Graduate Courses

PHYS 2373: Mathematical Methods in Physics

PHYS 2373
Credits: 3

This course for undergraduate honors majors and some first year graduate students will prepare you for most of the mathematical techniques required in most first year physics graduate courses, at Pitt or elsewhere. The course will include: Theory and applications of analytic functions, with emphasis on contour integration and infinite series. Review of finite-dimensional linear vector spaces, leading to an introduction to Hilbert spaces. Applications to ordinary and partial differential equations, including introduction to the most commonly used special functions.

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Ayres Freitas 2015-2016FallSyllabus: DL

PHYS 2513: Dynamical Systems

PHYS 2513
Credits: 3

The Lagrangian and Hamiltonian formulations of classical mechanics will be emphasized. Topics will be chosen from among the following list: conservation theorems, small oscillations, rigid-body motion, canonical transformations, an introduction to the theory of chaotic motions, Navier Stokes equation, relativistic Lagrangian mechanics, classical field theory, and Noether's theorem.

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Brian Batell 2015-2016FallSyllabus: DL

PHYS 2541: Thermodynamics and Statistical Mechanics I

PHYS 2541
Credits: 3

This graduate core course provides the background in thermodynamics and statistical mechanics required for admission to candidacy for the Ph.D. in physics or astronomy. Topics include thermodynamics, ensemble theory (microcanonical, canonical and grand canonical ensembles), classical and quantum (Bose-Einstein and Fermi-Dirac) statistics, classical and quantum ideal gases, and other applications.

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Roger Mong 2016-2017SpringSyllabus: DL

PHYS 2555: Advanced Classical Electricity and Magnetism

PHYS 2555
Credits: 4

This is a four-credit course in classical electricity and magnetism, based on Maxwell's Equations. Both the underlying physical concepts and the mathematical formulation of the theory will be explored. The theory will be applied to a variety of physical systems. The topics will include: electrostatics, magnetostatics, electromagnetic induction, properties of electromagnetic waves, interaction of electromagnetic waves with materials, waveguides and cavities, radiation and antennas, multipole fields, scattering of electromagnetic waves, and the special theory of relativity. Additional topics will be covered if time permits. Students are expected to have the mathematical background provided by Physics 2373: Mathematical Methods in Physics.

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Robert P. Devaty 2015-2016SpringSyllabus: DL

PHYS 2565: Nonrelativistic Quantum Mechanics I

PHYS 2565
Credits: 3

This course is the first half of a systematic survey of nonrelativistic quantum mechanics. Topics to be covered include: prehistory of quantum theory, matrix mechanics, wave mechanics, general formalism of quantum theory (equivalence of matrix and wave mechanics). Simple quantum systems: two state systems, 1D, 3D potential problems, potential scattering, stationary state and time-dependent perturbation theory.

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David Jasnow 2014-2015FallSyllabus: DL

PHYS 2566: Nonrelativistic Quantum Mechanics II

PHYS 2566
Credits: 3

The second term of this course applies the previously developed ideas and techniques of quantum mechanics to more complicated systems. Time-independent and time-dependent perturbation theories are developed and applied. Formal scattering theory and approximation methods will be presented. Applications are expected to include the interaction of electromagnetic radiation with matter; resonance scattering and bound states; identical particles and an introduction to second quantization; and, if time and other considerations permit, a brief introduction to relativistic quantum mechanics. Prerequisite(s): Non-relativistic quantum mechanics 1 (PHYS 2565 or equivalent).

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Tao Han 2016-2017SpringSyllabus: DL

PHYS 2997: Teaching of Astronomy and Physics

PHYS 2997
Credits: 1

This is a mandatory course for all physics graduate students. The overall objective of this course is to prepare incoming graduate students for their duties as Teaching Assistants (TAs) and lay the foundation for any subsequent teaching role they may assume. This course will introduce students to the principles of learning and physics education research-based curricular and pegagogical approaches using concrete examples. There will be opportunity to reflect upon various aspects of the course and teaching and learning in general.

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Russell J. Clark 2016-2017FallSyllabus: DL

PHYS 2998: Teaching of Physics/Astronomy, Practicum

PHYS 2998

This course is required of all graduate students fulfilling the department teaching requirement. This requirement involves full responsibility for teaching undergraduate recitations or labs, and in some cases for advanced graduate students, a course in physics and astronomy during one term.

PHYS 2999: Physics and Astronomy Colloquium

PHYS 2999
Credits: 1

The Physics and Astronomy Colloquium, held jointly with the Carnegie Mellon University Physics Department, provides an opportunity for all faculty and students to hear invited lectures and discuss problems of current interest to members of the Physics and Astronomy Department. The talks are intended for faculty and students from all areas, and thereby constitute a unifying element for the department. Also, talks of even broader interest are occasionally presented. The weekly one-hour Monday colloquium lectures are generally evenly split between the University of Pittsburgh and Carnegie Mellon University throughout the course of the academic year. Registered students must make a short, 1-paragraph summary of at least 10 colloquium lectures to receive credit.

ProfessorCourse YearCourse SemesterDownload
James A Mueller 2012-2013SpringSyllabus: DL

PHYS 3101: Special Topics - Topological Phases of Matter

PHYS 3101

This course will give a broad overview of topological phases. Many of these phases are realized in solid state materials and exhibit remarkable bulk and surface properties. Topics covered will include recently discovered topological insulators, quantum Hall phases, concepts such as anyons and charge fractionalization, topological superconductors, Majorana excitations and their use as qubits, and quantum error corrections with surface code. This course will focus on both the theorectical aspects of topological phases, as well as experimental results used to identify such phases. Course grading will depend on homework problem sets, reading published papers, and a presentation on a recent study relevant to the course material. 

[Pre-requisite: Advanced course on quantum mechanics. Solid state physics is also preferrable, but not required]

PHYS 3102: Special Topics - SrTiO3: The Hydrogen Atom of Solid State Physics

PHYS 3102

SrTiO3: The Hydrogen Atom of Solid State Physics This special topics course will cover a number of modern areas in condensed matter physics, materials science, nanoscience and engineering, viewed through the prism of a single material system, SrTiO3. In this sense it will be both exceptionally broad and deep. Each topic will describe a fundamental set of concepts, using examples that will include SrTiO3 but also other material systems or toy models as well. Students may work through exercises that help to create a comprehensive mosaic of information and concepts related to research in the field of complex oxides and oxide interfaces. The course website is:

ProfessorCourse YearCourse SemesterDownload
Jeremy Levy 2014-2015SpringSyllabus: DL


Credits: 3

ASTRON 2000: Research and Thesis - MS Degree


This course is available to students who are pursuing a Masters degree with a thesis option in Phyiscs and Astronomy and have completed their comprehensive exam.

ASTRON 3000: Research and Dissertation PhD


This course is available to students who are pursuing a Ph.D. degree in Physics and Astronomy and have completed their comprehensive exam.

ASTRON 3550: Stellar Structure

Credits: 3

This is a graduate course in Stellar Astrophysics covering three primary topics: Stellar Interiors, Stellar Atmospheres, and Stellar Evolution. Stellar Interiors will cover polytropes, nuclear energy generation and convective energy transport. Stellar Atmospheres will cover the basics of radiative transfer and model atmospheres. Stellar Evolution will be taught using a hands-on approach based on the MESA code, an open source code for stellar evolution. Grades will be based on homework sets and a final research project that the student will complete using MESA.

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Carlos Badenes 2014-2015SpringSyllabus: DL

ASTRON 3580: Galactic and Extra-galactic Astronomy

Credits: 3

Galaxies are the fundamental building blocks of the present Universe. This class will give an overview of galaxies, their properties, and their formation and evolution with an emphasis on current research areas. Topics will include observational properties (morphology, masses, colors, concentrations), scaling relations, evolution with redshift, stellar populations, gas and dust, dynamics and dark matter, evolution and mergers, and active galaxies.

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Carlos Badenes 2015-2016SpringSyllabus: DL

ASTRON 3705: Astronomical Techniques

Credits: 3

This class will expose students to the basics of astronomical data analysis, with an emphasis on statistical techniques and the development of practical programming skills. Topics may include the nature of random and systematic errors, fitting and likelihood techniques, hypothesis testing, astronomical instrumentation and data reduction, and the use of large survey data sets.

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Jeffrey A Newman 2016-2017SpringSyllabus: DL

ASTRON 3785: Cosmology

Credits: 3

This class will give an overview of the standard cosmological model and the wide range of observational tests. Topics include the expansion history of the Universe, thermodynamic history, nucleosynthesis, recombination, inflation, perturbations and the microwave background, structure formation, evidence for dark matter and dark energy, and future probes of dark energy.

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Andrew R Zentner 2015-2016FallSyllabus: DL

ASTRON 3902: Directed Study


This is an elective course available to graduate students where a project is carried out under the direction of a faculty member in the phyiscs and astronomy department.

ASTRON 3907: Directed Research


Specific research topic carried out under the direction of a faculty member as part of progress toward their PhD.

FTDB 3999 : Full Time Dissertation Study

FTDB 3999

Doctoral candidates who have completed all credit requirements for the degree, including any minimum dissertation credit requirements, and are working full-time on their dissertation may register for this course. While the course carries no credits and no grade, students who enroll in "full-time dissertation study" are considered by the University to have full-time registration status.

PHYS 3000: Research and Dissertation/ PhD

PHYS 3000

This course is available to students who are pursuing a Ph.D. degree in Physics and Astronomy and have completed their comprehensive exam.

PHYS 3274: Computational Methods

PHYS 3274
Credits: 3

In this course learn how to connect a variety of numerical and computational techniques to problems arising in classical mechanics, classical chaos, quantum mechanics, and statistical mechanics. Numerical techniques include numerical integration, Monte Carlo methods, simulation, data modeling, numerical linear algebra, and solution of different equations. Computational topics include an introduction to the linux operating system, use of class libraries, object-oriented programming, templates and elementary graphics. Students should be familiar with the C programming at an elementary level.

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Joseph Boudreau 2015-2016FallSyllabus: DL

PHYS 3373: Advanced Math Methods

PHYS 3373
Credits: 3

The topic will be group theory, with applications to quantum mechanics and some particle physics. No previous knowledge of group theory is required, but students should be familiar with ideas from vector spaces in linear algebra. 

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Ralph Z Roskies 2015-2016FallSyllabus: DL

PHYS 3542: Advanced Statistical Physics

PHYS 3542
Credits: 3

This course will cover the statistics of interacting particles, phases and phase transitions.

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Roger Mong 2015-2016SpringSyllabus: DL

PHYS 3707: Intro to Many-Body Physics

PHYS 3707

This is a one-term nuts-and-bolts introduction to the quantum physics of interacting, many-particle systems. The course includes second quantization, many body physics, and a brief introduction to relativistic quantum mechanics and the Dirac equation. Throughout there will be discussion of applications of the techniques and concepts in various subfields of physics. The approach will generally be intuitive and hands-on. The course typically will begin with second quantization for fermionic and bosonic systems, with examples typically involving electrons, phonons and photons, arising from the quantization of the electromagnetic field. Applications will typically include the interacting electron gas and plasmons; the interaction of the radiation field and matter; electron-phonon interactions; and dressed electrons and the polaron problem. There will typically be some discussion of condensation phenomena and superfluidity (typically Bogoliubov theory, broken symmetry and Goldstone bosons) and superconductivity (pairing, BCS and Landau-Ginzburg theories). There will generally be some exposure to Greens functions and Feynman diagrams.

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Eric S. Swanson 2014-2015FallSyllabus: DL

PHYS 3715: Solid State Physics

PHYS 3715

This is a one-term course on solid-state physics, which emphasizes the special ways one must think about crystalline materials. The course will allow students emphasizing this area to enhance their own research efforts, and it will permit other students to have an appreciation for an extremely large part of current research activity in physics. Roughly speaking, there will be three parts to the course. Some variation on emphasis can be expected depending on the instructor and on the interests of the class. (i) Phonons: Crystal lattices; diffraction and scattering; reciprocal lattice; lattice vibrations, quantization; thermal properties. (ii) Electrons: Free electron model; density of states; thermal properties; Bloch’s theorem, electron states and energy bands; semiconductor statistics; quasi-classical electron dynamics; Boltzmann equation and transport. (iii) Additional topics: Electron-electron and electron-phonon interactions; Hall effect; Landau levels; superconductivity; electromagnetic response.

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David W Snoke 2015-2016FallSyllabus: DL

PHYS 3716: Advanced Solid State Physics

PHYS 3716
Credits: 3

This is a second, graduate-level solid state physics course. The topics will be adjustable given the cross section of students taking the course and topical developments in the field. Topics suitable for this course include: a brief exposure to “practical” group theory; optics and spectroscopy relevant to the solid state including linear and non-linear response and complex dielectric constant; coherence and correlation including the density matrix Bloch equations, and optics; introduction to NMR; superconductivity beyond the Ginsburg-Landau theory; advanced topics in magnetism; advanced topics in transport theory.

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Robert P. Devaty 2016-2017SpringSyllabus: DL

PHYS 3717: Particle Physics

PHYS 3717

This is the first term of a two term sequence exposing the student to basic methods and recent developments in high energy physics. The first term of the sequence is suitable as a one-term course for students not specializing in high-energy physics. Particle physics involves completely relativistic phenomena and requires the generalization of non-relativistic quantum concepts to the relativistic regime in order to develop the phenomenological and calculational methods suitable for relativistic processes in which the number and type of particles can change. The course examines experimental and phenomenological foundations of particle physics. The known particles and fundamental interactions are investigated. Modern experimental techniques of particle physics are discussed (including basic properties of particle interactions with matter). General features of electromagnetic, weak, and strong interactions, and their associated symmetries, are explored.

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Daniel Boyanovsky 2015-2016FallSyllabus: DL

PHYS 3718: Advanced Particle Physics

PHYS 3718

This is the conclusion of the 2-term sequence Phys 3717/3718, which should be taken in order. This course covers the Standard Model in detail and includes: the phenomenology of weak interactions; group theory and the quark model; the parton model for deep inelastic scattering and other high energy processes; an introduction to gauge theories of electroweak and strong interactions. Various topics of current interest in particle physics beyond the Standard Model will also be discussed.

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Daniel Boyanovsky 2015-2016SpringSyllabus: DL

PHYS 3725: Special and General Relativity

PHYS 3725
Credits: 3

This course covers the basic conceptual foundations of general relativity starting from the special theory, with applications, calculational techniques and discussions of current observational probes. Topics include the equivalence principle, geodesic deviation, tidal forces, the description of gravitation as geometry, Schwarschild space time. Also covered are: solar system tests and post-Newtonian parameters; gravitational lensing; micro and macrolensing as probes of dark matter; observations; vacuum Einstein’s Equations and Schwarschild solution.

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Eric S. Swanson 2015-2016FallSyllabus: DL

PHYS 3726: Advanced General Relativity

PHYS 3726

The advanced course begins with a derivation of Einstein's equations and energy momentum tensors.The following are studied: stellar evolution, gravitational collapse, compact stars and black holes; gravitational radiation sources and detection; cosmology; the Friedmann-Robertson-Walker metric; the Standard Big Bang; successes and problems; inflation; dark energy and observations; cosmic microwave background and observations.

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Eric S. Swanson 2015-2016SpringSyllabus: DL

PHYS 3730: Introduction to Biophysics

PHYS 3730

In this course we will review useful physical ideas and techniques that have contributed significantly to recent developments in biophysical research. This includes: the use of statistical approaches for understanding gene regulation and signal transduction in biological and chemical networks; nonlinear dynamics for understanding biological pattern formation, ecology, and population dynamics; hydrodynamics for understanding cell motility and taxis; and information theory for signal processing in neuronal networks. The course will also introduce basic concepts in biology that range from molecular to cellular biology. Specific topics to be covered include: introduction to biology; microscopy techniques; basics of cell biology; genetics (the genetic code, gene replication, gene expression, genetic networks); molecular biology techniques; energy in biological systems and the statistical view of biological dynamics; entropy and free energy in biology; two-state models in biology and neurobiology.

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Hanna Salman 2013-2014SpringSyllabus: DL

PHYS 3765: Field Theory I

PHYS 3765

This is the first semester of a graduate course in Quantum Field Theory. The course develops the perturbative approach to relativistic field theory. The topics covered will be: Lorentz and Poincare groups; method of second quantization; free scalar field theory; free spin-1/2 field theory; field quantization; symmetries and conservation laws; interacting scalar field theories, Yukawa theory; perturbation theory and Feynman rules; elementary renormalization theory; quantum electrodynamics.

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Eric S. Swanson 2012-2013FallSyllabus: DL

PHYS 3766: Field Theory II

PHYS 3766

This is the second semester of a graduate course in Quantum Field Theory. It builds on the material covered in Phys 3765 (Field Theory 1), which is a prerequisite. The course further develops the techniques of relativistic quantum field theory, covering the path integral approach to field theory, additional topics in quantum electrodynamics, symmetry breaking, non-abelian gauge theories, and the Standard Model. In more detail, the topics covered will be: Green’s functions, asymptotic scattering theory, and the LSZ formalism; functional integration and the path integral; quantization of abelian (QED) and non-abelian (Yang-Mills) fields; the renomalization group; spontaneous symmetry breaking of global and local symmetries; the Standard Model.

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Eric S. Swanson 2012-2013SpringSyllabus: DL

PHYS 3770: Topics in Quantum Physics

PHYS 3770
Credits: 3

This course will serve as an introduction to the field of Quantum Information and Quantum Computing, beginning with basic concepts such as entanglement and state teleportation and building towards applications such as Shor’s algorithm, quantum cryptography, and quantum search.  Nielsen and Chuang’s Quantum Computation and Quantum Information will serve as the textbook for the course, and key topics including quantum bits, circuits, and algorithms  will be covered, as well as decoherence, quantum errors and correction schemes, and quantum measurement and noise.  We will focus especially on different physical implementations of quantum computing systems (ex. trapped ions and superconducting circuits), their challenges and advantages, and survey recent developments in the field.

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Michael Hatridge 2015-2016SpringSyllabus: DL

PHYS 3790: Particle Astrophysics

PHYS 3790

Particle physics plays an increasingly important role in astrophysics. This class will cover areas of common interest between these fields. Topics may include dark matter (particle abundances, particle candidates, direct and indirect detection), neutrino masses and oscillations, high energy cosmic rays and detection schemes, high density matter in neutron stars, models for inflation, baryogenesis, cosmological phase transitions, and models for dark energy.

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Daniel Boyanovsky 2012-2013SpringSyllabus: DL

PHYS 3902: Directed Study

PHYS 3902

This is an elective course available to graduate students where a project is carried out under the direction of a faculty member in the phyiscs and astronomy department.

PHYS 3903: Directed Study

PHYS 3903

Specific research topic carried out under the direction of a faculty member before officially joining the group.

PHYS 3907: Directed Research

PHYS 3907

Specific research topic carried out under the direction of a faculty member as part of progress toward their PhD.

PHYS 1341: Thermodynamics and Statistical Mechanics

PHYS 1341
Credits: 3

The properties of matter as described by thermodynamics, in which atomic structure is irrelevant, and by statistical mechanics, which is based on the atomic point of view.

PREQ: A "C" or better in all courses: PHYS 0477, MATH 0240 and MATH 0290 (or MATH 1270)

ProfessorCourse YearCourse SemesterDownload
Vladimir Savinov 2016-2017SpringSyllabus: DL

PHYS 1370: Introduction to Quantum Mechanics 1

PHYS 1370
Credits: 3

This course is an introduction to quantum mechanics for undergraduate honors majors and first-year graduate students who have not taken such a course.

PREQ: A "C" or better in both PHYS 0477 and MATH 0280 (or MATH 1180 or MATH 1185)

COREQ: PHYS 1331 and 1351

ProfessorCourse YearCourse SemesterDownload
David Pekker 2016-2017FallSyllabus: DL

PHYS 1371: Introduction to Quantum Mechanics II

PHYS 1371
Credits: 3

Physics 1371 will be a continuation of the material covered in Physics 1370 with special emphasis on applications of quantum mechanics. Topics to be covered are: multi-particle systems, time-independent perturbation theory and its application to the fine-structure and hyperfine structure of atoms, time-dependent perturbation theory and its application to the absorption and emission of light, and other approximation methods.

PREQ: A "C" or better in PHYS 1370

ProfessorCourse YearCourse SemesterDownload
David Pekker 2015-2016SpringSyllabus: DL

PHYS 1372: Electromagnetic Theory

PHYS 1372
Credits: 3

Advanced topics, including boundary-value problems and radiation theory.

PREQ: PHYS 0477, a "C" or better in both PHYS 1351 and MATH 0280


ProfessorCourse YearCourse SemesterDownload
Xiao-lun Wu 2015-2016SpringSyllabus: DL