## Course Catalog

### Physics Courses

Please note: Students outside Physics & Astronomy degree programs and who do not have an undergraduate degree in physics should consult with course instructors about pre-requisites prior to registering for Physics & Astronomy graduate courses.

**Physics 411-0 Classical Mechanics**

Review of Newtonian mechanics, conservation laws and rigid-body dynamics. Variational principle. Lagrangian mechanics, constraints, symmetry and conservation laws, non-potential forces, scattering, linear oscillations. Hamiltonian formulation, canonical transformations, Poisson brackets, perturbation theory. Continuum dynamics.

**Physics 411-1 Methods of Theoretical Physics**

The topics covered include: techniques for the solution of differential equations; approximations such as the method of steepest descent; techniques for integration; complex analysis; the special functions of mathematical physics; usage of Greens functions and eigenfunctions to solve differential equations; introduction to probability and statistics.

**Physics 412-1,2,3 Quantum Mechanics**

*First quarter*: Vector spaces and linear operators, postulates of quantum mechanics, observables and Hermitian operators, state vectors and quantum dynamics, stationary states, bound states, the harmonic oscillator, statistical interpretation and the Uncertainty Principle, symmetry and conservation laws, quantization of angular momentum, intrinsic spin, the Stern-Gerlach experiment, spherically symmetric potentials.

*Second quarter*: Feynman's path integral formulation, the classical limit, Schroedinger's wave equation, electromagnetic potentials, Aharonov-Bohm effects, Landau levels, Coulomb potential, approximation methods, variational principles, bound-state perturbation theory, Dirac's theory of the electron, electron spin, Dirac-Pauli equation, magnetic moment of the electron, fine structure of hydrogen, hyperfine interactions.

*Third quarter*: Identical particles, exchange symmetry, Hartree-Fock and Born-Oppenheimer approximations, atomic and molecular structure, quantized radiation, Fock states, coherent states, fluctuations of the radiation field, time-dependent perturbations, transition amplitudes, selection rules, spontaneous emission, photoelectric effect, scattering theory, light scattering.

**Physics 414-1,2 Electrodynamics**

*First quarter*: First quarter of a two-quarter class on Electrodynamics. Topics covered: Principles of Special Relativity and invariance. Relativistic electrodynamics as a classical field theory and action principles: for point particles, scalar fields, and vector fields, including Lagrangian formulation, principle of least action, symmetry principles, gauge invariance, the electromagnetic field tensor, covariant equations of electrodynamics and mechanics. Constant electromagnetic fields.

*Second quarter: *A continuation of the graduate course in electrodynamics. Electromagnetic waves, optics, propagation of laser beams, diffraction and interference phenomena. Electromagnetic fields in and around dielectric and magnetic materials. Propagation of electromagnetic waves in different dielectric and metallic media. Radiation and scattering, including relativistic radiation.

**Physics 416-0 Introduction to Statistical Mechanics**

Statistical mechanics and probability. Microstates and macrostates. Thermodynamic limit. Ensembles: microcanonical, canonical, grand canonical. Classical ideal gas: Maxwell-Boltzmann distribution. Quantum gases: Fermi-Dirac and Bose-Einstein distributions. Thermodynamic potentials. Interacting systems. Phase diagrams and phase transitions.

**Physics 420-0 Statistical Physics**

Correlation functions, measurement, and response theory. Spontaneous symmetry breaking and phase transitions, Landau theory of second-order phase transitions, fluctuations, scaling theory, and critical phenomena. Additional topics may include liquid crystals, magnets, superfluids, superconductors, or non-equilibrium processes relevant to biophysics and economics.

**Physics 421-0 Introduction to Superconductivity**

Lectures and experimental demonstrations on the basic theory and phenomenology of superconductivity and its applications. Fundamentals include the electrical and magnetic properties of superconductors, London’s theory of the electromagnetic response of superconductors, Landau and Ginzburg’s theory for the thermodynamics and magnetic properties of type I and type II superconductors, the origin of quantized magnetic flux, the Josephson effect, and the operation of Superconducting Quantum Interference Devices (SQUIDs) for high-precision magnetometry. Applications are wide ranging, from superconducting quantum electronics to superconducting radio-frequency cavities for particle accelerators.

**Physics 422-1,2,3 Condensed-Matter Physics**

*First quarter*: Periodic potentials, crystal lattices, x-ray diffraction. Electrons in metals: Drude model, electrons in periodic potentials, semiclassical approximation, Fermi surface, band structure. Electronic and thermal transport, Boltzmann equation, electron-electron interactions, screening.

*Second quarter*: Phonons: classical and quantum theory, electron-phonon interaction and scattering, optical properties of solids. Semiconductors: direct and indirect gap, intrinsic and extrinsic semiconductors, semiconductor devices, heterostructures, quantum Hall effect.

*Third quarter*: In-depth treatment of selected special topics, such as: Magnetism in solids: diamagnetism and paramagnetism, ferromagnetism, antiferromagnetism, formation of local moments, Kondo effect, RKKY interactions. Phenomenological theory of superconductivity. Transport and magnetic properties of superconductors: London equations, Ginzburg-Landau theory, Josephson effect, superconducting devices.

**Physics 424-1,2 Particle Physics**

*First Quarter*: Overview of modern particle physics and experimental techniques, the quark model, particle production, quantum chromodynamics, quark density functions. Weak interactions including W and Z properties, charged and neutral currents, CP violations, neutrinos, and heavy quarks.

*Second Quarter*: Overview of the Standard Model of particle physics. Deep-inelastic lepton scattering, neutrino oscillations, and collider physics. The experimental side of particle physics will be emphasized. Focus will be mainly on collider physics at the Tevatron and the upcoming Large Hadron Collider. Prerequisite: Physics 412-1 or consent of instructor.

**Physics 426-0 Nonlinear Optics**

Nonlinear optical susceptibilities, wave propagation and coupling in nonlinear media. Harmonic, sum, and difference frequency generation. Parametric amplification and oscillation, phase-conjugation via four-wave mixing, self-phase modulation and solitons. This course is the same as ELEC_ENG 406.

**Physics 427-0 Quantum Optics**

Review of quantum fields. Quantization of the electromagnetic field, photodetection theory. Direct, homodyne, and heterodyne detection. Squeezed and photon-number state generation, application to optical communication and interferometers. This course is the same as ELEC_ENG 407.

**Physics 428-1,2,3 Quantum Field Theory**

*First quarter*: Lagrangian field theory, relativistic Lagrangians and relativistic wave equations, symmetries and conservation laws, canonical quantization, covariant perturbation theory, the S-Matrix, cross sections and lifetimes, and elementary processes of quantum electrodynamics.

*Second and Third quarters:* Topics selected from the following: Path-integral formulation of field theory, renormalization, non-Abelian symmetries, spontaneous symmetry breaking, the standard model of particle physics. C, P, and CP violation. Standard model phenomenology, the parton model and deep inelastic scattering, anomalies, phase transitions, physics beyond the standard model, and non-perturbative methods. Prerequisites: Physics 412-1,2,3 or consent of instructor.

**Physics 430-0 Nonlinear Dynamics And Chaos**

This course covers the mathematics of nonlinear oscillations, fractal geometry, chaotic dynamics, the dynamics of complex systems, and physics applications of these ideas. Projects involving applications of nonlinear dynamics and chaos are integral to this course. Prerequisites: Undergraduate level classical mechanics and familiarity with computer programming.

**Physics 431-0 Physics of Continuous Media**

Fluids: Euler's equation, conservation laws, potential flow, viscosity, Navier-Stokes equations, Reynolds number, thermal conduction, diffusion, surface and sound waves. Solids: kinematics, stress and strain tensors, linear elasticity (Hooke's Law), finite elasticity. Complex fluids: constitutive relations, colloids, Einstein viscosity, sedimentation, granular media, gels, liquid crystals. Prerequisite: Physics 411-0 or consent of instructor.

**Physics 432-1,2 Many-Body Theory**

*First quarter*: Correlation, response and Green's functions for many-particle systems, Feynman perturbation theory, Dyson's equation, symmetry and conservation laws, Fermi liquids, quasiparticles, Landau's transport equation.

*Second quarter*: Electron-ion plasma, electron-phonon interaction, Kondo effect, BSC theory, Gorkov's equations, thermodynamic and magnetic properties of superconductors, transport equations and electromagnetic response of superconductors.

**Physics 434-0 Quantum Fluids, Solids, & Gases**

Bose-Einstein condensation, hydrodynamic and collisionless sound, superfluidity in Bose systems, broken symmetry and BCS pairing, excitations and particle-hole coherence, superfluid 4He and 3He in films and channels.

**Physics 435-0 Soft Matter Physics**

Physical principles and techniques used in the study of molecular materials and systems. Topics may include liquid crystals, polymers, floating monolayers, membranes, structured interfaces, self-assembly, complex and structured fluids, gels, colloids and emulsions, DNA.

**Physics 436-0 Mesoscopic and Nanometer Scale Physics**

Selected topics related to quantum effects in mesoscopic and nanometer scale systems. For example: quantum interference in disordered conductors, transport in semiconductor quantum dots, quantum Hall effect, Coulomb blockade and single-electron charging effects, mesoscopic superconductors and the proximity effect, spin-polarized transport.

**Physics 438-1,2,3 Interdisciplinary Nonlinear Dynamics**

This sequence is the same as BMDE 438, CHME 438, ECE 438, ESAM 438, MATH 438, MSCI 438, MECH 438.

*First quarter*: Example-oriented survey of nonlinear dynamical systems including chaos. Combines numerical, analytical and geometrical approaches to differential equations.

*Second and Third quarters*: Interdisciplinary theoretical, computational and experimental projects involving complex systems in science and engineering, directed by a cross-disciplinary faculty team.

**Physics 440-0 Advanced Topics in Nuclear Physics**

Specialized lectures on current research topics in nuclear physics.

**Physics 441-0 Statistical Methods for Physicists and Astronomers**

Data analysis in the modern age requires familiarity with many concepts and methods from statistics. This course provides an introduction to the basics as well as some of the most advanced techniques. The emphasis will be on practical problems from physics and astronomy, rather than on theory or on statistical methods from other fields. Prior knowledge of statistics is not required. This course is intended primarily for graduate students in Physics and Astronomy. Undergraduate students and students from other departments should contact the instructor.

**Physics 442-0 Advanced Topics in Particle Physics**

Specialized lectures on current research topics in particle physics.

**Physics 445-1, 2 General Relativity**

*First quarter*: Review of special relativity and Newtonian gravity; Gravity as geometry of curved spacetime; Geodesics and conservation laws; Schwarzschild geometry; Tests of general relativity and the Parametrized post-Newtonain formalism; Gravitational collapse and black holes; Rotating black holes and the Kerr geometry; Linearized gravity and gravitational waves; Cosmological models for the expanding Universe.

*Second quarter*: Differential geometry, tensors, covariant derivatives; Riemann curvature and the field equation in vacuum; Energy-momentum tensor, the Einstein equation; Perturbation theory, gauge transformations; Emission of gravitational radiation; More advanced applications as time permits, such as: relativistic stars, TOV equation and the Chandrasekhar limit, relativistic hydrodynamics; ADM formalism and numerical relativity; quantum mechanics in curved spacetime, inflationary cosmology.

**Physics 450-0 Advanced Topics in Condensed-Matter Physics**

Specialized lectures on current research topics in condensed-matter physics.

**Physics 460-0 Advanced Topics in Statistical Physic**

Specialized lectures on current research topics in statistical and biological physics.

**Physics 465-0 Advanced Topics in Nonlinear Dynamics**

Specialized lectures on current research topics in nonlinear and complex phenomena.

**Physics 470-0 Quantitative Biology**

Quantitative physics-based approach to molecular and cell biology, focused on developing an understanding of connections between biomolecule structure and dynamics, and behavior of cells. The course will also include review of topics from statistics of random variables and statistical data analysis relevant to biology and biophysics.

**Physics 471-0 Molecular Biophysics**

Protein structure, nucleic acids structure, forces that determine macromolecular structure, transport and diffusion, macromolecular assemblies, molecular machines and single molecule studies, x-ray crystallography, electron microscopy and image reconstruction, nuclear magnetic resonance, spectroscopy. This course is the same as IBIS 401.

**Physics 478-0 Fundamentals of Macromolecular Crystallography and NMR**

The course covers the principles and practical applications of macromolecular crystallography and NMR in contemporary structural biology research. Besides the key issues in macromolecular structure determination, students will also learn practical aspects of the design and performance of experiments, and will process and analyze experimental data. This course is the same as IBIS 408.

**Physics 479-0 Biophysical Methods for Macromolecular Analysis**

Principles and practical applications of biophysical methods in biological research, with an emphasis on macromolecular structure and function. Techniques covered include isothermal titration calorimetry, fluorescence (FRET and anisotropy), NMR, EXAFS, atomic absorption, Mossbauer and EPR spectroscopy, surface plasmon resonance, single molecule techniques (tweezers and AFM), analytical ultracentrifugation, electron microscopy, SAXS, and dynamic light scattering. This course is the same as IBIS 409.

**Physics 480-0 Advanced Topics in Atomic, Molecular, and Optical Physics**

Specialized lectures on current research topics in atomic, molecular, and optical physics.

**Physics 499-0: Independent Study**

This course allows students to work on a specific topic not covered by any lecture courses under the guidance of a faculty member of the Department of Physics and Astronomy. The student receives a letter grade (not P/NP) based on an evaluation conducted by the faculty member. This course carries the same credit as a lecture course. At most half of the courses taken by a first-year student can be 499-0.

**Physics 590-0: Research.**

A student enrolls in 590-0 when he or she is working in a research group. The student should enroll in the 590-0 corresponding to the faculty member leading that research group. The student receives a P/NP grade; this course does not carry credit toward the degree. Students not enrolled in letter-grade courses should enroll in at least one unit of 590-0.

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### Astrophysics Courses

**Astronomy 405-0 Basics of Radio Astronomy**

Survey of radio astronomy, emphasizing technical aspects; radiation, antennas, receivers, radio spectroscopy, interferometer arrays and aperture synthesis; radio emission mechanisms and cosmic rays.

**Astronomy 410-0 Astrophysical Radiative Processes and Transport**

Radiative processes important in astrophysics and the methods to model the propagation of radiation. Synchrotron and bremsstrahlung emission. Compton scattering. Plasma effects. Basic atomic and molecular processes. Example astronomical applications.

**Astronomy 414-0 Planetary Astrophysics**

Methods of exoplanet detection. The observed architecture of exoplanetary systems. The formation and evolution of planetary systems. Modeling exoplanet interiors and atmospheres. Exoplanet habitability and the search for biosignatures.

**Astronomy 416-0 Astrophysical Fluid Dynamics**

Dynamics of fluids as applied to astrophysical bodies. Topics include hydrostatics, shocks, waves, instabilities, and magnetohydrodynamics. Applications include atmospheres, stars, accretion disks, stellar winds, and galactic disks.

**Astronomy 421-0 Observational Astrophysics**

Geometric optics applied to the design of optical and X-ray telescopes. Diffraction and the Airy disk, radio and optical interferometry and aperture synthesis, adaptive optics, recent developments in detector technology, quantum and thermal noise in astronomy. Includes independent research projects using the CCD camera and 18-inch refractor in Dearborn Observatory.

**Astronomy 425-0 Stellar Astrophysics**

Physics of stellar interiors, stellar atmospheres, and star formation. Specific topics covered include: simple stellar models, nuclear energy generation, overview of evolutionary phases, degenerate stars (white dwarfs, neutron stars), radiative transfer, continuous and line opacities, interstellar gas and dust grains, gravitational collapse and protostars.

**Astronomy 429-0 Extragalactic Astrophysics and Cosmology**

Big bang cosmology, Friedman model, thermal history of the Universe, primordial nucleosynthesis, microwave background, dark matter, inflation, large-scale structure, galaxy formation, spiral and elliptical galaxies, groups and clusters of galaxies.

**Astronomy 441-0 Advanced Topics in Astrophysics**

Specialized lectures on current research topics in observational and theoretical astrophysics.

**Astronomy 443-0 Stellar Structure and Evolution**

Thermodynamics of stellar interiors, equations of stellar structure and radiation transfer, stellar atmospheres, thermonuclear reactions, weak interactions and nucleosynthesis, stellar stability and pulsation, evolution of binaries. Special topics may include novae and supernovae, stellar rotation, stellar magnetic fields, and cooling of neutron stars, white dwarfs, and brown dwarfs. Prerequisite: Astr 425-0 or consent of the instructor.

**Astronomy 448-0 Interstellar Gas and Radiation Processes**

Interstellar gas phases, absorption and emission lines, masers, bremsstrahlung, synchrotron radiation, excitation of atoms and molecules, thermal balance and cooling lines, equations of hydrodynamics, shocks, ionization fronts, supernova remnants, magnetohydrodynamic processes and turbulence, gravitational collapse and star formation, protostars, accretion disks, outflows. Prerequisite: Astr 425-0 or consent of the instructor.

**Astronomy 449-0 Stellar Dynamics**

Gravitational potential theory, regular and chaotic orbits, equilibrium and stability of collisionless stellar systems, galactic nuclei and supermassive black holes, galactic disk dynamics and spiral structure, interactions of stellar systems, kinetic theory of collisional systems, evolution of galaxies and star clusters, dark matter.

**Astronomy 451-0 High Energy Astrophysics**

This course covers a wide range of topics in modern high-energy astrophysics, focusing on the physics of compact objects and their observational manifestations across the electromagnetic spectrum, from the radio to gamma-ray bands, and through gravitational waves and neutrinos. The course includes a computational component, focusing on the numerical simulations of black hole accretion and outflows.