# Physics

Research opportunities in theoretical/computational physics are available in astrophysics, biophysics, chaos, condensed matter, nanoscience/nanomaterials, nuclear and particle physics, quantum computing, and relativity. Research opportunities in experimental physics are available in astronomy, atomic and molecular physics, biophysics, emergent phenomena, materials physics, nanoscale science, nonlinear systems, nuclear and particle physics, optics, soft-condensed-matter physics and technology, and surface physics.

**Degrees earned will be distributed as: "Master of Science" and "Doctor of Physics" without specialization specifications.**

**Master's Degree Requirements**

A minimum of 30 credit hours beyond the Bachelor’s degree with mastery of aspects of the physics curriculum. There are 2 options:

- Option A: Earning 24 credit hours of courses, 6 of research, writing a dissertation, and passing an oral exam;
- Option B: Earning 30 credit hours of courses and passing the physics qualifying exam.

**Doctoral Degree Requirements**

A minimum of 72 credit hours beyond the Bachelor’s degree (54 with an incoming Master’s); demonstrating mastery of the core physics curriculum as evidenced by passing the qualifying exam; demonstrating mastery of research in a subspecialty of physics by passing appropriate elective courses, planning a research topic, passing an oral preliminary exam, writing a dissertation, and passing a final oral defense.

**Student Financial Support**

Graduate teaching assistantships are available for new and continuing students. Research assistantships are available to continuing students and occasionally to new students. More than 95% of students are supported by assistantships.

## More Information

**Admission Requirements**

Bachelor's degree in physics or equivalent and related. General GRE and the GRE Physics subject test are accepted, but not required.

## Applicant Information

**Delivery Method:**On-Campus**Entrance Exam:**None**Interview Required:**Yes

## Application Deadlines

Please see program website for application deadlines.

## Faculty

- Harald Ade
- David E. Aspnes
- Robert J. Beichner
- Jerzy Bernholc
- John Michael Blondin
- John D. Brown
- Laura I. Clarke
- Karen E. Daniels
- William L. Ditto
- Daniel B. Dougherty
- Carla Frohlich
- Robert Golub
- Kenan Gundogdu
- Hans D. Hallen
- Paul R. Huffman
- Chueng Ryong Ji
- James P. Kneller
- Gail C. McLaughlin
- Lubos Mitas
- Robert Riehn
- Christopher M. Roland
- Maria C. Sagui
- Thomas M. Schaefer
- John E. Thomas
- Mithat Unsal
- Keith R. Weninger
- Albert R. Young
- Matthew Piron Green
- Alexander Kemper
- Divine Philip Kumah
- Shuang Fang Lim
- Richard Leigh Longland
- Hong Wang
- Julio Monti Belmonte
- Rongmon Bordoloi
- Mary Williard Elting
- Sebastian Konig
- Sharonda Leblanc
- Katherine Jean Mack
- Vladimir Skokov
- Dali Sun
- Jason Russell Bochinski
- Kazimierz Borkowski
- Abay Dinku
- Daniel Jacob Doucette
- Brand Irving Fortner
- Keith Heyward
- Parminder Kaur
- John H. Kelley
- Hayen Leendert
- Kent Leung
- Wenchang Lu
- Vijaya Mehta
- Zodiac T. Webster
- Ruth W. Chabay
- Kwong T. Chung
- James W. Cook Jr.
- Stephen R. Cotanch
- William Robert Davis
- Donald C. Ellison
- Raymond Earl Fornes
- Christopher Robert Gould
- David G. Haase
- Karen L. Johnston
- Fred Lado Jr.
- Jacqueline Krim
- George W. Parker III
- Richard R. Patty
- Stephen Reynolds
- Phillip J. Stiles

### Associate Professor

- Ian Roederer

### Assistant Professor

- Xingcheng Lin

### Teaching Professor

- Aaron Titus

### Teaching Assistant Professor

- Kasey Wagoner

### Lecturer

- Federico Portillo Chaves

## Courses

**PY 501**

**Quantum Physics I**(3 credit hours)

Basic principles of quantum physics with emphasis on selected applications to atoms, molecules, solids, nuclei, and elementary particles. PY 501 - first semester in two-semester sequence in quantum mechanics; PY 502 - second semester of sequence. Credit for both PY 401 and PY 501 is not allowed.

Prerequisite: Graduate Level Status in Physics or Physics Departmental Approval

*Typically offered in Spring only*

**PY 502**

**Quantum Physics II**(3 credit hours)

Basic principles of quantum physics with emphasis on selected applications to atoms, molecules, solids, nuclei and elementary particles. PY 502 - second semester in two-semester sequence in quantum mechanics; first semester of sequence is PY501. Credit for both PY 402 and PY 502 is not allowed.

Prerequisite: PY 501

*Typically offered in Fall only*

**PY 506**

**Nuclear and Subatomic Physics**(3 credit hours)

Introduction to nuclear and subatomic phenomena: properties of nuclear radiations and detectors, accelerators, nuclear forces and nuclear structure, elementary particles, fundamental symmetries and conservation laws.

*Typically offered in Fall only*

**PY 507**

**Elementary Particle Physics**(3 credit hours)

Introduction to fundamental symmetries and dynamics of quarks and leptons. The Standard Model, Dirac equation, Feynman rules in QED and QCD, the Higgs mechanism and electroweak unification.

*Typically offered in Spring only*

**PY 509**

**General Relativity**(3 credit hours)

This course provides in-depth knowledge of general relativity covering Einstein's equation, Schwarzschild metric, Kerr metric, Friedman-Robertson-Walker metric, Christoffel symbols, Killing vectors, Riemann curvature, and Ricci tensors. Theoretical computations are compared with data including the precession rate of the perihelion for Mercury and the deflection in the solar eclipse, the geodelic affect and the frame-dragging effect measured in the Gravity Probe B experiment.

*Typically offered in Spring only*

First semester of a two-semester sequence in particle and continuum mechanics at the intermediate level. Focuses on single-particle dynamics: Elementary Newtonian mechanics, harmonic oscillator, central force motion, conservation laws, motion in non-inertial frames, Coriolis and centrifugal forces, Lagrangian dynamics, Hamilton's equations.

*Typically offered in Spring only*

Second semester of a two-semester sequence in particle and continuum mechanics at the intermediate level. Focuses on dynamics of systems of particles and continua: center of mass, collisions, rigid bodies, inertia tensor, principal axes, stress and strain tensors, mechanical properties of fluids and solids; waves in discrete and continuum systems, coupled oscillators, normal modes, elements of special relativity.

Prerequisite: C- or better in PY 411

*Typically offered in Fall only*

First semester of a two-semester sequence. An intermediate course in electromagnetic theory using the methods of vector calculus. Electrostatic field and potential, dielectrics, solution to Laplace's and Poisson's equations, magnetic fields of steady currents.

*Typically offered in Fall only*

A continuation of PY 414. Electromagnetic induction, magnetic fields in matter, Maxwell's equations, wave guides, radiation.

Prerequisite: C- o better in PY 414

*Typically offered in Spring only*

**PY 516**

**Physical Optics**(3 credit hours)

Physical optics with major emphasis on wave properties of light. Boundary conditions, interference and diffraction, optics of thin films, fiber optics and applications to absorption, scattering and laser operation. A background in Maxwell's equations and vector analysis required.

Prerequisite: PY 415

*Typically offered in Fall only*

**PY 517**

**Atomic and Molecular Physics**(3 credit hours)

The quantum mechanical treatment of structure and spectra for atoms and molecules. The hydrogen atom, helium atom, multielectron atoms, selection rules, diatomic and simple polyatomic molecules and nuclear magnetic resonance spectroscopy.

*Typically offered in Spring only*

**PY 519**

**Biological Physics**(3 credit hours)

This course presents the application of physics principles and methods to problems in biological systems. Important biological molecules, their structures and their processes are introduced for physical scientists. Functional mechanisms are analyzed with concepts from thermodynamics, statistical mechanics, fluid mechanics, and electrostatics. Modern experimental methods and computational approaches to molecular and cellular level biological phenomena are emphasized.

Prerequisite: PY 413 or Graduate Standing

*Typically offered in Spring only*

**PY 525**

**Computational Physics**(3 credit hours)

Computational approach to solving physics problems using standard software relevant for physicists. Electrostatic potentials, data analysis, Monte Carlo simulations, Fourier optics, particle orbits, Schrodinger's equation. Examples and assignments for each topic are chosen to complement other physics courses.

Prerequisite: CSC 112 or equivalent; Corequisite: PY 401 and Graduate Standing or departmental permission

*Typically offered in Fall only*

Concepts in plasma physics, basics of thermonuclear reactions; charged particle collisions, single particle motions and drifts, radiation from plasmas and plasma waves, fluid theory of plasmas, formation and heating of plasmas, plasma confinement, fusion devices and other plasma applications.

*Typically offered in Fall only*

This course expands on the treatment of plasmas as a system of coupled fluids and introduces the foundations of plasma kinetic theory. Derivation of the plasma kinetic equation and the Vlasov equation serve as the starting point to introduce the kinetic study of plasma systems. From this introduction of the governing equations for full kinetic treatment, methods for analyzing plasma response to electromagnetic and electrostatic perturbations using the linearized Vlasov model for uncorrelated plasmas are introduced. Kinetic stability of Vlasov plasmas is introduced and the Nyquist method is used to determine conditions for kinetic stability. The concept of correlated plasmas is then introduced through the introduction of reduced distribution functions and the BBGKY heirarchy. Finally, simple correlated systems and the Liouville model for two-system correlation is covered to look at the impact of particle correlation due to collisions and coulomb interaction.

Prerequisite: NE 528

*Typically offered in Spring only*

**PY 543**

**Astrophysics**(3 credit hours)

Basic physics necessary to investigate, from observational data, internal conditions and evolution of stars. This includes the formation and structure of spectral lines, methods of energy generation and transport, stellar structure, degeneracy, white dwarfs, and neutron stars.

*Typically offered in Spring only*

**PY 552**

**Condensed Matter Physics I**(3 credit hours)

Basic considerations of crystalline solids, metals, conductors and semiconductors.

Prerequisite: C- or better in PY 401; Graduate standing or departmental permission

*Typically offered in Spring only*

Polymer microstructures, solutions, physical states (including amorphous polymers, crystalline polymers, polymer melts, melting of polymers, glass-transition, and other transitions), polymer blends, mechanical properties, and viscoelasticity and flow, multicomponent polymer systems, and modern polymer topics. The physics of polymer fibers. Graduate standing or permission of instructor.

*Typically offered in Fall only*

**PY 581**

**Matter & Interactions for Teachers I**(3 credit hours)

First semester (mechanics) of a two-semester sequence intended to broaden and deepen the knowledge of high school physics teachers about introductory-level physics from a contemporary point of view. The course includes an introduction to computational physics. Departmental permission is required: the course is normally restricted to in-service high-school physics teachers.

*Typically offered in Spring only*

**PY 582**

**Matter & Interactions for Teachers II**(3 credit hours)

Second semester (electricity and magnetism) of a two-semester sequence intended to broaden and deepen the knowledge of high-school physics teachers of introductory-level physics from a contemporary point of view. The course includes an introduction to computational physics. Departmental permission is required: the course is normally restricted to in-service high-school physics teachers. The PY 581 prerequisite may be waived with strong background in physics and mathematics.

*Typically offered in Fall only*

**PY 589/ECE 489/ECE 589/MSE 489/MSE 589/PY 489**

**Solid State Solar and Thermal Energy Harvesting**(3 credit hours)

This course studies the fundamental and recent advances of energy harvesting from two of the most abundant sources, namely solar and thermal energies. The first part of the course focuses on photovoltaic science and technology. The characteristics and design of common types of solar cells is discussed, and the known approaches to increasing solar cell efficiency will be introduced. After the review of the physics of solar cells, we will discuss advanced topics and recent progresses in solar cell technology. The second part of the course is focused on thermoelectric effect. The basic physical properties, Seebeck coefficient, electrical and thermal conductivities, are discussed and analyzed through the Boltzmann transport formalism. Advanced subject such as carrier scattering time approximations in relation to dimensionality and the density of states are studied. Different approaches for further increasing efficiencies are discussed including energy filtering, quantum confinement, size effects, band structure engineering, and phonon confinement.

*Typically offered in Spring only*

**PY 590**

**Special Topics In Physics**(1-6 credit hours)

Investigations in physics under staff guidance. May consist of literature reviews, experimental or theoretical projects, or special-topics lectures. Credits Arranged

*Typically offered in Fall, Spring, and Summer*

**PY 599**

**Special Topics in Physics**(1-6 credit hours)

Investigations in physics under staff guidance. May consist of literature reviews, experimental or theoretical projects, or special-topics lectures. Credits arranged

*Typically offered in Fall, Spring, and Summer*

**PY 601**

**Seminar**(1 credit hours)

Reports on topics of current interest in physics. Several sections are offered so that students with common research interests may be grouped together.

*Typically offered in Fall and Spring*

**PY 610**

**Special Topics**(1-6 credit hours)

Investigations in physics under staff guidance. May consist of literature reviews, experimental or theoretical projects, or special topics lectures. Credits Arranged.

*Typically offered in Fall and Spring*

**PY 693**

**Master's Supervised Research**(1-9 credit hours)

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Master's student

*Typically offered in Spring only*

**PY 695**

**Master's Thesis Research**(1-9 credit hours)

Thesis Research

Prerequisite: Master's student

*Typically offered in Fall, Spring, and Summer*

**PY 699**

**Master's Thesis Preparation**(1-9 credit hours)

For students who have completed all credit hour requirements and full-time enrollment for the master's degree and are writing and defending their thesis. Credits Arranged

Prerequisite: Master's student

*Typically offered in Summer only*

**PY 711**

**Advanced Quantum Mechanics I**(3 credit hours)

Introduction to relativistic quantum theory of Dirac particles and the positron. Other topics including second quantization technique and its application to many-body problems, radiation theory, and quantization of the electromagnetic field.

Prerequisite: PY 782

*Typically offered in Fall only*

**PY 712**

**Advanced Quantum Mechanics II**(3 credit hours)

A general propagator treatment of Dirac particles, photons, and scalar and vector mesons. Applications of Feynman graphs and rules illustrating basic techniques employed in the treatment of electromagnetic, weak, and strong interactions. Renormalization theory, the effects of radiative corrections, and aspects of the general Lorentz covariant theory of quantized fields.

Prerequisite: PY 711

*Typically offered in Spring only*

**PY 721**

**Statistical Physics I**(3 credit hours)

Basic elements of kinetic theory and equilibrium statistical mechanics, both classical and quantum; applications of the techniques developed to various ideal models of noninteracting particles. The final exam is the Department qualifying exam for statistical mechanics.

*Typically offered in Spring only*

**PY 722**

**Statistical Physics II**(3 credit hours)

A continuation of PY 721, with emphasis on the static and dynamic properties of real (interacting) systems. Topics including equilibrium theory of fluids and linear response theory of time-dependent phenomena.

Prerequisite: PY 721

*Typically offered in Fall only*

**PY 753**

**Condensed Matter Physics II**(3 credit hours)

The properties of semiconductors, superconductors, magnets, ferroelectrics, and crystalline defects and dislocations.

Prerequisite: PY 552

*Typically offered in Fall only*

**PY 781**

**Quantum Mechanics I**(3 credit hours)

Fundamental concepts and formulations, including interpretation and techniques. Application of theory to simple physical systems, such as the free particle, the harmonic oscillator, the particle in a potential well, and central force problems. Other topics include approximation methods, identical particles and spin, transformation theory, symmetries and invariance, and an introduction to quantum theory of scattering and angular momentum.

*Typically offered in Fall only*

**PY 782**

**Quantum Mechanics II**(3 credit hours)

Fundamental concepts and formulations, including interpretation and techniques, and the application of theory to simple physical systems, such as the free particle, the harmonic oscillator, the particle in a potential well, and central force problems. Other topics include approximation methods, identical particles and spin, transformation theory, symmetries and invariance, and an introduction to the quantum theory of scattering and angular momentum. The final exam is the Department qualifying exam for quantum mechanics.

Prerequisite: PY 781 and Graduate standing

*Typically offered in Spring only*

**PY 783**

**Advanced Classical Mechanics I**(3 credit hours)

Introduction to theoretical physics in preparation for advanced study. Emphasis on classical mechanics, special relativity, and the motion of charged particles. Topics include variational principles, Hamiltonian dynamics, canonical transformation theory, structure of the Lorentz group, and elementary dynamics of unquantized fields. The final exam is the Department qualifying exam for classical mechanics.

*Typically offered in Fall only*

**PY 785**

**Advanced Electricity and Magnetism I**(3 credit hours)

Topics including techniques for solution of potential problems, development of Maxwell's equations; wave equations, energy, force and momentum relations of an electromagnetic field; covariant formulation of electrodynamics; radiation from accelerated charges.

Prerequisite: PY 415; Graduate standing

*Typically offered in Fall only*

**PY 786**

**Advanced Electricity and Magnetism II**(3 credit hours)

This is the second semester of a two-semester series, focusing on time-dependent phenomena. Building on Maxwell's Equations, topics include conduction, induction, and magnetodynamics; physics of transformers, motors, and generators; plane waves: propagation in homogeneous and anisotropic media, coherent and incoherent superposition (short-pulse optics, Stokes parameters); wave physics at planar interfaces: reflection, transmission, multilayer phenomena, and plasmonics; waveguides including optical fibers-and energy transfer; radiation and scattering: Green functions, retardation physics, Lienard-Wiechert potentials; interference (constructive and destructive), shock waves; diffraction: Fresnel and Fraunhofer diffraction, Gaussian beams (photon spin, orbital angular momentum, topological charge); special relativity: Lorentz transformations, 4-vectors, nominal paradoxes, synchrotron radiation, and tensor formulation.

Prerequisite: PY 785 and Graduate Standing

*Typically offered in Spring only*

**PY 790**

**Special Topics in Physics**(1-99 credit hours)

**PY 801**

**Seminar**(1 credit hours)

Reports on topics of current interest in physics. Several sections offered so that students with common research interests may be grouped together.

*Typically offered in Fall and Spring*

**PY 810**

**Special Topics In Physics**(1-6 credit hours)

Investigations in physics under staff guidance. May consist of literature reviews, experimental or theoretical projects or special topics lectures. Credits Arranged

*Typically offered in Fall and Spring*

**PY 885**

**Doctoral Supervised Teaching**(1-3 credit hours)

Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment and evaluate the student upon completion of the assignment.

Prerequisite: Doctoral student

*Typically offered in Spring only*

**PY 893**

**Doctoral Supervised Research**(1-9 credit hours)

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Doctoral student

*Typically offered in Spring only*

**PY 895**

**Doctoral Dissertation Research**(1-9 credit hours)

Dissertation Research

Prerequisite: Doctoral student

*Typically offered in Fall, Spring, and Summer*

**PY 896**

**Summer Dissertation Research**(1 credit hours)

For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.

Prerequisite: Doctoral student

*Typically offered in Summer only*

**PY 899**

**Doctoral Dissertation Preparation**(1-9 credit hours)

For students who have completed all credit hour requirements, full-time enrollment, preliminary examination, and residency requirements for the doctoral degree, and are writing and defending their dissertations.

Prerequisite: Doctoral student

*Typically offered in Fall, Spring, and Summer*