## Graduate Courses in Physics

The numbering sequence at Old Dominon University places undergraduate courses at the 100, 200, 300, and 400 levels. Courses that may have graduate, as well as undergraduate students enrolled, are listed in a dual mode, e.g., 456/556. Graduate students may enroll in the 500, 600, 700 and 800 levels. Master's and doctoral courses are dual-listed at 700/800 levels. Courses marked with + may not be counted for credit in physics graduate programs.

### Physics - PHYS

**PHYS 503. Electronic Instrumentation. 3 Credits.**

**PHYS 506. Observational Astronomy. 3 Credits. Lecture 3 hours; **Observational techniques in astronomy with emphasis on constellation identification, celestial movements, and telescopic observation. Individualized night observations are required.

**PHYS 508. Astronomy for Teachers. 3 Credits. Lecture 3 hours; **A course in astronomy dealing with stars and stellar systems. Topics will include observational astronomy, the electromagnetic spectrum, relativity, stellar and galactic structures, cosmology, and the search for extraterrestrial intelligence.

**PHYS 513. Methods of Experimental Physics. 3 Credits. Laboratory 6 hours; **Experiments in classical and modern physics, designed to develop skills in the collection, analysis, and interpretation of experimental data.

**PHYS 515. Introduction to Nuclear Particle Physics. 3 Credits. Lecture 3 hours; **

An introduction to the structure of the atomic nucleus, natural and artificial radioactivity, nuclear decay processes and stability of nuclei, nuclear reactions, properties of nuclear forces, and nuclear models. Also, particle phenomenology, experimental techniques and the standard model. Topics include the spectra of leptons, mesons, and baryons; strong, weak, and electromagnetic interactions.

**PHYS 516. Introduction to Solid State Physics. 3 Credits. Lecture 3 hours;**

Introduction to solid state physics and materials science, with emphasis placed on the applications of each topic to experimental and analytical techniques. Topics include crystallography, thermal and vibrational properties of crystals and semiconductors, metals and the band theory of solids, superconductivity and the magnetic properties of materials.

**PHYS 517. Introduction to Particle Accelerator Physics. 3 Credits. Lecture 3 hours; **Introduction to the historical development and applications of particle accelerators to the fields of nuclear physics, particle physics, material sciences, and medical therapy and the design and physics of particle accelerators. Aspects of linear accelerators, circular accelerators such as cyclotrons, betatrons, synchrotrons, and storage rings, and recirculated linacs are covered. Topics include linear and non-linear single particle motion in accelerators, collective effects and beam stability in particle accelerators, and the electromagnetic radiation emitted by relativistic particles in accelerators. Up to date descriptions of the most modern particle accelerators will be included, as well as applications such as fixed target nuclear physics arrangements, colliding beam accelerators for high energy physics research, advanced storage ring sources of X-Rays, advanced neutron sources, radiation and radioactive material sources, and cancer therapy devices.

**PHYS 520. Introductory Computational Physics. 3 Credits. Lecture 2 hours; Laboratory 2 hours; **Introduction of computational methods and visualization techniques for problem solving in physics.

**PHYS 525. Electromagnetism I. 3 Credits. Lecture, 3 hours. **

A study of the classical theory and phenomena of electricity and magnetism. Topics include the calculation of electric and magnetic fields, magnetic and dielectric properties of matter, and an introduction to Maxwell's equations.

**PHYS 551. Theoretical Mechanics. 3 Credits. Lecture 3 hours; **

A mathematical study of the concepts of mechanics. Vector calculus methods are used. Topics include mechanics of a system of particles, Lagrangian mechanics, Hamilton's canonical equations, and motion of a rigid body.

**PHYS 552. Introduction to Quantum Mechanics. 3 Credits. Lecture 3 hours; **Prerequisites: PHYS 319 and 323. Introduction to the physical and mathematical structure of quantum theory, including the historical and experimental origins of the subject. The curriculum includes techniques for solving the Schrodinger wave equation, particularly for the harmonic oscillator and the hydrogen atom.

**PHYS 553. Electromagnetism II. 3 Credits. Lecture 3 hours; **

A course in electrodynamics developed from Maxwell's Equations. Topics include Maxwell's Equations, Conservation Laws, Electromagnetic Waves, Potentials and Fields, Radiation, and the interplay of electrodynamics and special relativity.

**PHYS 554. Thermal and Statistical Physics. 3 Credits. Lecture 3 hours;**

A study of the fundamental concepts of thermodynamics, kinetic theory, and statistical mechanics. Topics include the thermodynamics of simple systems, kinetic theory of gases, statistical mechanics of gases and an introduction to quantum statistics.

**PHYS 556. Intermediate Quantum Mechanics. 3 Credits. Lecture 3 hours; **

A study of the experimental basis of quantum mechanics, basic postulates, solution of the wave equation for simple systems, uncertainty relations, potential barriers, wave packets, angular momentum, symmetry properties of wave functions, Pauli exclusion principle, Dirac notation, perturbation theory, and scattering. (offered fall).

**PHYS 597. Special Problems and Research. 1-3 Credits; **Prerequisite: permission of the instructor. These courses afford the student an opportunity to pursue individual study and research.

**PHYS 601. Mathematical Methods in Physics. 3 Credits. Lecture 3 hours; **Basic mathematical methods and their applications: infinite series, functions of complex variables, complex analysis, Fourier series, Fourier and LaPlace transformations.

**PHYS 603. Classical Mechanics. 3 Credits. Lecture 3 hours; **Particle in a central-force field. Dynamics in a rotating reference frame. Lagrangian and Hamiltonian formulations. Small occilations. Kinematics and dynamics of a rigid body. Canonical transformation, Hamilton-Jacobi theory.

**PHYS 604. Classical Electrodynamics I. 3 Credits. Lecture 3 hours; **Electrostatics: Glauss' Law and Poisson and Laplace equations. Methods for the solution of boundary-value problems with rectangular, cylindrical, and spherical symmetry. Expansion in multipoles. Dielectrics. Magnetostatics and Faraday's law.

**PHYS 621. Quantum Mechanics I. 3 Credits. Lecture 3 hours; **Mathematical foundations of Hilbert spaces. Background on Hamiltonian mechanics and electro-magnetism. Postulates of Quantum Mechanics, measurements and Schroedinger equation. Simple systems. Schroedinger Equation in 1-3 dimensions and solutions for specific systems. Symmetries and angular momentum. Time-independent perturbation theory.

**PHYS 695. Selected Topics in Pure and Applied Physics. 1-3 Credits;**

Prerequisite: permission of the instructor.

**PHYS 696. Special Topics in Accelerator Physics. 3 Credits;**

Special topics related to particle accelerators and their applications. Departmental approval required.

**PHYS 697. Seminar. 1 Credit;**

**PHYS 698. Research. 3 Credits;**

**PHYS 699. Research. 3 Credits;**

**PHYS 701. Mathematical Methods of Physics II. 3 Credits. Lecture, 3 hours; **Prerequisite: PHYS 601. Group theory, Lie groups and Lie algebras, differential geometry, tensor fields on manifolds, integral calculus of differential forms.

**PHYS 704. Classical Electrodynamics II. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 604. Electrodynamics: Maxwell equations, plane electromagnetic waves and wave propagation, waveguides, radiating systems, special theory of relativity, including the dynamics of relativistic particles and electromagnetic fields.

**PHYS 707. Statistical Mechanics. 3 Credits. Lecture 3 hours; **

rerequisite: PHYS 603. Review of thermodynamics. Classical statistical mechanics and applications. The virial expansion. Quantum statistical mechanics and the micro-canonical, canonical, and grand-canonical ensembles. The Fermi and Bose gases, and applications. Superfulids.

**PHYS 711. Computational Physics. 3 Credits. Lecture 3 hours; **

Studies of high level computer languages. Computational techniques used in physics. Numerical techniques for differential and integral problems. Algebraic processing languages. Introduction to scientific visualization techniques.

**PHYS 721. Quantum Mechanics II. 3 Credits. Lecture 3 hours; **

Prerequisite: PHYS 621. Further development of quantum mechanics. Multi-particle states, bosons and fermions. Classical Limit. Variational principle, time-dependent perturbation theory and scattering. Path integral formulation. Symmetry and groups, addition of angular moments. Examples from solid state, atomic, nuclear, and particle physics.

**PHYS 722. Nuclear and Particle Physics I. 3 Credits. Lecture 3 hours; **

Prerequisite: PHYS 621. Nuclear forces, models of nuclear structure and reactions, hadron and lepton scattering, introduction to constituent quark model and hadron spectroscopy.

**PHYS 723. Nuclear and Particle Physics II. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 722 or PHYS 822. Discrete and continous symmetries and application to particle physics, SU(2) and SU(3) symmetries and static properties of haldon. Klein-Gordon and Dirac equations, quantum electrodynamics and Feynman rules, strong and weak interactions, Standard Model and physics beyond the Standard Model.

**PHYS 724. Solid State I. 3 Credits. Lecture 3 hours; **

Prerequisite: PHYS 621. The first part of the condensed matter course incudes electronic and lattice properties of solids, band structures of metals, semiconductors and insulators, dynamics of electron and phonons, electromagnetic and optical properties of metals and doped semiconductors, phenomenology of superconductivity and magnetism, and selected experimental methods of solid state physics.

**PHYS 727. Atomic Physics. 3 Credits. Lecture 3 hours; **

Prerequisite: permission of the instructor. Irreducible tensor methods. Radiative excitation and ionization processes. Atom-atom scattering. Time-evolution of atomic observables in external fields. Multiple channel quantum defect theory and complex atomic and molecular spectra.

**PHYS 731. Advanced Seminar I. 1 Credit. Lecture 1 hour; **

Written and oral communication skills as applied to physics. Data display techniques for scientific reports.

**PHYS 732. Advanced Seminar II. 1 Credit. Lecture 1 hour; **

Methodology of scientific information retrieval. Organization of information in selected research areas.

**PHYS 750. Quantum Electronics. 3 Credits.** **Lecture, 3 hours; **

Prerequisite: PHYS 604. Interaction of quantized electromagnetic field with matter, including photon coherence, theory of laser, nonlinear optics and selected applications.

**PHYS 754. Accelerator Physics. 3 Credits. Lecture, 3 hours; **

Prerequisites: PHYS 601, PHYS 603, and PHYS 704 or PHYS 804. Department approval required. Overview of the underlying physics of modern particle accelerators. Acceleration, beam transport, nonlinear dynamics, coherent synchrotron radiation, wakefields and impedances, collective effects, phase space cooling, free-electron lasers, novel methods of acceleration, accelerator systems.

**PHYS 760. Low Temperature Physics. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 604, PHYS 707 or PHYS 807, and PHYS 721 or PHYS 821. Properties and behavior of materials and systems at low temperature. Bose and Fermi systems, superconductivity, superfluidity, condensates.

**PHYS 797. Research. 1-6 Credits;**

**PHYS 801. Mathematical Methods of Physics II. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 601. Group theory, Lie groups and Lie algebras, differential geometry, tensor fields on manifolds, integral calculus of differential forms.

**PHYS 804. Classical Electrodynamics II. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 604. Electrodynamics: Maxwell equations, plane electromagnetic waves and wave propagation, waveguides, radiating systems, special theory of relativity, including the dynamics of relativistic particles and electromagnetic fields.

**PHYS 807. Statistical Mechanics. 3 Credits.** **Lecture 3 hours; **Prerequisite: PHYS 603. Review of thermodynamics. Classical statistical mechanics and applications. The virial expansion. Quantum statistical mechanics and the micro-canonical, canonical, and grand-canonical ensembles. The Fermi and Bose gases, and applications. Superfulids.

**PHYS 811. Computational Physics. 3 Credits. Lecture 3 hours; **

Studies of high level computer languages. Computational techniques used in physics. Numerical techniques for differential and integral problems. Algebraic processing languages. Introduction to scientific visualization techniques.

**PHYS 821. Quantum Mechanics II. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 621. Further development of quantum mechanics. Multi-particle states, bosons and fermions. Classical Limit. Variational principle, time-dependent perturbation theory and scattering. Path integral formulation. Symmetry and groups, addition of angular moments. Examples from solid state, atomic,nuclear and particle physics.

**PHYS 822. Nuclear and Particle Physics I. 3 Credits.** **Lecture 3 hours; **

Prerequisite: PHYS 621. Nuclear forces, models of nuclear structure and reactions, hadron and lepton scattering, introduction to constituent quark model and hadron spectroscopy.

**PHYS 823. Nuclear and Particle Physics II. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 722 or PHYS 822. Discrete and continous symmetries and application to particle physics, SU(2) and SU(3) symmetries and static properties of haldon. Klein-Gordon and Dirac equations, quantum electrodynamics and Feynman rules, strong and weak interactions. Standard Model and physics beyond the Standard Model.

**PHYS 824. Solid State I. 3 Credits. Lecture 3 hours; **Prerequisite: PHYS 621. The first part of the condensed matter course incudes electronic and lattice properties of solids, band structures of metals, semiconductors and insulators, dynamics of electron and phonons, electromagnetic and optical properties of metals and doped semiconductors, phenomenology of superconductivity and magnetism, and selected experimental methods of solid state physics.

**PHYS 825. Solid State II. 3 Credits. Lecture, 3 hours; **Prerequisite: PHYS 724 or PHYS 824. The second part of the condensed matter course is mostly focused on many body and collective effects in condensed matter, including phase transitions, Bose and Fermi quantum liquids, superfluidity, superconductivity and magnetism, and properties of mesoscopic and low-dimensional systems.

**PHYS 827. Atomic Physics. 3 Credits. Lecture 3 hours; **Prerequisite: permission of the instructor. Irreducible tensor methods. Radiative excitation and ionization processes. Atom-atom scattering. Time-evolution of atomic observables in external fields. Multiple channel quantum defect theory and complex atomic and molecular spectra.

**PHYS 831. Advanced Seminar I. 1 Credit. Lecture 1 hour; **

Written and oral communication skills as applied to physics. Data display techniques for scientific reports.

**PHYS 832. Advanced Seminar II. 1 Credit. Lecture 1 hour; **

Methodology of scientific information retrieval. Organization of information in selected research areas.

**PHYS 842. Advanced Quantum Mechanics. 3 Credits. Lecture 3 hours; **Prerequisites: PHYS 704, PHYS 721. Introduction to relativistic quantum mechanics; symmetries in relativistic wave equations; solutions to relativistic wave equations for bound states and scattering processes; classical field theory and role of symmetries in construction of conserved currents; introduction to second quantization of fields.

**PHYS 850. Quantum Electronics. 3 Credits. Lecture, 3 hours; **Prerequisite: PHYS 604. Interaction of quantized electromagnetic field with matter, including photon coherence, theory of laser, nonlinear optics and selected applications.

**PHYS 853. Atomic & Molecular Physics. 3 Credits.**

**PHYS 854. Accelerator Physics. 3 Credits. Lecture, 3 hours; **Prerequisites: PHYS 601, PHYS 603, and PHYS 704 or PHYS 804. Department approval required. Overview of the underlying physics of modern particle accelerators. Acceleration, beam transport, nonlinear dynamics, coherent synchrotron radiation, wakefields and impedances, collective effects, phase space cooling, free-electron lasers, novel methods of acceleration, accelerator systems.

**PHYS 857. Plasma Physics. 3 Credits.**

**PHYS 859. Classical Mechanics and Electromagnetism in Accelerator Physics. 3 Credits. Lecture, 3 hours; **Prerequisites: PHYS 601, PHYS 603, and PHYS 704 or PHYS 804. Further development of classical mechanics and electromagnetism and their application to accelerator physics: LaGrangian and Hamiltonian formulation of equations of motion, canonical transformations, adiabatic invariants, linear and nonlinear resonances. Liouvilles theorem, solutions of Maxwells equation in cavities and waveguides, wakefields, radiation and retarded potentials, synchrotron radiation.

**PHYS 860. Low Temperature Physics. 3 Credits. Lecture 3 hours; **

Prerequisite: PHYS 604, and PHYS 707 or PHYS 807, and PHYS 721 orPHYS 821. Properties and behavior of materials and systems at low temperature. Bose and Fermi systems, superconductivity, superfluidity, condensates.

**PHYS 861. Nuclear Physics. 3 Credits.**

**PHYS 862. Nuclear Physics. 3 Credits.**

**PHYS 871. Introduction to Quantum Field Theory. 3 Credits. Lecture, 3 hours; **Prerequisites: PHYS 842. Quantization of the Klein-Gordon field, interactions in quantum field theory and Feynman diagrams, quantization of the Dirac field, quantization of the electromagnetic field, quantum electrodynamics, renormalization, quantum chromodynamics and asymptotic freedom.

**PHYS 898. Doctoral Research. 1-12 Credits.**

**PHYS 899. Dissertation. 1-9 Credits.**