## Core Courses

Phy 517 Statistical Mechanics (3)

An introduction to statistical methods and the description of a variety of phenomena on a statistical basis. Thermodynamics, statistical mechanics, and kinetic theory are presented from a unified point of view. Topics include elements of probability theory, interaction between macroscopic systems and their parameters, equilibrium, ensembles, classical and quantum statistics, systems of interacting particles, Boltzmann equation, irreversible processes, and fluctuations. This course is intended for physics graduate students on the masters track. Prerequisite: Phy 547or Phy 605. Students can only receive credit for either Phy 517 or Phy 602.

Phy 527 Classical Mechanics (3)

The fundamental principles of classical mechanics are covered. These include the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton’s principle, conserved quantities, rigid bodies, Hamiltonian formulation and canonical equations, canonical transformations and generating functions, Liouville’s theorem. This course is intended for physics graduate students on the masters track. Students can only receive credit for either Phy 527 or Phy 601.

Phy 537 Electrodynamics 1 (3)

An in-depth survey of classical electrodynamics. Topics include: special relativity, motion of charges in electromagnetic fields, Maxwell's equations, energy and momentum in the electromagnetic field, electrostatics, the propagation and generation of electromagnetic waves. This course is intended for physics graduate students on the masters track. Students can only receive credit for either Phy 537 or Phy 603.

Phy 539 Electrodynamics 2 (3)

An in-depth survey of classical electrodynamics in material media. Topics: conductors, dielectrics, magnetostatics, superconductivity, the interaction of electromagnetic waves with matter, including reflection, diffraction, scattering, and the diffraction of x-rays by crystals. This course is intended for physics graduate students on the masters track. Prerequisite: Phy 537/Phy 603. Students can only receive credit for either Phy 539 or Phy 604.

Phy 547 Quantum Mechanics 1 (3)

This foundations of quantum mechanics course includes a review of Schroedinger's equation and proceeds to Heisenberg formalism and its properties, basic principles and structure of quantum mechanics, states, observables, measurements and their mathematical descriptions, representation and transformation theory, bound states and scattering, applications to harmonic oscillator and central potentials. This course is intended for physics graduate students on the masters track. Students can only receive credit for either Phy 547 or Phy 605.

Phy 557 Quantum Mechanics 2 (3)

This second semester of quantum mechanics includes discussion of angular momentum, rotation, Clebsch-Gordan coefficients, Wigner-Eckart theorem, approximation methods, perturbation, variation and WKB approaches, identical particles, Thomas-Fermi model, Hartree-Fock equation, and the semiclassical theory of radiation. This course is intended for physics graduate students on the masters track. Prerequisite: Phy 547/Phy 605 or equivalent with permission of instructor. Students can only receive credit for either Phy 557 or Phy 606.

Phy 577 Computational Methods (3)

Applications of modern computational methods to current topics in physics. Basics of coding and use of standard software packages. Prerequisite Phy 527 or Phy 601, and Phy 509. Students who have received credit for APHY477/477Y cannot receive credit for this course.

Phy 587 Solid State Physics 1 (3)

A broad survey of the phenomena of solid state physics. Symmetries of crystals and diffraction from periodic structures; vibrational states and electronic band structures in crystalline metals, semiconductors, and insulators; thermal, transport and optical properties of solids. Prerequisites: Phy 517 or Phy 602, and Phy 547 or Phy 605. Students who have received credit for APHY487 cannot receive credit for this course.

Phy 601 Classical Mechanics (3)

The fundamental principles of classical mechanics are covered. These include the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies, Hamiltonian formulation and canonical equations, canonical transformations and generating functions, Liouville's theorem. This course is intended for physics graduate students on the doctoral track. Students can only receive credit for either Phy 527 or Phy 601.

Phy 602 Statistical Mechanics (3)

An introduction to statistical methods and the description of a variety of phenomena on a statistical basis. Thermodynamics, statistical mechanics, and kinetic theory are presented from a unified point of view. Topics include elements of probability theory, interaction between macroscopic systems and their parameters, equilibrium, ensembles, classical and quantum statistics, systems of interacting particles, Boltzmann equation, irreversible processes, and fluctuations. This course is intended for physics graduate students on the doctoral track. Prerequisites: Phy 605. Students can only receive credit for either Phy 517 or Phy 602.

Phy 603 Electrodynamics 1 (3)

An in-depth survey of classical electrodynamics. Topics include: special relativity, motion of charges in electromagnetic fields, Maxwell's equations, energy and momentum in the electromagnetic field, electrostatics, the propagation and generation of electromagnetic waves. This course is intended for physics graduate students on the doctoral track. Students can only receive credit for either Phy 537 or Phy 603.

Phy 604 Electrodynamics 2 (3)

An in-depth survey of classical electrodynamics in material media. Topics: conductors, dielectrics, magnetostatics, superconductivity, the interaction of electromagnetic waves with matter, including reflection, diffraction, scattering, and the diffraction of x-rays by crystals. This course is intended for physics graduate students on the doctoral track. Prerequisite: Phy 603. Students can only receive credit for either Phy 539 or Phy 604.

Phy 605 Quantum Mechanics 1 (3)

This foundations of quantum mechanics course includes a review of Schroedinger's equation and proceeds to Heisenberg formalism and its properties, basic principles and structure of quantum mechanics, states, observables, measurements and their mathematical descriptions, representation and transformation theory, bound states and scattering, applications to harmonic oscillator and central potentials. This course is intended for physics graduate students on the doctoral track. Students can only receive credit for either Phy 547 or Phy 605.

Phy 606 Quantum Mechanics 2 (3)

This second semester of quantum mechanics includes discussion of angular momentum, rotation, Clebsch-Gordan coefficients, Wigner-Eckart theorem, approximation methods, perturbation, variation and WKB approaches, identical particles, Thomas-Fermi model, Hartree-Fock equation, and the semiclassical theory of radiation. This course is intended for physics graduate students on the doctoral track. Prerequisite: Phy 605 or equivalent with permission of instructor. Students can only receive credit for either Phy 557 or Phy 606.

## Electives

Phy 504 Biophysics and Bioimaging (3)

This course provides a broad study of biophysics from the perspective of imaging. The course covers the theory of light, light interaction with biological tissues, cells and molecules, color vision, microscopic image formation, color vision, fluorescence, interference-based imaging, holography, X-Ray imaging, FLIM, FRAP, FRET, spectral imaging, and super-resolution approaches (STORM/STED/PALM/SIM).

Phy 506 Electromagnetism I: Introduction to Statics (3)

Electrostatics and magnetostatics in vacuum and in materials. The mathematics of vector fields will be introduced, including a review of vector calculus. Potential formulations of the electrostatic and magnetostatic fields will be introduced. Methods for solving boundary value problems will be practiced including separation of variables and orthogonal function expansions and multipole expansions. Students who received credit for Phy 470 cannot receive credit for this course.

Phy 508 Mathematical Methods in Physics (3)

Topics in theoretical and applied physics will be studied using both analytical and numerical approaches. Formal descriptions of phenomena and interpretations of results will involve a variety of classical and modern mathematical techniques. Prerequisite: Phy 507. Students who have received credit for APHY409/409Y cannot receive credit for this course.

Phy 509 Programming in Physics (3)

Applications of modern computational methods to current topics in physics. Basics of coding and use of standard software packages. Prerequisites: Phy 340 and Phy 440 or equivalent.

Phy 511 Electromagnetism II: Introduction to Electrodynamics (3)

Electrodynamics in vacuum and materials. Topics will include electromagnetic induction and displacement current, Maxwell's equations, energy and momentum in electromagnetic fields, electromagnetic waves and radiation. Students who received credit for Phy 480 cannot receive credit for this course.

Phy 514 Introduction to Thermodynamics and Statistical Physics (3)

Thermodynamic systems and variables; the laws of thermodynamics. Thermodynamic potentials and applications, ideal and real gas relations; changes of phase, introduction to probability theory; elementary kinetic theory of gases; micro and macro-states of simple quantum-mechanical systems; Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics. Students who receive credit for Phy 460 cannot receive credit for this course.

Phy 515 Electronics (3)

Topics covered in this course include transistors and their characteristics, electronic circuits, field effect transistors and applications, amplifiers, low and high frequency response, operational amplifiers, consideration of control-circuit design, fast-switching and counting devices, integrated circuits and their designs. Two class periods and one three-hour laboratory each week. Only one version may be taken for credit. Offered fall semester only.

Phy 516 Electronics Projects (3)

Hands on independent study electronics projects. Prerequisite: Phy 515 and consent of instructor.

Phy 524 Introduction to Classical Mechanics (3)

Fundamentals of Newtonian mechanics: conservation theorems, central forces, motion in non-inertial frames, rigid-body motion. Lagrange's and Hamilton's equations. Offered fall semester. Students who received credit for Phy 410 cannot receive credit for this course.

Phy 525 Information Physics (3)

The basic principles of information theory and their relation to the laws of physics. Probability and entropy as tools for inductive reasoning. The Cox axioms. Bayes' theorem and its application to elementary data analysis. Relative entropy, the method of maximum entropy and the foundations of statistical mechanics and thermodynamics. Information geometry, the Fisher-Rao information metric. Derivation of quantum mechanics from information theory. Prerequisites: Graduate status or consent of the instructor. Students who have received credit for APHY 425 cannot receive credit for this course.

Phy 526 Introduction to Particle Physics (3)

A broad survey of the phenomena of particle physics. Experimental methods. Classification of particles, quantum numbers, and interactions. External and internal symmetries. Electromagnetic, strong, and weak interactions; resonances; unitary symmetry; recent topics. Students who have received credit for APHY426/426Y cannot receive credit for this course.

Phy 528 The Physics of Radiation Therapy (3)

This course will be taught at a level such that it will be accessible to ambitious undergraduate students also. The course focuses on radiation therapy physics with special emphasis on clinical applications. The course provides basic radiation physics and physical aspects of treatment planning using photon and electron beams and brachytherapy sources. The course consists of three parts: (i) Part I deals with the basic physics of radiation. (ii) Part II deals with classical radiation therapy, which includes dosimetry and treatment planning. (iii) Part III focuses on modern radiation therapy, which deals with conformal and intensity-modulated radiation therapy, stereotactic radiosurgery, high dose rate brachytherapy and prostate implants. The course will also involve lectures by Medical Physics experts from local hospitals. Students will write a report on a topic selected in consultation with the teacher. Prerequisites: Phy 340 and Phy 440 or equivalent.

Phy 530 Optics (3)

This course provides a broad introduction to optics, including both theory and experiment. The geometrical and wave theories of light propagation will be introduced along with their applications such as imaging systems (e.g. microscopes, and telescopes), lasers and polarization optics. The course will include 5 labs covering the material presented in lecture. Students who have received credit for APHY430 cannot receive credit for this course. Students who have received credit for APHY430 cannot receive credit for this course.

Phy 533 Physics Measurements (3)

This course offers theoretical and experimental aspects of measurements, data acquisition and test design in physics and engineering. It introduces students to the National Instruments LabVIEW, a graphical programming platform that allows integration of different software and hardware modules into a single project. The course will cover fundamentals of measurement (statistical error, sampling theory and so on), discuss sensor theory, and offer instruction on virtual instrumentation, such as data logging, signal processing, and graphical user interface design. The course will include several labs covering the material presented in lecture. Prerequisites: Phy 335Z, or permission of instructor.

Phy 540 Introduction to Quantum Physics I (3)

Introduction to non-relativistic quantum mechanics; wave functions, amplitudes and probabilities; the superposition of quantum states, the Heisenberg uncertainty principle. Time evolution: the Schroedinger equation, stationary states, two-state systems. Motion in one-dimensional potentials: tunneling, particle in a box, harmonic oscillator. Offered fall semester. Students who received credit for Phy 440 cannot receive credit for this course.

Phy 542 Introduction to General Relativity (3)

Review of special relativity. Introduction to tensor analysis and the geometry of curved spaces. Einstein's equations. Applications to gravitational waves, black holes and expanding universes. Students who have received credit for APHY442 cannot receive credit for this course.

Phy 543 Introduction to Cosmology (3)

An introduction to cosmology, the study of the structure and evolution of the Universe. Topics: Newtonian cosmology, elements of general relativity (metric, geodesics, Einstein equations), Friedman equations and their solutions, dark matter, dark energy, inflation, introduction to quantum gravity. Students who have received credit for APHY443/443Y cannot receive credit for this course.

Phy 544 Theory and Techniques of Biophysics and Biophysical Chemistry (3)

Comprehensive study of the physical chemistry of biopolymers; structure- confirmation-function interrelations, including systematic coverage of theoretical and experimental aspects of such topics as solution thermal dynamics, hydrodynamics, and optical and magnetic characteristics. Prerequisites: One year of biochemistry and one year of physical chemistry.

Phy 545 Physics of Nuclear Medicine (3)

The fundamental physics of nuclear medicine is explored. Topics to be covered include implantation and imaging of radioisotopes, brachytherapy and implantation for the treatment of tumors.

Phy 546 Laser Physics and Applications (3)

This course provides a broad introduction to lasers, including theory spontaneous and simulated emission, design of optical resonators and laser beam propagation. The course will also cover the design of various types of lasers and laser applications, such as holography, microscopy and spectroscopy. Prerequisite: Phy 250. Students who have taken APHY446/446Y cannot receive credit for this course.

Phy 548 Medical Imaging (3)

This introduction to the physics of radiography includes discussions of CAT, PET, MRI, SPECT, fluoroscopy, and nuclear medicine. Image quality assessment concepts such as contrast, MTF, DQE(f), and ROC will also be covered. Students who have received credit for APHY448/448Y cannot receive credit for this course.

Phy 549 Quantum Information, Computation, and Foundations (3)

Quantum theory has many mysterious features, such as entanglement and the probabilistic nature of measurements, which seem to defy understanding in terms of the mechanistic clockwork picture of reality that underlies classical physics. What do these features suggest about the nature of physical reality? For example, is there really “spooky action at a distance” in Nature, as Einstein quipped? In this course, we investigate possible answers to these questions, and form an understanding as to why these questions matter. In particular, we look at recent work which views quantum theory as a theory of information manipulation, and see that this provides extraordinary new insights into the nature of physical reality, which leads to new technological possibilities (such as quantum cryptography and entanglement-assisted computation) that harness quantum weirdness, and even helps us to derive the mathematics of quantum theory from simple physical assumptions. Students who have received credit for APHY449/449Y cannot receive credit for this course.

Phy 550 Introduction to Quantum Physics II (3)

Quantum motion in central potentials; angular momentum and spin; the hydrogen atom. Identical Particles. The structure of atoms and molecules, the periodic table. Stationary-state and time-dependent perturbation theory. Scattering theory. Students who received credit for Phy 450 cannot receive credit for this course.

Phy 551 (Csi 551, Inf 551) Bayesian Data Analysis and Signal Processing (3)

This course will introduce both the principles and practice of Bayesian and maximum entropy methods for data analysis, signal processing, and machine learning. This is a hands-on course that will introduce MATLAB computing language for software development. Students will learn to write their own Bayesian computer programs to solve problems relevant to physics, chemistry, biology, earth science, and signal processing, as well as hypothesis testing and error analysis. Optimization techniques to be covered include gradient ascent, fixed-point methods, and Markov chain Monte Carlo sampling techniques. Prerequisites: Csi 201, Mat 214, or equivalents, or permission of instructor. Phy 509 or equivalent programming experience with permission of the instructor. Students who have received credit for APHY/ICSI/CINF451 cannot receive credit for this course.

Phy 552 Astroparticle Physics (3)

An in-depth discussion of precision cosmology: dark matter, dark energy, and the Cosmic Microwave Background radiation, from experimental/technological,observational, mathematical/theoretical, phenomenological, and computational perspectives. Introduction to intragalactic and extragalactic gamma-ray/x-ray astronomy, the study of cosmic rays, and astrophysical neutrinos, as well as experimental searches for extra/higher spatial dimensions and constraints on Lorentz invariance violation via various particle astrophysics detection methods. Prerequisites: Phy 443 and 320, or permission of instructor.

Phy 553 Microprocessor Applications (3)

This course describes applications of microprocessors to data collection and process control. Topics include the capabilities of typical microprocessors and the techniques used to interface them to external devices, input/output programming, use of the data and address busses, interrupt handling, direct memory access, and data communications; characteristics of peripheral devices such as keyboards, printers, A/D and D/A converters, sensors, and actuators. Only one version of Phy 453/553 may be taken for credit.

Phy 554 Microprocessors Applications Laboratory (3)

This course complements the theoretical development presented in A Phy 553. It centers around practical laboratory applications in both hardware and software of a particular microprocessor. Students will prototype a minimum system and expanded system. Applications include keyboard, printer, display, A/D, D/A, and control functions. A knowledge of a microprocessor and digital logic functions is desirable. Prerequisite(s): Phy 515 or permission of instructor or Phy 553.

Phy 558 Physics of Radiation Detectors (3)

Radiation is everywhere, and radiation detectors have multi-disciplinary applications, ranging from particle physics, nuclear engineering, physical chemistry, to medical physics. New radiation detectors are constantly developed in laboratories around the world. This course will encompass theories, methodologies and technologies in order to understand the conceptual basis of radiation devices. It will also cover the statistics, and data analysis methods and softwares used in the context of radiation detectors. Students who have received credit for APHY458/458Y cannot receive credit for this course.

Phy 559 Symmetry in Physics (3)

Symmetry is a fundamental principle by which we organize our knowledge of the physical world. Symmetry expresses not only visible regularities, such as the periodic structure of crystals and fractal structure of snowflakes, but also regularities that underpin the laws of classical and quantum physics. In this course, we investigate physical symmetries using two powerful mathematical tools-group theory (and their matrix representations) and the theory of functional equations. Specific topics include the connection between symmetry and conservation laws in classical and quantum mechanics; the origin of spin; atomic selection rules and the rules for identical particles in quantum mechanics; scaling laws in dynamical systems (which underlie fractal structures such as the Mandelbrot set); the harnessing of symmetry to systematically derive probability theory, information theory and quantum theory; and applications of symmetry methods in other disciplines such as mathematics and economics. Prerequisites: Phy 235 and Phy 440, or permission of instructor. Students who have received credit for APHY459/459Y cannot receive credit for this course.

Phy 560 Atoms and Molecules (3)

A broad survey of the phenomena in atomic and molecular physics. Atomic structure and spectroscopy, scattering and collisions; molecular structure, electronic, rotational and vibrational spectra, photon excitations, scattering and collisions. Prerequisite(s): Phy 517 and Phy 587 or equivalent or permission of instructor.

Phy 562 Structure and Properties of Materials (3)

The physics of real materials: the structure of crystalline and amorphous solids; x-ray diffraction and electron microscopy; the thermodynamics and kinetics of phase transformations; crystallographic defects and their relation to mechanical properties. Offered spring semester only. Prerequisite: Phy 517 and Phy 587 or permission of instructor.

Phy 566 X-Ray optics, Analysis and Imaging (3)

A broad survey of x-ray optics and their uses. Introduction to the theory of x-ray interaction with matter, including refraction, diffraction, total reflection, image formation, fluorescence, absorption, and surface roughness. Applications include x-ray astronomy, microscopy, lithography, materials analysis and medical imaging. A paper and presentation are required. Prerequisite Phy 587 or permission of instructor. Students who have received credit for APHY466/466Y cannot receive credit for this course.

Phy 568 Particle Physics (3)

Particle interactions and symmetries. Introduction to classification and the quark model. Calculation of elementary processes using Feynman diagrams. Prerequisite: Phy 547.

Phy 571 Introduction to Neutrino Astronomy (3)

An introduction to the burgeoning field of Neutrino Astronomy. Neutrinos are one of the most abundant particles in Nature, and are produced in a variety of extra-terrestrial sources, e.g., interaction of cosmic rays with the earth's atmosphere, our Sun, Supernovae, Active Galactic Nuclei, the Big Bang. This course will give a broad overview of the underlying physics, detection techniques and results. Prerequisites: Phy 240 or Phy 440, or permission of instructor. Students who receive credit for Phy 471/471Y cannot receive credit for this course.

Phy 572 Fluid Mechanics (3)

Most fluids are described by the Navier-Stokes equation. Simplifications or approximations are often needed to extract the physics from this complicated equation. Topics covered include: 1) Static fluids, pressure and surfaces; 2) The Euler equation, d'Alembert's paradox, Bernoulli's equation and circulation; 3) Viscosity, damping and the Reynolds number; 4) Boundary layers and turbulence; 5) Waves and sound propagation. Prerequisites: Phy 320 and Mat 214 or equivalent.

Phy 580 Electron Diffraction and Microscopy (3)

Topics covered which are related to electron diffraction and microscopy include the kinematic theory of electron diffraction, reciprocal lattices and fine structure of diffraction patterns, electron guns and electron lenses, the operation and calibration of electron microscopes, the dynamical theory of diffraction contrast, images of various defects in solids, analysis of dislocations and interfaces, many-beam effects and weak-beam images, phase contrast, lattice images and multislice method, sample preparation and analytical electron microscopy techniques. The course includes hands-on electron microscope experiments. Prerequisite Phy 587.

Phy 588 Solid State Physics II (3)

A broad survey of the phenomena of solid state physics (continuation of Solid State Physics I). Superconductivity; magnetic and dielectric properties of materials; spectroscopy with photons and electrons; point and line defects; surfaces and interfaces; alloys; noncrystalline solids. Prerequisite: Phy 587. Students who have received credit for APHY488 cannot receive credit for this course.

Phy 620 Quantum Field Theory (3)

Lorentz and Poincare symmetries. Noether's theorem. Classical and quantum free fields: scalar, Weyl, Dirac and electromagnetic fields. Interacting fields: perturbation theory, Feynman diagrams. Renormalization. Decay rates and cross sections. Path integrals. Quantum electrodynamics. Non-Abelian gauge theories: Quantum Chromodynamics and the Weinberg-Salam-Glashow model.

Phy 632 Spectroscopy: Magnetic Resonance (3)

This course will develop a foundation for the understanding of modern magnetic resonance spectroscopy including both NMR and EPR. Topics will include, quantum mechanics of spins, and the density matrix, Fourier transform experiments, spin relaxation, double resonance, field gradients and imaging, two-dimensional experiments, multiple quantum coherence, protein structure and dynamics, solid state NMR and magic angle spinning. Prerequisite: Phy 557.

Phy 651 Method for Investigation of Electronic Structures of Atomic, Molecular and Solid State Systems 1 (3)

Procedures for quantitative study of electronic structures and properties of atoms, small molecules, large molecules and solid state materials. Topics include Hartree-Fock and Many-Body theories for atomic systems and small molecules, empirical and approximate procedures for large molecules especially for systems of biological interest, band-structure and cluster approaches to solid state systems including metallic, semiconductor, ionic crystal and molecular solids, impurity centers in these systems and surfaces and interfaces. Prerequisites: Phy 587.

Phy 652 Methods for Investigation of Electronic Structures of Atomic, Molecular and Solid State Systems 2 (3)

Procedures for quantitative study of electronic structures and properties of atoms, small molecules, large molecules and solid state materials. Topics include Hartree-Fock and Many-Body theories for atomic systems and small molecules, empirical and approximate procedures for large molecules especially for systems of biological interest, band-structure and cluster approaches to solid state systems including metallic, semiconductor, ionic crystal and molecular solids, impurity centers in these systems and surfaces and interfaces. Prerequisites: Phy 587.

## Research, Seminar and Special Topics Courses

Phy 680 Seminar in Physics (1)

Faculty led seminars in ongoing physics research. Emphasis is placed developing skills to explain and discuss current research.

Phy 695 Introduction to Research Problems in Physics (1-12)

Individually directed investigation into areas of current research interest in the department. Prerequisite: Consent of faculty member who will act as supervisor for the investigation.

Phy 699 Master's Thesis in Physics (1-12)

Up to 6 credits can be used for graduation.

Phy 782 Advanced Topics in Physics (3)

Selected topics in physics.

Phy 784 Special Topics in Physics (1)

Selected coverage of specialized topics.

Phy 810 Research in Physics (1-15)

Research in physics for students working beyond the master's degree level. Consent of the department chair or the doctoral students advisory committee required. A student registering for this course indicates the portion of the total semester-load devoted to it by listing an appropriate number of "load equivalent units" instead of credits. Residence credit earned in this course becomes applicable upon satisfactory completion of all other requirements established for the Ph.D. degree in physics. Prerequisite: Consent of faculty member who will act as supervisor for the investigation.

Phy 899 Doctoral Dissertation (1)

Course grading is Load Only and does not earn credit. Appropriate for doctoral students engaged in research and writing of the dissertation. Prerequisite: Admission to doctoral candidacy.