College of Arts and Sciences
(An asterisk [*] denotes associate membership in University Graduate School faculty.)
Master of Science, Master of Arts for Teachers, and Doctor of Philosophy. The department also participates in the Ph.D. programs in astrophysics, chemical physics, and mathematical physics (described elsewhere in this bulletin).
(See also general University Graduate School requirements.)
Outside Minor in Physics
Courses at the 300 level listed below may be taken for graduate credit only by M.A.T. students in physics; those at the 400 level or above are available for graduate credit to all graduate students.
P301 Physics III (3 cr.)
P500 Seminar (1 cr.) Reports on current literature. Graduate students and staff participate.
P504 Practicum in Physics Laboratory Instruction (1 cr.) Practical aspects of teaching physics labs. Meets the week before classes and one hour per week during the semester to discuss goals, effective teaching techniques, grading standards, AI-student relations, and administrative procedures as applied to P201. Students enrolling in this course teach a section of P201 laboratory.
P506 Electricity and Magnetism I (4 cr.) Three hours of lectures and one hour of recitation. Development of Maxwell's equations. Conservation laws. Problems in electrostatics and magnetostatics. Introduction to the special functions of mathematical physics. Time-dependent solutions of Maxwell's equations. Motion of particles in given electromagnetic fields. Elementary theory of radiation. Plane waves in dielectric and conducting media. Dipole and quadruple radiation from nonrelativistic systems.
P507 Electricity and Magnetism II (4 cr.) Three hours of lectures and one hour of recitation. Further development of radiation theory. Fourier analysis of radiation field and photons. Scattering and diffraction of electromagnetic waves. Special relativity. Covariant formulation of electromagnetic field theory.
P508 Current Research in Physics (1 cr.) Presentations by faculty members designed to give incoming graduate students an overview of research opportunities in the department.
P511 Quantum Mechanics I (4 cr.) Three hours of lectures and one hour of recitation. Basic principles, the Schrödinger equation, wave functions, and physical interpretation. Bound and continuum states in one-dimensional systems. Bound states in central potential; hydrogen atom. Variational method. Time-independent perturbation theory.
P512 Quantum Mechanics II (4 cr.) P: P511. Three hours of lectures and one hour of recitation. Time-dependent perturbation theory. Schrödinger, Heisenberg and interaction pictures. Elementary theory of scattering. Rotations and angular momentum. Other symmetries. Nonrelativistic, many-particle quantum mechanics, symmetry and antisymmetry of wave functions, and Hartree-Fock theory of atoms and nuclei.
P521 Classical Mechanics (3 cr.) Vector and tensor analysis. Lagrangian and Hamiltonian dynamics. Conservation laws and variational principles. Two-body motion, many-particle systems, and rigid-body motion. Canonical transformations and Hamilton-Jacobi theory. Continuum mechanics with introduction to complex variables.
P522 Advanced Classical Mechanics (3 cr.) Mathematical methods of classical mechanics; exterior differential forms, with applications to Hamiltonian dynamics. Dynamical systems and nonlinear phenomena; chaotic motion, period doubling, and approach to chaos.
P535 Introduction to Nuclear and Particle Physics (3 cr.) P: P453 or equivalent. Survey of the properties and interactions of nuclei and elementary particles. Experimental probes of subatomic structure. Basic features and symmetries of electromagnetic, strong and weak forces. Models of hadron and nuclear structure. The role of nuclear and particle interactions in stars and the evolution of the universe.
P540 Digital Electronics (3 cr.) Digital logic, storage elements, timing elements, arithmetic devices, digital-to-analog and analog-to-digital conversion. Course has lectures and labs emphasizing design, construction, and analysis of circuits using discrete gates and programmable devices.
P541 Analog Electronics (3 cr.) Amplifier and oscillator characteristics feedback systems, bipolar transistors, field-effect transistors, optoelectronic devices, amplifier design, power supplies, and the analysis of circuits using computer-aided techniques.
P548 Mathematical Methods for Biology (3 cr.) P: consent of instructor. See MATH M548.
P551 Modern Physics Laboratory (3 cr.) Graduate-level laboratory; experiments on selected aspects of atomic, condensed-matter, and nuclear physics.
P556 Statistical Physics (3 cr.) The laws of thermodynamics; thermal equilibrium, entropy, and thermodynamic potentials. Principles of classical and quantum statistical mechanics. Partition functions and statistical ensembles. Statistical basis of the laws of thermodynamics. Elementary kinetic theory.
P557 Solid State Physics (3 cr.) P: P453 or equivalent. Atomic theory of solids. Crystal and band theory. Thermal and electromagnetic properties of periodic structures.
P570 Introduction to Accelerator Physics (3 cr.) P: approval of instructor. Overview of accelerator development and accelerator technologies. Transverse phase space motion and longitudinal synchrotron motion of a particle in an accelerator. Practical accelerator lattice design. Design issues relevant to synchrotron light sources. Basics of free electron lasers. Spin dynamics in cyclic accelerators and storage rings.
P571 Special Topics in Physics of Beams (3 cr.) P: approval of instructor.
P575 Introductory Biophysics (3 cr.) Overview of cellular components; basic structures of proteins, nucleotides, and biological membranes; solution physics of biological molecules; mechanics and motions of biopolymers; physical chemistry of binding affinity and kinetics; physics of transport and signal transduction; biophysical techniques such as microscopy and spectroscopy; mathematical modeling of biological systems; biophysics in the post-genome era.
P581 Modeling and Computation in Biophysics (3 cr.) Introduction to modeling and computational methods applied to phenomena in Biophysics. Topics: Population Dynamics. Reaction Kinetics. Biological Oscillators. Coupled Reaction Networks. Network Theory. Molecular Motors. Limit Cycles. Reaction Diffusion Models. The Heart. Turning Instability. Bacterial Patterns. Angiogenesis.
P582 Biological and Artificial Neural Networks (3 cr.) Biological details of neurons relevant to computation. Artificial neural network theories and models, and relation to statistical physics. Living neural networks and critical evaluation of neural network theories. Students' final projects will consist of programming networks and applying them to current research topics.
P583 Signal Processing and Information Theory in Biology (3 cr.) Probability and statistics. Filtering. Correlation functions and power spectra. Time invariant and time-varying systems. Shannon Information. Coding and decoding. Processing of sensory signals and other applications to Neurobiology and Psychophysics.
P607 Group Representations (3 cr.) P: consent of instructor. Elements of group theory. Representation theory of finite and infinite compact groups. Study of the point crystal, symmetric, rotation, Lorentz, and other classical groups as time permits. Normally offered in alternate years; see also MATH M607-M608.
P609 Computational Physics (3 cr.) Designed to introduce students (1) to numerical methods for quadrature, solution of integral and differential equations, and linear algebra; and (2) to the use of computation and computer graphics to simulate the behavior of complex physical systems. Topics will vary.
P610 Computational Physics II (3 cr.) Second semester of computational physics focusing on more advanced topics, e.g., fractals, kinetic growth models, models in statistical mechanics, quantum systems and fast fourier transforms, parallel computing.
P615-P616 Physics of the Solid State I-II (3-3 cr.) P: P512. Mechanical, thermal, electric, and magnetic properties of solids; crystal structure; band theory; semiconductors; phonons; transport phenomena; superconductivity; superfluidity; and imperfections. Usually given in alternate years.
P621 Relativistic Quantum Field Theory I (4 cr.) P: P512. Introduction to quantum field theory, symmetries, Feynman diagrams, quantum electrodynamics, and renormalization.
P622 Relativistic Quantum Field Theory II (4 cr.) P: P621. Non-Abelian gauge field theory, classical properties, quantization and renormalization, symmetries and their roles, and nonperturbative methods.
P625 Quantum Many-Body Theory I (3 cr.) P: P512. Elements of nonrelativistic quantum field theory: second quantization, fields, Green's functions, the linked-cluster expansion, and Dyson's equations. Development of diagrammatic techniques and application to the degenerate electron gas and imperfect Fermi gas. Canonical transformations and BCS theory. Finite-temperature (Matsubara), Green's functions, and applications.
P626 Quantum Many-Body Theory II-Nuclear (3 cr.) P: P625. Continued development of nonrelativistic, many-body techniques, with an emphasis on nuclear physics: real-time, finite-temperature Green's functions, path-integral methods, Grassmann algebra, generating functionals, and relativistic many-body theory. Applications to nuclear matter and nuclei.
P627 Quantum Many-Body Theory II-Condensed Matter (3 cr.) P: P625. Continued development of nonrelativistic many-body techniques with an emphasis on condensed-matter physics: properties of real metals, superconductors, superfluids, Ginzburg-Landau theory, critical phenomena, order parameters and broken symmetry, ordered systems, and systems with reduced dimensionality.
G630 Nuclear Astrophysics (3 cr.) P: A451-A452, P453-P454, or consent of instructor. R: A550, P611. Fundamental properties of nuclei and nuclear reactions and the applications of nuclear physics to astronomy. The static and dynamic properties of nuclei; nuclear reaction rates at low and high energies. Energy generation and element synthesis in stars; the origin and evolution of the element abundances in cosmic rays.
P633-P634 Theory of the Nucleus I-II (3-3 cr.) P: P512. Nuclear forces, the two-nucleon problem, systematics and electromagnetic properties of nuclei, nuclear models, nuclear scattering and reactions, theory of beta-decay, and theory of nuclear matter.
P635-P636 Frontier Particle Physics I-II (3-3 cr.) This course focuses on the frontier of particle physics. Topics include Standard-Model physics, neutrino masses, tests of fundamental symmetries, anomalies, grand unified theories, higher-dimensional theories, supersymmetry, composite models, supergravities, string and superstring theory.
P637 Theory of Gravitation I (3 cr.) Introduction to the general theory of relativity, stress-energy tensor, parallel transport, geodesics, Einstein's equation, differential geometry, manifolds, general covariance, bending of light, perihelion advance. Modern cosmology: Robertson-Walker metric, equations of state, Friedmann equations, Hubble's law, redshift, cosmological constant, inflation, quintessence, cosmic microwave background, Big Bang nucleosynthesis, structure formation. See MATH M637.
P638 Theory of Gravitation II (3 cr.) Gravitation waves, Schwarzschild geometry and black holes, Kerr metric, Reissner-Nordstrom metric, extremal black holes, Penrose diagrams, Hawking radiation, Lie derivatives, isometries and Killing vectors, variational principle and the Palatini formalism, spinors in general relativity, vierbeins, gravitation as a gauge theory, quantum gravity. See MATH M638.
P640 Subatomic Physics I (3 cr.) P: P512, C: P621. Experimental methods and theoretic description of particle and nuclear physics: applied relativistic quantum mechanics, symmetries of fundamental interactions, experimental techniques, structure of the nucleon, electromagnetic and weak interactions, elementary particles, and the Standard Model. PHYS P640 may be substituted for P633 in degree requirements.
P641 Subatomic Physics II (3 cr.) P: P640. Quarks and gluons in QCD, the parton model, strong interactions at low energies, nuclear environment and models, nuclear thermodynamics and subatomic physics in cosmology and astrophysics. PHYS P641 may be substituted for P634 in degree requirements.
P647 Mathematical Physics (3 cr.) P: P501 or P502, P521, or MATH M442. Topics vary from year to year. Integral equations, including Green's function techniques, linear vector spaces, and elements of quantum mechanical angular momentum theory. For students of experimental and theoretical physics. May be taught in alternate years by members of Departments of Physics or Mathematics, with corresponding shift in emphasis; see MATH M647.
P657 Statistical Physics II (3 cr.) Continuation of P556. Topics include advanced kinetic and transport theory, phase transitions, and nonequilibrium statistical mechanics.
P665 Scattering Theory (3 cr.) P: P506, P511. Theoretical tools for analysis of scattering experiments. Electromagnetic theory, classical and quantum particle dynamics.
P671 Special Topics in Accelerator Physics (3 cr.) P: P570, P521. Nonlinear dynamics: betatron phase space distortion due to the nonlinear forces. Methods of dealing with nonlinear perturbations. Multi-particle dynamics: microwave and coupled bunch instabilities. Physics of electron cooling and stochastic cooling. Advanced acceleration techniques: inverse free electron laser acceleration, wakefield and two-beam acceleration.
P672 Special Topics in Accelerator Technology and Instrumentation (3 cr.) P: consent of instructor.
P676 Selected Topics in Biophysics (3 cr.) This course presents papers on current topics in biophysics, together with key classical papers related to those topics. Student participation in discussions is essential. Each student is expected to write two essays on two of the topics presented.
P700 Topics in Theoretical Physics (cr. arr.)
P743 Topics in Mathematical Physics (3 cr.) P: consent of instructor. For advanced students. Several topics in mathematical physics studied in depth; lectures and student reports on assigned literature. Content varies from year to year. May be taught in alternate years by members of Departments of Physics or Mathematics, with corresponding shift in emphasis; see MATH M743.
P800 Research (cr. arr.) Experimental and theoretical investigations of current problems; individual staff guidance. S/F grading.
P801 Readings (cr. arr.) Readings in physics literature; individual staff guidance. S/F grading.
P802 Research (cr. arr.) Experimental and theoretical investigations of current problems; individual staff guidance. Graded by letter grade.
P803 Readings (cr. arr.) Readings in physics literature; individual staff guidance. Graded by letter grade.
G750 Topics in Astrophysical Sciences (1-3 cr.)