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Graduate Study and Research in Physics Department, Study notes of Solid State Physics

The Physics Department offers graduate study and research which leads to the Ph.D. degree. The department consists of thirty instructional faculty members, fifteen additional physicists in purely research positions, and 60 full-time graduate students. The department offers a wide range of undergraduate and graduate courses of instruction. It also has strong links with the Applied Science Department and Computational Science Cluster. Research areas include Atomic and Optical Physics, Computational Physics, Condensed Matter Physics, Nuclear and Hadronic Physics, and High Energy Particle Physics.

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Physics •  113
The Physics Department offers graduate study and research which leads to the
Ph.D. degree. The department consists of thirty instructional faculty members,
fifteen additional physicists in purely research positions, and 60 full-time graduate
students. Additions to the research areas
listed below include plasma and non-linear
physics and related research includes
accelerator physics (in cooperation with
Jefferson Lab) and material characterization
(in cooperation with NASA-Langley Research
Center). The department offers a wide range
of undergraduate and graduate courses
of instruction. It also has strong links with
the Applied Science Department and
Computational Science Cluster.
Atomic and Optical Physics
Experimental research areas include intense laser-matter interaction, femtosecond laser
physics, slow and stored light, ultra-cold quantum gases (Bose-Einstein condensates and
degenerate Fermi gases), and the study of biological systems using AMO techniques.
The theory program includes the study of classical trajectories and chaos in atomic and
molecular systems and their correlation with quantum mechanics.
Computational Physics
Research in this area includes the studies of turbulence, macroscopic nonlinear systems,
soliton theory, wave propagation, signal processing, Monte Carlo simulations, ab initio
calculations and lattice quantum chromodynamics. These studies have applications within
many fields of physics, including laser science, wave dynamics, quantum computing, plasma
physics, condensed matter physics, nuclear physics and particle physics.
Condensed Matter Physics
There are active experimental and theoretical programs in superconductivity, magnetism,
thin film deposition, carbon nanomaterials, nuclear magnetic resonance and ultrafast
laser studies of materials. A new ultra-high field NMR facility with a 17.6 Tesla magnet,
available at only a handful of other schools, provides opportunities for structure and
dynamics studies in physical and biological materials.
Nuclear and Hadronic Physics
William & Mary has an active program in nuclear and hadronic physics, complemented
by its proximity to Jefferson Lab. This state-of-the-art facility provides a high-energy
electron beam used primarily for studying the substructure of the proton and neutron at
the quark and gluon level. Current experimental and theoretical research is focused on
understanding the basic properties of the nucleon, including the origin and distribution
of its spin, charge and magnetic moment. Also at Jefferson Lab, the experimental nuclear
group is embarked on precision experiments to search for physics beyond the Standard
Model at the TeV scale.
High Energy Particle Physics
Particle physics research is aimed at possible new physics that lies beyond the current
standard model of known elementary particles and their interactions. Theoretical research
includes work on grand unified theories, supersymmetry, extra spatial dimensions and
cosmology. The experimental high energy group is active in the search for neutrino
oscillations using a neutrino beam produced at Fermilab, currently the largest proton-
antiproton collider in the world. The department maintains labs for detector construction
and testing, a polarized target lab and a computing farm for large-scale data analysis.
PHYSICS DEPARTMENT
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Physics • 113

T

he Physics Department offers graduate study and research which leads to the Ph.D. degree. The department consists of thirty instructional faculty members, fifteen additional physicists in purely research positions, and 60 full-time graduate students. Additions to the research areas listed below include plasma and non-linear physics and related research includes accelerator physics (in cooperation with Jefferson Lab) and material characterization (in cooperation with NASA-Langley Research Center). The department offers a wide range of undergraduate and graduate courses of instruction. It also has strong links with the Applied Science Department and Computational Science Cluster. Atomic and Optical Physics Experimental research areas include intense laser-matter interaction, femtosecond laser physics, slow and stored light, ultra-cold quantum gases (Bose-Einstein condensates and degenerate Fermi gases), and the study of biological systems using AMO techniques. The theory program includes the study of classical trajectories and chaos in atomic and molecular systems and their correlation with quantum mechanics. Computational Physics Research in this area includes the studies of turbulence, macroscopic nonlinear systems, soliton theory, wave propagation, signal processing, Monte Carlo simulations, ab initio calculations and lattice quantum chromodynamics. These studies have applications within many fields of physics, including laser science, wave dynamics, quantum computing, plasma physics, condensed matter physics, nuclear physics and particle physics. Condensed Matter Physics There are active experimental and theoretical programs in superconductivity, magnetism, thin film deposition, carbon nanomaterials, nuclear magnetic resonance and ultrafast laser studies of materials. A new ultra-high field NMR facility with a 17.6 Tesla magnet, available at only a handful of other schools, provides opportunities for structure and dynamics studies in physical and biological materials. Nuclear and Hadronic Physics William & Mary has an active program in nuclear and hadronic physics, complemented by its proximity to Jefferson Lab. This state-of-the-art facility provides a high-energy electron beam used primarily for studying the substructure of the proton and neutron at the quark and gluon level. Current experimental and theoretical research is focused on understanding the basic properties of the nucleon, including the origin and distribution of its spin, charge and magnetic moment. Also at Jefferson Lab, the experimental nuclear group is embarked on precision experiments to search for physics beyond the Standard Model at the TeV scale. High Energy Particle Physics Particle physics research is aimed at possible new physics that lies beyond the current standard model of known elementary particles and their interactions. Theoretical research includes work on grand unified theories, supersymmetry, extra spatial dimensions and cosmology. The experimental high energy group is active in the search for neutrino oscillations using a neutrino beam produced at Fermilab, currently the largest proton- antiproton collider in the world. The department maintains labs for detector construction and testing, a polarized target lab and a computing farm for large-scale data analysis.

PHYSICS DEPARTMENT

114 • Physics

Faculty CHAIR David S. Armstrong Chancellor Professor (Ph.D., British Columbia). GRADUATE DIRECTOR Jeffrey K. Nelson Cornelia B. Talbot Term Distinguished Associate Professor of Physics (Ph.D., Minnesota). PROFESSORS Todd D. Averett (Ph.D., Virginia), Carl E. Carlson Class of 1962 Professor (Ph.D., Columbia), Christopher D. Carone (Ph.D., Harvard), William E. Cooke (Ph.D., MIT), John B. Delos (Ph.D., MIT), Keith A. Griffioen (Ph.D., Stanford), Gina L. Hoatson (Ph.D., East Anglia), Henry Krakauer (Ph.D., Brandeis), R. Alejandra Lukaszew Virginia Microelectronics Consortium Distinguished Professor of Applied Science and Physics (Ph.D., Wayne State), Dennis M. Manos CSX Professor of Applied Science (Ph.D., Ohio State), Robert D. McKeown Governor’s Distinguished CEBAF Professor (Ph.D., Princeton), Michael R. Pennington Governor’s Distinguished CEBAF Professor (Ph.D., London), Charles F. Perdrisat (D.Sc., ETH, Zurich), Marc T. Sher (Ph.D., Colorado), Eugene R. Tracy Chancellor Professor (Ph.D., Maryland), George M. Vahala (Ph.D., Iowa), and Shiwei Zhang (Ph.D., Cornell). ASSOCIATE PROFESSORS Joshua Erlich (Ph.D., MIT), Irina Novikova (Ph.D., Texas A&M), and Konstantinos N. Orginos (Ph.D., Brown). ASSISTANT PROFESSORS Seth A. M. Aubin (Ph.D., SUNY, Stony Brook), Wouter Deconinck (Ph.D., Michigan), Michael A. Kordosky (Ph.D., Texas, Austin), M. Mumtaz Qazilbash (Ph.D., Maryland, College Park), Enrico Rossi (Ph.D., Texas, Austin), and Patricia L. Vahle (Ph.D., Texas, Austin). PROFESSORS EMERITI Roy L. Champion Chancellor Professor (Ph.D., Florida), Morton Eckhause (Ph.D., Carnegie-Mellon), Franz L. Gross (Ph.D., Princeton), John R. Kane (Ph.D., Carnegie-Mellon), William J. Kossler (Ph.D., Princeton), John L. McKnight (Ph.D., Yale), Kenneth G. Petzinger (Ph.D., Pennsylvania), Edward A. Remler (Ph.D., North Carolina), Harlan E. Schone (Ph.D., California, Berkeley), Hans C. von Baeyer Chancellor Professor (Ph.D., Vanderbilt), J. Dirk Walecka Governor’s Distinguished CEBAF Professor (Ph.D., MIT), and Robert E. Welsh Chancellor Professor (Ph.D., Pennsylvania State). TJNAF PROFESSOR Roger D. Carlini (Ph.D., New Mexico). ADJUNCT PROFESSORS Peter E. Bosted (Ph.D., MIT), Alfred R. Osborne (Ph.D., Houston), Anne C. Reilly (Ph.D., Michigan), David Richards (Ph.D., Cambridge), Marc Vanderhaeghen (Ph.D., Ghent), Gwyn P. Williams (Ph.D., Sheffield), and Stuart A. Wolf (Ph.D., Rutgers). ADJUNCT ASSOCIATE PROFESSOR Paul M. Danehy (Ph.D., Stanford). ADJUNCT ASSISTANT PROFESSOR William Detmold (Ph.D., Adelaide). RESEARCH PROFESSOR Malathy Devi Venkataraman (Ph.D., Kerala). RESEARCH ASSOCIATE PROFESSOR D. Chris Benner (Ph.D., Arizona). RESEARCH ASSISTANT PROFESSOR Eugeniy Mikhailov (Ph.D., Texas A&M). DIRECTOR OF TEACHING LABS A. Dayle Hancock (Ph.D., U. Houston).

General Description The mission of the Physics Department at the College of William and Mary is the creation and dissemination of knowledge of the physical world through teaching, research, and public service. The Department is committed to excellence in its teaching. At the graduate level, the Department offers a full complement of courses consistent with the requirements of a doctoral program. The department recognizes that faculty research activity is an essential ingredient in sustaining excellence in teaching. The Department carries out experimental and theoretical research in many subfields,

116 • Physics

M.S. degree. Otherwise, the Physics faculty will consider the qualifying exam score, along with academic performance in course work and research performance (if any), in order to determine whether the standards for a Master of Science degree are met. The candidate is required to register for Colloquium, (PHYS 650) for a minimum of two semesters of residence. In addition, the candidate must accumulate 32 credit hours, including regis- tering for PHYS 651 or 652 to obtain a minimum of two semesters teaching experience

Degree Requirements for the Doctor of Philosophy (See general College requirements in the section entitled ‘Graduate Regulations’ in this catalog.) The candidate must complete a program of courses required by the Department. This program depends on the candidate’s preparation and special interests, but, in addition to the master’s level courses, will include: PHYS 611, 721, an additional semester of Col- loquium, and either Teaching or Research. The candidate must pass examinations that test familiarity with the principal fields of physics. Details of procedure will vary. It is required that the candidate pass the qualifying examination and demonstrate competence in several advanced topics courses. The candidate must perform research, which is an original and substantial contribution. The dissertation must be approved by a faculty committee and successfully defended in a public oral examination. Students have seven (7) years from the term of admission to the graduate program for the completion of all M.S./Ph.D. degree requirements. Extensions to this limit are considered according to the extension policy as outlined in the section entitled ‘Graduate Regulations’ at the front of this catalog.

Description of Courses Unless otherwise noted, all courses are graded using standard grading [A, B, C, D, F] scheme (See VI. Grading and Academic Progress in the section entitled ‘Graduate Regulations’ in this catalog) and may not be repeated for credit (See Repeated Courses requirements in the section entitled ‘Graduate Regulations’ in this catalog).

600. Independent Study. Fall, Spring (3,3) Staff. Course concerning special topics in physics not covered in regular course offerings. This course may be repeated for credit if instructor determines there will be no duplication of material. 601. Classical Mechanics. Fall (4) Deconinck. The mechanics of particles and rigid bodies, methods of lagrangian and hamiltonian mechanics, relativistic mechanics, approximation techniques. 603. Mathematical Physics. Fall (4) Vahala. Complex variables and analytic functions. Vector spaces (finite dimensional and infinite dimensional), operators and matrix representations. 610. Classical Electricity and Magnetism-I. Spring (4) Cooke. Electrostatics. Solution of boundary value problems. Green’s functions and direct solution of Laplace’s equation. Magnetostatics and steady currents. Maxwell’s equations and plane wave solutions.

Physics • 117

611. Classical Electricity and Magnetism-II.

Fall (3) Cooke. Prerequisite: PHYS 610.

Waves inside conducting boundaries. Radiation from simple current systems, spherical waves and multipole radiation. Covariant formulation of electromagnetism. Interaction of radiation with matter.

621. Quantum Mechanics-I.

Fall (4) Orginos.

Axiomatic development of wave mechanics and the Schroedinger equation in one and three dimensions; wave packets, scattering theory.

622. Quantum Mechanics-II.

Spring (4) Zhang. Prerequisite: PHYS 621.

Scattering theory; spin; matrix methods; symmetry; perturbation theory and other approximate methods; identical particles.

630. Statistical Physics and Thermodynamics.

Spring (4) Delos. Prerequisites: PHYS 601, PHYS 621.

Statistical ensembles and averages, classical equilibrium, thermodynamics and statistical mechanics, quantum statistics, kinetic theory and transport properties.

650. Physics Colloquium.

Fall and Spring (1,1) Armstrong. Graded Pass/Fail. This course may be repeated for credit.

Includes presentations by invited speakers on areas of active research in physics. The course also will include an overview of physics research at William and Mary and training in the responsible and ethical conduct of research.

651, 652. Teaching Physics.

Fall and Spring (2,2) Armstrong. Graded Pass/Fail. This course may be repeated for credit.

Designed for entering students teaching a lab or tutoring one of our undergraduate courses. Respective faculty will instruct students in relevant ways.

690. Advanced Topics in Physics.

Fall and Spring (Hours and credits to be arranged.) Staff.

Special topics of current interest. This course may be repeated for credit when the instructor determines there will not be a duplication of material.

695. Research. Fall and Spring (1-12) Armstrong. This course may be repeated for credit. 702. Advanced Mathematical Physics.

Spring (3) Staff. Prerequisite: PHYS 603. (Not offered Spring 2013)

Differential equations, Green’s functions, some hypergeometric functions, group theory, representation of groups.

721. Field Theory and Relativistic Quantum Mechanics.

Fall (3) Carone. Prerequisite: PHYS 622.

Classical field theories, Dirac Equation, canonical quantization, Interacting field theories, Feynman diagrams. Relation to non-relativistic many-body theory, and applications to atomic transitions. Quantum electrodynamics and introduction to radiative corrections.