core graduate courses in physics as listed in (a), (c) gaining experimental experience either through master's or doctoral research, or (if student's research is theoretical) by performing an experimental project deemed adequate by the director of graduate studies, (d) passing at least three other advanced graduate-level courses that have been approved by the director of graduate studies. A Ph.D. candidate is also expected to take a preliminary doctoral oral examination within the first three years of graduate study in physics at UNC–Chapel Hill. The oral examination is concerned mainly with the student's dissertation research project. A minor is not required, but may be elected, in which case requirement (c) above is replaced by the requirement that the student pass at least five graduate-level courses selected from no more than two departments, with no fewer than two courses in either department. The minor program must be approved in advance by the minor department. Teaching experience, as part of professional training, is required of all doctoral candidates. This experience can be gained through laboratory or lecture instruction as a teaching assistant, either for two semesters or until teaching competence is acquired.

The astrophysics Ph.D. track requirements are similar except that the course requirements are PHYS 701, 711, 721, 741 and ASTR 701, 702, 703, 704, 705 and an additional 700-level course. The Ph.D. written exam covers ASTR 701 and ASTR 702 instead of PHYS 712 and PHYS 722. To gain familiarity with experimental astrophysics or observational astronomy, a student must pass ASTR 519/719, earn an M.S. degree that involves experimental or observational research in astrophysics, or perform other experimental/observational research deemed suitable by the director of graduate studies.

Research Interests

*Astronomy and Astrophysics.* Research includes the formation, structure, and evolution of stars, our Milky Way galaxy, evolution and dynamics of galaxies, gamma ray bursters, cosmology, numerical relativity and sources of gravitational radiation, stellar seismology and quasars, exo-planets, and interstellar medium physics. UNC–Chapel Hill has guaranteed observing time on the 4.1-meter SOAR Telescope in Chile and on the 11-meter SALT Telescope in South Africa. UNC–Chapel Hill operates a number of smaller robotic telescopes as well, and maintains multiple astronomical instrumentation labs dedicated to adaptive optics and state-of-the-art spectroscopy.

*Biological and Medical Physics.* Experimental studies include manipulation and force measurement techniques with applications to DNA, molecular motors, cells, and cilia; hydration effects in adsorption of biochemicals. There is also a strong focus on the theoretical and experimental translational research in medical imaging technologies, including radiotherapy instruments based on carbon nanotube X-ray emitters such as single-cell irradiation and in vivo micro-CT; optical coherence tomography with nanoparticle molecular imaging agents; systems level implementation of tomographic imaging instruments.

*Condensed-Matter Physics.* Experimental and Theoretical Studies of Nanomaterials. Atomic scale studies of devices and nanoelectromechanical systems, including quantum computation and transport, actuating nanomotors and sensors, amorphous materials, semiconductors, superconductors, the optical properties of solids, charge transport in solids and fluids, epitaxial growth, magnetic materials and heterostructures.

*Field Theory, Particle Physics, Cosmology, Gravitation and Relativity. *Research includes gauge field theories, quantum chromodynamics, electroweak theory, grand unified theories, string theory, supersymmetry, supergravity, quantum gravity, theoretical cosmology, numerical relativity, gravitational radiation, and relativistic astrophysics.

*Materials Science and Materials Physics.* Experimental and theoretical research in the design, synthesis, integration, and characterization of novel solid state materials, including nanostructured materials such as quantum dots, carbon nanotubes and nanorods, quasi-crystals, and metallic glass. Applications of novel materials for solar energy, electron field emission, probes and sensors, and data storage. Applications include flat-panel displays, an X-ray system for biomedical imaging, and rechargeable batteries.

*Nuclear Physics.* Experimental and theoretical work includes neutrino oscillations and neutrino mass measurements, fundamental symmetries and weak interactions in supernovae. The structure and evolution of stars are investigated using nuclear probes. The origin of the elements in the universe is studied using local accelerator facilities. The nature of the nuclear force and properties of few-body systems. Polarized beams of light ions and gamma-rays and polarized 3He target. Applied nuclear physics.

Facilities and Equipment

Research in physics and astronomy is carried out in laboratories on and off the Chapel Hill campus. Within Phillips Hall and Chapman Hall there are several major research laboratories including the "nanomanipulator" (a combination of a scanning electron microscope, an atomic force microscope, and sophisticated visualization graphics), the Keck Laboratory for Atomic Imaging and Manipulation, which includes two transmission electron microscopes, and the Goodman Laboratory for Astronomical Instrumentation. Other facilities include apparatus for nuclear magnetic resonance studies, scanning probe microscopes, and Raman and optical spectrometers. For synthesis and fabrication, major facilities include molecular beam epitaxy, microwave plasma-enhanced chemical vapor deposition, laser ablation, and photolithography and reactive ion etching. Resources for highly parallel computing are provided by UNC's Information and Technology Services, as well as by national centers.

The department is a partner in the Triangle Universities Nuclear Laboratory and plays a major role in experiments using the Laboratory for Experimental Nuclear Astrophysics (LENA), Tandem Accelerator, and the High-Intensity Gamma-Ray Source at the Free Electron Laser facility. UNC–Chapel Hill has an active program in low-background physics at the KURF underground facility near Blacksburg, VA. UNC–Chapel Hill has a 0.6-meter on-campus telescope, and is a major partner in the 4.1-meter SOAR Telescope in Chile and the 11-meter Southern African Large Telescope (SALT) in South Africa. The department operates the PROMPT array of robotic telescopes in Chile and manages the SkyNet array of robotic telescopes. Numerous national laboratories, including Oak Ridge, Brookhaven, NIST, Los Alamos and Argonne, as well as KamLAND, NRAO, NOAO, the Hubble Space Telescope, and the Chandra X-ray Observatory, are also vital parts of our research efforts.

Fellowships and Assistantships

Teaching Assistantships (with stipends of $17,160 for nine months) are available to qualified graduate students. Summer employment is usually available. The duties of assistants include supervising laboratory classes in elementary physics or astronomy, assisting in the supervision of advanced laboratories, teaching recitation sections, and grading papers. Graduate School fellowships are available for well-qualified applicants to the department's graduate program. Graduate students can usually be supported in the summer by teaching or research.

Research assistantships are also offered, especially to those who have completed a year or two of graduate work. The stipend is at least $22,881 for the calendar year.

Application forms for admission, including graduate appointments, should be completed online at gradschool.unc.edu/admissions.

Courses for Graduate and Advanced Undergraduate Students

**ASTR**

**501 Astrophysics I (Stellar Astrophysics) (3). **Prerequisites, ASTR 301, MATH 383, and PHYS 331. Permission of the instructor for students lacking the prerequisites. An introduction to the study of stellar structure and evolution. Topics covered include observational techniques, stellar structure and energy transport, nuclear energy sources, evolution off the main-sequence, and supernovae.

**502 Astrophysics II (Modern Research in Astrophysics) (3). **Prerequisites, ASTR 301 and MATH 383; pre- or corequisite, PHYS 331. An introduction to modern research in astrophysics based on scientific journal articles addressing a current topic of interest in galactic or extragalactic astrophysics, including training in computer modeling and statistical analysis, culminating in the completion of a research project.

**503 Structure and Evolution of Galaxies (3). **Prerequisites, ASTR 301, MATH 383, and PHYS 331. Internal dynamics and structure of galaxies; physics of star formation, active galactic nuclei, and galaxy interactions; large-scale clustering and environment-dependent physical processes; evolution of the galaxy population over cosmic time.

**504 Cosmology (3). **Prerequisites, ASTR 301 and PHYS 301; pre- or corequisite, PHYS 321. An introduction to modern cosmology: the study of the contents and evolution of the universe. Covers expanding spacetime, the thermal history of the early universe, including nucleosynthesis and the cosmic microwave background, the inflationary model for the origins of cosmic structure, and the growth of that structure though time.

**505 Physics of Interstellar Gas (3). **Prerequisites, ASTR 301, MATH 383, and PHYS 331. Surveys the physical processes governing the interstellar medium (ISM), which takes up the "refuse" of old stars while providing fuel for young stars forming. Covers the processes regulating the galactic gas budget and the corresponding observational diagnostics. Topics: radiative transfer, line formation mechanisms, continuum radiation, gas dynamics, star formation.

**519 Observational Astronomy (4). **Prerequisite, ASTR 102; pre- or corequisite, PHYS 331. Permission of the instructor for students lacking the prerequisite. A course designed to familiarize the student with observational techniques in optical and radio astronomy, including application of photography, spectroscopy, photometry, and radio methods. Three lecture and three laboratory hours a week.

Courses for Graduate and Advanced Undergraduate Students

**PHYS**

**405 Biological Physics (BIOL 431) (3). **Prerequisites, PHYS 116 and 117. How diffusion, entropy, electrostatics, and hydrophobicity generate order and force in biology. Topics include DNA manipulation, intracellular transport, cell division, molecular motors, single molecule biophysics techniques, nerve impulses, neuroscience.

**410 Teaching and Learning Physics (4). **Prerequisites, PHYS 116 and 117. Permission of the instructor for students lacking the prerequisites. Learning how to teach physics using current research-based methods. Includes extensive fieldwork in high school and college environments. Meets part of the licensure requirements for North Carolina public school teaching.

**415 Optics (3). **Prerequisites, PHYS 311 and 312. Permission of the instructor for students lacking the prerequisites. Elements of geometrical optics; Huygens' principles, interference, diffraction, and polarization. Elements of the electromagnetic theory of light; Fresnel's equations, dispersion, absorption, and scattering. Photons. Lasers and quantum optics.

**422 Physics of the Earth's Interior (GEOL 422) (3). **Prerequisites, MATH 383 and either PHYS 201 and 211, or 301 and 311. Origin of the solar system: the nebular hypothesis. Evolution of the earth and its accretionary history. Earthquakes: plate tectonics and the interior of the earth. The earth's magnetic field. Mantle convection.

**424 General Physics I (4). **PHYS 104 equivalent, specifically for certification of high school teachers.

**425 General Physics II (4). **PHYS 105 equivalent, specifically for certification of high school teachers.

**471 Physics of Solid State Electronic Devices (3). **Prerequisite, PHYS 117; pre- or corequisite, PHYS 211 or 311. Properties of crystal lattices, electrons in energy bands, behavior of majority and minority charge carriers, PN junctions related to the structure and function of semiconductor diodes, transistors, display devices.

**472 Chemistry and Physics of Electronic Materials Processing (APPL 472, CHEM 472) (3). **Prerequisite, CHEM 482 or PHYS 117. Permission of the instructor. A survey of materials processing and characterization used in fabricating microelectronic devices. Crystal growth, thin film deposition and etching, and microlithography.

**481L Advanced Laboratory I (2). **Prerequisite, PHYS 351 or 352. Permission of the instructor for students lacking the prerequisite. Selected experiments illustrating modern techniques such as the use of laser technology to study the interaction of electromagnetic fields and matter. Six laboratory hours a week.

**482L Advanced Laboratory II (2). **Prerequisite, PHYS 481. Permission of the instructor for students lacking the prerequisite. Independent laboratory research projects. Scientific writing and oral presentations, abstracts, and reports. Six laboratory hours per week.

**491L Materials Laboratory I (APPL 491L) (2). **Prerequisites, APPL 470 and PHYS 351. Structure determination and measurement of the optical, electrical, and magnetic properties of solids.

**492L Materials Laboratory II (APPL 492L) (2). **Prerequisite, APPL 491L or PHYS 491L. Continuation of PHYS 491L with emphasis on low- and high-temperature behavior, the physical and chemical behavior of lattice imperfections and amorphous materials, and the nature of radiation damage.

**510 Seminar for Physics and Astronomy Teaching Assistants (1). **How students learn and understand physics and astronomy. How to teach using current research-based methods.

**521 Applications of Quantum Mechanics (3). **Prerequisite, PHYS 321. Emphasizes atomic physics but includes topics from nuclear, solid state, and particle physics, such as energy levels, the periodic system, selection rules, and fundamentals of spectroscopy.

**543 Nuclear Physics (3). **Prerequisite, PHYS 321. Permission of the instructor for students lacking the prerequisite. Structure of nucleons and nuclei, nuclear models, forces and interactions, nuclear reactions.

**545 Introductory Elementary Particle Physics (3). **Prerequisites, PHYS 312 and 321. Relativistic kinematics, symmetries and conservation laws, elementary particles and bound states, gauge theories, quantum electrodynamics, chromodynamics, electroweak unification, standard model and beyond.

**573 Introductory Solid State Physics (APPL 573) (3). **Prerequisite, PHYS 321. Permission of the instructor for students lacking the prerequisite. Crystal symmetry, types of crystalline solids; electron and mechanical waves in crystals, electrical and magnetic properties of solids, semiconductors; low temperature phenomena; imperfections in nearly perfect crystals.

**581 Renewable Electric Power Systems (3). **Prerequisites, BIOL 101L, and 202 or 271; and PHYS 131, and 131L or 281L, and 201 or 301, and 211 or 311, and 351; pre-or corequisites, CHEM 261 and 481. Broad and quantitative study of renewable electric power systems: wind systems, photovoltaic cells, distributed generation (concentrating solar power, microhydro, biomass), and the economics of these technologies.

**582 Decarbonizing Fuels (3). **Prerequisites, BIOL 101L, and 202 or 271; and PHYS 131, and 131L or 281L, and 201 or 301, and 211 or 311, and 351; pre- or corequisites, CHEM 261 and 481. Assess quantitatively the feasibility of powering humanity without increasing release of climate-altering carbon dioxide and other organic greenhouse gases into the atmosphere. Can these gases be removed? Which bio-chemical-physical novelties may scale to meet growing demand and at what cost?

**585 Imaging Science: From Cells to Stars (3). **Prerequisites, MATH 233 and PHYS 118. Fundamentals of imaging as applied to biological, medical and astronomy imaging systems. Physics of radiation and particle sources, image formation and detection physics. Principles of optics, coherence, Fourier methods, statistics, especially as they cross disciplinary boundaries for new opportunities in imaging.

**594 Nonlinear Dynamics (MATH 594) (3). **Prerequisite, MATH 383. Permission of the instructor for students lacking the prerequisite. Interdisciplinary introduction to nonlinear dynamics and chaos. Fixed points, bifurcations, strange attractors, with applications to physics, biology, chemistry, finance.

**631 Mathematical Methods of Theoretical Physics I (3). **Prerequisites, MATH 383 and PHYS 128. Vector fields, curvilinear coordinates, functions of complex variables, linear differential equations of second order, Fourier series, integral transforms, delta sequence.

**632 Mathematical Methods of Theoretical Physics II (3). **Prerequisite, PHYS 631. Permission of the instructor for students lacking the prerequisite. Partial differential equations, special functions, Green functions, variational methods, traveling waves, and scattering.

**633 Scientific Programming (3). **Prerequisite, MATH 528 or 529, or PHYS 631 or 632. Required preparation, elementary Fortran, C, or Pascal programming. Structured programming in Fortran or Pascal; use of secondary storage and program packages; numerical methods for advanced problems, error propagation and computational efficiency; symbolic mathematics by computer.

660 Fluid Dynamics (ENVR 452, GEOL 560, MASC 560) (3). See MASC 560 for description.

**671L Independent Laboratory I (3). **Prerequisites, PHYS 301 and 312. Permission of the instructor for students lacking the prerequisites. Six laboratory hours a week.

672L Independent Laboratory II (3). Prerequisites, PHYS 301 and 312. Permission of the instructor for students lacking the prerequisites. Six laboratory hours.

Courses for Graduate Students

**ASTR**

**701 Stellar Interiors, Evolution, and Populations (3). **Stellar structure and evolution including: equations of stellar structure, stellar models, star and planet formation, fusion and nucleosynthesis, stellar evolution, stellar remnants, and the comparison of theory to observations.

**702 High Energy Astrophysics (3). **Prerequisites, PHYS 711 and 721. White dwarfs and neutron stars: physical properties and observational manifestations. Extragalactic radio sources, relativistic jets and supermassive black holes. Particle acceleration and radiative processes in hot plasmas. Accretion phenomena. X-ray and gamma-ray astrophysics.

**703 Structure and Evolution of Galaxies (3). **Internal dynamics and structure of galaxies; physics of star formation, active galactic nuclei, and galaxy interactions; large-scale clustering and environment-dependent physical processes; evolution of the galaxy population over cosmic time.

**704 Cosmology (3). **Corequisite, PHYS 701. General relativity and cosmological world models; thermal history of the early universe, nucleosynthesis, and the cosmic microwave background; growth of structure through cosmic time.

**705 Astrophysical Atmospheres (3). **Prerequisites PHYS 711 and 721. Radiative transfer, opacities, spectral line formation, energy transport, models, chemical abundance determination, interstellar chemistry, magnetic fields. Applications to observations of planetary, stellar and solar, galactic (ISM) and intergalactic gaseous atmospheres.

**719 Astronomical Data (4). **Required preparation, physics-based cosmology course or permission of the instructor. A course designed to familiarize the student with observational techniques in optical and radio astronomy, including application of photography, spectroscopy, photometry, and radio methods. Three lecture and three laboratory hours a week.

**891 Seminar in Astrophysics (1–21). **Recent observational and theoretical developments in stellar, galactic, and extragalactic astrophysics.

Courses for Graduate Students

**PHYS**

**The PHYS 821 and PHYS 896 sequence alternates with PHYS 822 and 823.*

**701 Classical Dynamics (3). **Required preparation, advanced undergraduate mechanics. Variational principles, Lagrangian and Hamiltonian mechanics. Symmetries and conservation laws. Two-body problems, perturbations, and small oscillations, rigid-body motion. Relation of classical to quantum mechanics.

**711 Electromagnetic Theory I (3). **Prerequisites, PHYS 631 and 632. Electrostatics, magnetostatics, time-varying fields, Maxwell's equations.

**712 Electromagnetic Theory II (3). **Prerequisite, PHYS 711. Plane electromagnetic waves and wave propagation, wave guides and resonant cavities, simple radiating systems, scattering and diffraction, special theory of relativity, radiation by moving charges.

**715 Visualization in Science (COMP 715, MTSC 715) (3). **See COMP 715 for description.

**721 Quantum Mechanics (3). **Prerequisite, PHYS 321. Review of nonrelativistic quantum mechanics. Spin, angular momentum, perturbation theory, scattering, identical particles, Hartree-Fock method, Dirac equation, radiation theory.

**722 Quantum Mechanics (3). **Prerequisite, PHYS 321. Review of nonrelativistic quantum mechanics. Spin, angular momentum, perturbation theory, scattering, identical particles, Hartree-Fock method, Dirac equation, radiation theory.

**741 Statistical Mechanics (3). **Prerequisites, PHYS 701 and 721. Classical and quantal statistical mechanics, ensembles, partition functions, ideal Fermi and Bose gases.

**771L Advanced Spectroscopic Techniques (3). **Prerequisite, PHYS 301 or 312. Permission of the instructor for students lacking the prerequisite. Advanced spectroscopic techniques, including Rutherford backscattering-channeling, perturbed angular correlation, Raman scattering, electron paramagnetic resonance, nuclear magnetic resonance, optical absorption, and Hall effect. Two hours of lecture and three hours of laboratory a week.

**772L Advanced Spectroscopic Techniques (3). **Prerequisite, PHYS 301 or 312. Permission of the instructor for students lacking the prerequisite. Advanced spectroscopic techniques, including Rutherford backscattering-channeling, perturbed angular correlation, Raman scattering, electron paramagnetic resonance, nuclear magnetic resonance, optical absorption and Hall effect. One hour of lecture and five hours of laboratory a week.

***821 Advanced Quantum Mechanics (3). **Prerequisite, PHYS 722. Advanced angular momentum, atomic and molecular theory, many-body theory, quantum field theory.

***822 Field Theory (3). **Prerequisite, PHYS 722. Quantum field theory, path integrals, gauge invariance, renormalization group, Higgs mechanism, electroweak theory, quantum chromodynamics, Standard Model, unified field theories.

***823 Field Theory (3). **Prerequisite, PHYS 722. Quantum field theory, path integrals, gauge invariance, renormalization group, Higgs mechanism, electroweak theory, quantum chromodynamics, Standard Model, unified field theories.

**824 Group Theory and its Applications (3). **Required preparation, knowledge of matrices, mechanics and quantum mechanics. Discrete and continuous groups. Representation theory. Application to atomic, molecular, solid state, nuclear and particle physics.

**827 Principles of Chemical Physics (CHEM 788) (3). **Prerequisite, CHEM 781 or PHYS 321. Permission of the instructor for students lacking the prerequisite. The quantum mechanics of molecules and their aggregates. Atomic orbitals, Hartree-Fock methods for atoms and molecules. Special topics of interest to the instructor and research students.

**829 Principles of Magnetic Resonance (3). **Prerequisite, CHEM 781 or PHYS 721. Permission of the instructor for students lacking the prerequisite.

**831 Differential Geometry in Modern Physics (3). **Prerequisites, PHYS 701, 711, and 712. Applications to electrodynamics, general relativity and nonabelian gauge theories of methods of differential geometry, including tensors, spinors, differential forms, connections and curvature, covariant exterior derivatives, and Lie derivatives.

**832 General Theory of Relativity (3). **Prerequisite, PHYS 831. Permission of the instructor for students lacking the prerequisite. Differential geometry of space-time. Tensor fields and forms. Curvature, geodesics. Einstein's gravitational field equations. Tests of Einstein's theory. Applications to astrophysics and cosmology.

**861 Nuclear Physics (3). **Prerequisites, PHYS 543 and 721. Nuclear reactions, scattering, Nuclear structure, Nuclear astrophysics.

**862 Nuclear Physics (3). **Prerequisites, PHYS 543 and 721. Overview of Standard Model of particle physics. Fundamental symmetries and weak interactions. Neutrino physics. Particle-astrophysics and cosmology.

**871 Solid State Physics (MTSC 871) (3). **Prerequisite, PHYS 321. Topics considered include those of PHYS 573, but at a more advanced level, and in addition a detailed discussion of the interaction of waves (electromagnetic, elastic and electron waves) with periodic structures, e.g., X-ray diffraction, phonons, band theory of metals and semiconductors.

**872 Solid State Physics (MTSC 872) (3). **Prerequisite, PHYS 321. Topics considered include those of PHYS 573, but at a more advanced level, and in addition a detailed discussion of the interaction of waves (electromagnetic, elastic, and electron waves) with periodic structures, e.g., X-ray diffraction, phonons, band theory of metals and semiconductors.

**873 Theory of the Solid State (3). **Prerequisite, PHYS 722. Calculation of one-electron energy band structure. Electron-hole correlation effect and excitons. Theory of spin waves. Many-body techniques in solid state problems including theory of superconductivity.

**883 Current Advances in Physics (3). **Permission of the instructor. In recent years, elementary particle physics, amorphous solids, neutrinos, and electron microscopy have been among the topics discussed.

**893 Seminar in Solid State Physics (1–21). **Research topics in condensed-matter physics, with emphasis on current experimental and theoretical studies.

**895 Seminar in Nuclear Physics (1–21). **Current research topics in low-energy nuclear physics, especially as related to the interests of the Triangle Universities Nuclear Laboratory.

***896 Seminar in Particle Physics (1–21). **Symmetries, gauge theories, asymptotic freedom, unified theories of weak and electromagnetic interactions, and recent developments in field theory.

**897 Seminar in Theoretical Physics (1–21). **Topics from current theoretical research including, but not restricted to, field theory, particle physics, gravitation, and relativity.

**899 Seminar in Professional Practice (1–21). **Required preparation, Ph.D. written exam passed. The role and responsibilities of a physicist in the industrial or corporate environment and as a consultant.

**901 Research (1–21). **10 or more laboratory or computation hours a week.

**992 Master's (Non-Thesis) (3). **

**993 Master's Research and Thesis (3). **

**994 Doctoral Research and Dissertation (3). **Fall or spring. Staff.