#### PHYS 413. Classical Mechanics (3)

An introduction to classical mechanics. Lagrangian and Hamiltonian formulations, conservation laws, kinematics and dynamics, Poisson brackets, Liouville Theorem, canonical transformation, and action angle variables.

#### PHYS 414. **Foundations of Statistical Mechanics** (3)

Noninteracting systems, statistical mechanics of solids, liquids, gases, fluctuations, irreversible processes, phase transformations. Statistical mechanics provides a set of universal principles to describe the physics of complex systems, irrespective of their microscopic details. This course is a self-contained introduction to the mathematical foundations of the subject, starting from basic concepts of probability and the dynamics of classical systems in phase space, covering topics like ergodicity, chaos, and master equations. Using this framework we systematically derive the laws of equilibrium thermodynamics and show how they are a limiting case of recently discovered fluctuation theorems that are valid arbitrarily far from equilibrium. Along the way we explore the many facets and consequences of these laws: entropy as information, universal bounds on the efficiency of engines, the fluctuation-dissipation relation and Onsager reciprocity. Finally, we connect these ideas to the quantum realm, via the physics of decoherence and quantum master equations. The course is open to students from all backgrounds who have basic familiarity with undergraduate classical and quantum physics (a previous statistical mechanics course is helpful but not necessary). Examples in class and in the problem sets highlight the broad interdisciplinary scope of statistical mechanics, from biophysics to machine learning to quantum information.

#### PHYS 420. Introduction to Biological Physics (3)

This course explores the intersection of physics and biology: how do fundamental physical laws constrain life processes inside the cell, shaping biological organization and dynamics? We will start at the molecular level, introducing the basic ideas of nonequilibrium statistical physics and thermodynamics required to describe the fluctuating environment of the cell. This allows us to build up a theoretical framework for a variety of elaborate cellular machines: the molecular motors driving cell movement, the chaperones that assist protein folding, the information-processing circuitry of genetic regulatory networks. The emphasis throughout will be on simple, quantitative models that can tackle the inherent randomness and variability of cellular phenomena We will also examine how to verify these models through the rich toolbox of biophysical experimental and computational technologies. The course should be accessible to students from diverse backgrounds in the physical and life sciences: we will explain both the biological details and develop the necessary mathematical / physical ideas in a self-contained manner.

#### PHYS 423. Classical Electromagnetism (3)

Electromagnetic theory in the classical limit. Gauge invariance and special relativity. Applications to electrostatic, magnetostatic, and radiation problems using advanced mathematical techniques. Dielectric, magnetic, and conducting materials. Wave propagation in open and confined geometries. Radiation from accelerating charges. Cherenkov, synchrotron, and transition radiation.

#### PHYS 426. Contemporary Physical Optics (3)

See PHYS 326. Additional work required.

#### PHYS 427. Quantum Electronics. (3)

An introduction to theoretical and practical quantum electronics covering topics in quantum optics, laser physics, and nonlinear optics. Topics to be addressed include the physics of two-level quantum systems including the density matrix formalism, rate equations, and semiclassical radiation theory; laser operation including oscillation, gain, resonator optics, transverse and longitudinal modes, Q-switching, mode-locking, and coherence; and nonlinear optics including the nonlinear susceptibility, parametric interactions, stimulated processes, and self-action. Recommended preparation for PHYS 427: PHYS 331 or PHYS 481. Offered as PHYS 327 and PHYS 427.

#### PHYS 428. Cosmology and Structure (3)

Distances to galaxies. The content of the distant universe. Large scale structure and galaxy clusters. Physical cosmology. Structure and galaxy formation and evolution. Testing cosmological models. Offered as ASTR 328, PHYS 328, ASTR 428, and PHYS 428. Prereq: ASTR 222.

#### PHYS 430. Experimental Methods in Biophysics (3)

There is an extensive array of powerful and elegant tools used to obtain quantitative and qualitative information about the physics of biology. New, cutting-edge techniques are being developed by labs around the world every day. To solve important problems in biophysics, an understanding of the capabilities and limitations of the current instrumental methods is needed. This course will focus on the physical principles of biophysical instrumentation so that appropriate choices and efficient use of measurement tools can be made. Exposure to instrumentation in core facilities around campus will link lectures to practical demonstrations of the operation of instrumentation. Techniques applied to a diversity of biological macromolecules and assemblies from the molecular level of proteins, nucleic acids, lipids, up to higher organization of cells, cellular organisms and tissues will be discussed. Topics covered include spectroscopic methods (IR/vis/UV/X-ray regions of the electromagnetic spectrum, absorption, fluorescence, circular dichroism, dynamic light scattering, Raman, electron paramagnetic resonance, NMR), microscopy techniques (electron, atomic force, scanning tunneling, optical), separation techniques (sedimentation, centrifugation, chromatography), crystallography, calorimetry, mass spectrometry, single molecule detection, cell sorting, functional genomics and proteomics and laboratory evolution. Biological examples from historical and current literature will be used to demonstrate the merits of each of the methods.

#### PHYS 431. Physics of Nuclear Magnetic Resonance Imaging (3)

Description of physical principles underlying the spin behavior in MR and Fourier imaging in multi-dimensions. Introduction of conventional, fast, and chemical-shift imaging techniques. Spin echo, gradient echo, and variable flip-angle methods. Projection reconstruction and sampling theorems. Bloch equations, T1 and T2 relaxation times, rf penetration, diffusion and perfusion. Flow imaging, MR angiography, and functional brain imaging. Sequence and coil design. Prerequisite: PHYS 122 or PHYS 124 or EBME 410, or consent of instructor.

#### PHYS 436. Modern Cosmology (3)

See PHYS 336

#### PHYS 438. Introduction to Surface Science (3)

Geometric, chemical, and electronic structure of surfaces and interfaces between solid, liquid, and gas, contrasting surface properties with those of the bulk. Surface and interface thermodynamics, surface energy and surface tension in liquid and solid systems, surface shape effects, two-dimensional lattice, adsorption phenomena, the interactions of electrons, ions, and photons with a surface, and experimental techniques in surface science. Prerequisite: PHYS 315, CHEM 335, or consent of instructor.

#### PHYS 441. Physics of Condensed Matter I (3)

Crystal structure, X-ray diffraction, band theory and applications. Free electron theory of metals and electrons in magnetic fields. Prerequisite: Consent of instructor.

#### PHYS 442. Physics of Condensed Matter II (3)

(Continuation of PHYS 441.) Lattice vibrations, thermal properties of solids, semiconductors, magnetic properties of solids, and superconductivity. Prerequisites: PHYS 441 and consent of instructor.

#### PHYS 447. Physics of Liquid Crystals (3)

#### PHYS 449. Methods of Mathematical Physics I (3)

See PHYS 349. Additional work required.

#### PHYS 450. Methods of Mathematical Physics (3)

See PHYS 350. Additional work required.

#### PHYS 451. Empirical Foundations of the Standard Model I (3)

The experimental basis for modeling the electroweak and strong interactions in terms of fundamental fermions, quarks and leptons, and gauge bosons, photons, the weak bosons, and gluons; particle accelerators and detection techniques; phenomenology of particle reactions, decays, and hadronic structure; space-time and internal symmetries; symmetry breaking. Prerequisite: consent of instructor.

#### PHYS 452. Empirical Foundations of the Standard Model II (3)

(Continuation of PHYS 451) Tests of the predictions of the broken SU(2) x U(1) gauge-symmetric model of the electroweak interactions and the color-SU(3) model of the strong interactions. Structure of the weak currents, the quark mixing matrix, and the gauge-boson couplings. Exploration of the Higgs sector and the coupling of the Higgs to quarks and leptons. Heavy-quark physics. Calculation of hadronic processes using partonic distribution functions. CP violation, neutrino masses, fermion nonconservation, and possible extensions of the Standard Model. Prerequisite: PHYS 451 or consent of instructor.

#### PHYS 465. General Relativity (3)

This is a first course in general relativity. The techniques of tensor analysis will be developed and used to describe the effects of gravity and Einstein’s theory. Consequences of the theory as well as its experimental tests will be discussed. An introduction to cosmology will be given. Prerequisite: consent of the instructor.

#### PHYS 472. Graduate Physics Laboratory (3)

A series of projects designed to introduce the student to modern research techniques such as automated data acquisition. Students will be assessed as to their individual needs and a sequence of projects will be established for each individual. Topics may include low temperature phenomena, nuclear gamma ray detection and measurement and optics.

#### PHYS 481. Quantum Mechanics I (3)

Quantum mechanics with examples of applications. Schroedinger method; matrix and operator methods. Approximation methods including JBWK, variational, and various perturbation methods. Applications to atomic, molecular and nuclear physics including both bound states and scattering problems. Applications of group theory to quantum mechanics. Prerequisite: consent of instructor.

#### PHYS 482. Quantum Mechanics II (3)

Continuation of PHYS 481. Prerequisite: PHYS 481 or consent of instructor.

#### PHYS 491. Modern Physics for Innovation I

The first half of a two-semester sequence providing an understanding of physics as a basis for successfully launching new high-tech ventures. The course will examine physical limitations to present technologies, and the use of physics to identify potential opportunities for new venture creation. The course will provide experience in using physics for both identification of incremental improvements, and as the basis for alternative technologies. Case studies will be used to illustrate recent commerically successful (and unsuccessful) physics-based venture creation, and will illustrate characteristics for success. Admission to this course requires consent of the instructor.

#### PHYS 492. Modern Physics for Innovation II

Continuation of PHYS 491, with an emphasis on current and prospective opportunities for Physics Entrepreneurship. Longer term opportunities for Physics Entrepreneurship in emerging areas, including (but not be limited to) nanoscale physics and nanotechnology; biophysics and applications to biotechnology; physics-based opportunities in the context of information technology. Prerequisite: PHYS 491.

#### PHYS 493. Feasibility and Technology Analysis (3)

#### PHYS 522. Nonlinear Optics (3)

Classical phenomenology and Maxwell’s equations in media; Maxwell-Bloch equations. Theory of nonlinear wave interactions and propagation. Properties of optical fibers and nonlinear materials. Theory of nonlinear propagation, solitons, inverse scattering transforms, optical chaos. Applications to lasers, optical bistability, self-induced transparency, and stimulated light scattering. Prerequisites: PHYS 423 and PHYS 481.

#### PHYS 539. Special Topics Seminar (1-3)

Individual or small group instruction on topics of current interest. Topics include, but are not limited to, particle physics, astrophysics, optics, condensed matter physics, biophysics, imaging. Several such courses may be offered concurrently.

#### PHYS 541. Quantum Theory of the Solid State (3)

Elementary excitations in solids, including lattice vibrations, spin waves, helicons, and polarons. Quasiparticles and collective coordinates. BCS theory of superconductivity. Quasicrystals. Transport properties. Conduction electrons in magnetic fields and the quantum Hall effect. Green function methods of many-body systems. Prerequisite: PHYS 482 and consent of instructor.

#### PHYS 542. Quantum Theory of the Solid State II (3)

Continuation of PHYS 541. Prerequisite: PHYS 541 and consent of instructor.

#### PHYS 544. Advanced Theory of Materials (3)

Density functional theory: successes and limitations. Electronic structure and total energy calculation methods. Simulations of structure of solids, molecular dynamics. Experimental probes: particle-solid interactions. Applications to various classes of materials: metals and their alloys, semiconductors, narrow band systems. Defective solids: point defects, surfaces and interfaces; and artificially structured materials: Prerequisite: PHYS 442 or consent of instructor.

#### PHYS 545. Advanced Topics in the Physics of Many Particle Systems I (3)

The matter field; Hartree-Fock approximation; equations of motion for elementary excitations. Ground-state Green functions; spectral representation; perturbation expansion for Green functions; Dyson equation; density-fluctuation propagators and linear response functions. Applications to plasmas, normal Fermi liquids, spin systems, superfluid Bose systems, and superconductors. Prerequisite: PHYS 482 and consent of instructor.

#### PHYS 546. Advanced Topics in the Physics of Many Particle Systems II (3)

See PHYS 545. Prerequisite: PHYS 545 and consent of instructor.

#### PHYS 551. Theoretical Nuclear Physics I (3)

Physical properties of the nucleus, nuclear structure and nuclear models, nuclear scattering, and nuclear transformations from a theoretical viewpoint. Prerequisite: PHYS 482 and consent of instructor.

#### PHYS 552. Theoretical Nuclear Physics II (3)

See PHYS 551. Prerequisite: PHYS 551 and consent of instructor.

#### PHYS 559. Special Topics Seminar (3)

#### PHYS 561. Cosmic Ray and High-Energy Astrophysics (3)

Advanced topics in experimental cosmic ray physics and high-energy astrophysics. Prerequisite: consent of instructor.

#### PHYS 565. General Theory of Relativity (3)

Review of special relativity, principle of equivalence, tensor analysis. Einstein field equations, tests of general relativity, post-Newtonian method, gravitational radiation, relativistic astrophysics, symmetries of space-time. Prerequisite: Consent of instructor.

#### PHYS 566. Cosmology (3)

Homogeneity and isotropy of the universe, Robertson-Walker metric, red shifts and distances, number counts, steady state model, Friedmann models, microwave radiation background, nucleosynthesis, galaxy formation. Prerequisite: PHYS 565 and consent of instructor.

#### PHYS 579. Special Topics Seminar (3)

In-depth examination of a cutting-edge topic of current interest. New topic is selected each semester.

#### PHYS 581. Quantum Mechanics III (3)

Continuation of PHYS 482. The methods of quantum field theory applied to the nonrelativistic many-body problem, radiation theory, and relativistic particle physics. Second quantization using canonical and path-integration techniques. Constrained systems and gauge theories. Graphical perturbative methods and graph summation approaches. Topological aspects of field theories. Prerequisite: PHYS 482 and consent of instructor.

#### PHYS 591. Gauge Field Theory I (3)

Noether’s Theorem, symmetries and conserved currents, functional integral techniques, quantization, Feynman rules, anomalies, QED, electroweak interactions, QCD, renormalization, renormalization group, asymptotic freedom, and assorted other topics. Prerequisite: consent of instructor.

#### PHYS 592. Gauge Field Theory II (3)

Electroweak theory; spontaneous symmetry breaking; renormalization group. Strong interactions; grand unified theories and theories beyond the Standard Model. PHYS 592 will explore in depth the field theoretic basis of the Standard Model of particle physics and some of its most important extensions. Prerequisite: consent of instructor.

#### PHYS 595. Applications of Quantum Field Theory in Modern Physics (3)

Basics elements of Quantum Field Theory, Applications of Quantum Field Theory to condensed matter systems, particle physics and cosmology. Strong, Weak and Electromagnetic Forces, Two-dimensional (2D) condensed matter systems, Neutrino Oscillations, The Dark Matter Problem. Prerequisite: PHYS 481

#### PHYS 601. Research in Physics (credit as arranged)

#### PHYS 651. Thesis (M.S.) (credit as arranged)

#### PHYS 701. Dissertation (Ph.D.) (credit as arranged)

#### PHYS 841 Teaching Physics Concepts I (2)

See PHYS 341. This course number applies for public school teachers.

#### PHYS 842 Teaching Physics Concepts II (2)

Continuation of Teaching Physics Concepts I. See PHYS 342. This course number applies for public school teachers.