### Attention Spring 2021 Students

All physics courses in the spring 2021 semester will adhere to the hybrid model guidelines established by Carnegie Mellon. To see which courses will be taught in which manner, check out our COURSE TRACKER PAGE.

# Graduate Courses

For the most up-to-date information on current and upcoming courses, including course times and locations, visit the university-wide schedule of classes. All graduate courses at the University of Pittsburgh qualify for credit in our program.

Looking for undergraduate courses? View them here.

## 33-650: General Relativity |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Tiziana Di Matteo | 2020-2021 | Fall - 9 units | Download |

General Relativity is the classical theory of gravity. It is widely recognized as a beautiful theory - equating gravity and the geometry of spacetime leads to a profound conceptual change in the way we regard the universe. The predictions of the theory are relevant to systems as varied as high precision measurements of the earth's gravitational field or the strongly curved space-times around black holes. In this course, we will gradually develop an understanding of the geometries which are the solutions of the Einstein equation, with an emphasis on their relevance to physical situations. We will motivate the theory step by step and eventually introduce the Einstein equation itself. | |||

Typical Textbook(s): |
Gravity, An Introduction to Einstein's General Relativity by James Hartle |
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Prerequisites: |
33-211 and 33-339 |

## 33-652: Introduction to String Theory |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Ira Rothstein | 2017-2018 | Fall - 9 units | N/A |

The two triumphs of 20th century physics, quantum mechanics and general relativity, are monuments to the progress of science, yet they have to be synthesized into a theory of quantum gravity. A leading candidate for such a theory is "string theory", which not only accounts for gravity in a quantum mechanical setting but also unifies gravity with all the other fundamental forces. As such, it is sometimes called a "theory of everything". This course is an introduction to the theory of String Theory. A familiarity with tensors and Einstein summation as well as a basic level of understanding of quantum mechanics is expected. | |||

Typical Textbook(s): |
A First Course in String Theory by B. Zwiebach |
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Prerequisites: |
33-650 |

## 33-658: Quantum Computation and Quantum Information Theory |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Ira Rothstein | 2020-2021 | Fall - 10 units | Download |

This course provides an overview of recent developments in quantum computation and quantum information theory. The topics include: an introduction to quantum mechanics, quantum channels, both ideal and noisy, quantum cryptography, quantum data compression, quantum error corrections and quantum gates. The class includes code writing on publicly available quantum computers. | |||

Typical Textbook(s): |
Quantum Processes Systems and Information by Schumacher and Westmoreland |
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Prerequisites: |
33-234 |

## 33-659: Quantum Hall Effect and Topological Insulators |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Di Xiao | 2020-2021 | Fall - 12 units | Download |

This course will introduce students to the topic of topological insulators and related phenomena using the Berry phase a unifying concept. In the first half of the semester, we will cover basic concepts such as Berry phase, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. Linear response theory will be discussed in relation to the Hall conductance. In the second half, we will move on to explain topological phases of matter such as Chern insulators and two- and three-dimensional topological insulators. Various techniques to calculate the topological indices will be introduced and connection to real materials will be discussed. Numerical studies of various tight-binding models provide intuitive understandings and will be an essential part of this course. | |||

Prerequisites: |
33-448 |

## 33-755: Quantum Mechanics I |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Michael Widom | 2020-2021 | Fall - 12 units | View |

This course is the first semester of a two-semester Quantum Mechanics sequence for graduate students. It introduces fundamental concepts of quantum mechanics as well as time evolution and quantum dynamics. Topics covered include wave mechanics and matrix mechanics, addition of angular momentum plus applications, bound states, harmonic oscillator, hydrogen atom, etc. | |||

Typical Textbook(s): |
Quantum Mechanics, Vol. I by Cohen-Tannoudji |

## 33-756: Quantum Mechanics II |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Colin Morningstar | 2020-2021 | Spring - 12 units | Download |

This course is the second semester of a two-semester Quantum Mechanics sequence for graduate students. It focuses on qualitative methods and approximations in quantum mechanics, including time-independent and time-dependent perturbation theory, scattering and semiclassical methods as well as harmonic oscillator and quantized fields. Applications are made to atomic, molecular and solid matter. Systems of identical particles are treated including many electron atoms or entangled states. | |||

Typical Textbook(s): |
Quantum Mechanics, Vol. II by Cohen-Tannoudji |
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Prerequisites: |
33-755 and 33-759 |

## 33-758: Quantum Computation and Quantum Information Theory |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Robert Griffiths | 2013-2014 | Spring - 12 units | Download |

This course, taught in collaboration with the Computer Science Department, provides an overview of recent developments in quantum computation and quantum information theory. The topics include: an introduction to quantum mechanics, quantum channels, both ideal and noisy, quantum cryptography, an introduction to computational complexity, Shor's factorization algorithm, Grover's search algorithm, and proposals for the physical realization of quantum devices, such as correlated photons, ions in traps, and nuclear magnetic resonance. 3 hrs. lecture plus weekly seminar. A 10-unit version of the course, 33-658, does not include the seminar. |
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Typical Textbook(s): |
Quantum Computation and Quantum Information by Nielsen and Chuang |

## 33-759: Introduction to Mathematical Physics I |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Tina Kahniashvili | 2020-2021 | Fall - 12 units | Download |

This course is an introduction to methods of mathematical analysis used in solving physical problems. Emphasis is placed both upon the generality of the methods, through a variety of sample problems, and upon their underlying principles. Topics normally covered include matrix algebra (normal modes, diagonalization, symmetry properties), complex variables and analytic functions, differential equations (Laplace's equation and separation of variables, special functions and their analytic properties), orthogonal systems of functions. 3 hrs. lecture and recitation. | |||

Typical Textbook(s): |
Mathematical Methods for Physicists by G. Arfken |

## 33-761: Classical Electrodynamics I |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Riccardo Penco | 2020-2021 | Fall - 12 units | Download |

This course deals with the static and dynamic properties of the electromagnetic field as described by Maxwell's equations. Among the topics emphasized are solutions of Laplace's, Poisson's and wave equations, effects of boundaries, Green's functions, multipole expansions, emission and propagation of electromagnetic radiation and the response of dielectrics, metals, magnetizable bodies to fields. 3 hrs. lecture. | |||

Typical Textbook(s): |
Classical Electrodynamics by J.D. Jackson |
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Prerequisites: |
33-339 |

## 33-762: Classical Electrodynamics II |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Riccardo Penco | 2018-2019 | Spring - 12 units | Download |

The applications of electromagnetic theory to various physical systems is the main emphasis of this course. The topics discussed include the theory of wave guides, scattering of electromagnetic waves, index of refraction, special relativity and foundation of optics. 3 hrs. lecture. | |||

Typical Textbook(s): |
Classical Electrodynamics by J.D. Jackson |

## 33-765: Statistical Mechanics |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Ira Rothstein | 2020-2021 | Spring - 12 units | Download |

This course develops the methods of statistical mechanics and uses them to calculate observable properties of systems in thermodynamic equilibrium. Topics treated include the principles of classical thermodynamics, canonical and grand canonical ensembles for classical and quantum mechanical systems, partition functions and statistical thermodynamics, fluctuations, ideal gases of quanta, atoms and polyatomic molecules, degeneracy of Fermi and Bose gases, chemical equilibrium, ideal para-magnetics and introduction to simple interacting systems. | |||

Typical Textbook(s): |
Statistical Mechanics by R.K. PathriaStatistical and Thermal Physics by Reif |

## 33-767: Biophysics: From Basic Concepts to Current Research |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Shiladitya Banerjee | 2020-2021 | Spring - 12 units | Download |

This course mixes lectures and student presentations on advanced topics in Biological Physics. In the course, students will gain a deep appreciation of the fact that very basic physical and chemical principles underlie many central life processes. Life is not only compatible with the laws of physics and chemistry, rather, it exploits them in ingenious ways. After taking the course, students should be able to name examples of such situations for which they can provide a coherent line of reasoning that outlines these connections. They will be able to explain key experiments by which these connections either have been found or are nowadays routinely established, and outline simple back-of-the-envelope estimates by which one can convince oneself of either the validity or inapplicability of certain popular models and ideas. They should also have become sufficiently familiar with the key terminology frequently encountered in biology, such that they can start to further educate themselves by consulting biological and biophysical literature. | |||

Typical Textbook(s): |
Physics Biology of the Cell by Rob Phillips et al. |

## 33-769: Quantum Mechanics III: Many Body and Relativistic Systems |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Ira Rothstein | 2016-2017 | Fall - 12 units | N/A |

The first main theme of this course is quantum mechanics applied to selected many-body problems in atomic, nuclear and condensed matter physics. The second main theme is relativistic quantum mechanics. Creation and annihilation operators are introduced and used to discuss Hartree-Fock theory as well as electromagnetic radiation. The Dirac equation is introduced and applied to the hydrogen atom. | |||

Prerequisites: |
33-756 and 33-761 |

## 33-770: Field Theory I |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Colin Morningstar | 2019-2020 | Fall - 12 units | Download |

This is a first course in relativistic quantum field theory. Topics include canonical and path integrals, quantization of fields, the Klein-Gordon and Dirac equation, as well as photon fields, Feynman diagram techniques, calculation of scattering cross section, methods of renormalization, and quantum electrodynamics. | |||

Prerequisites: |
33-769 |

## 33-771: Field Theory II |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Colin Morningstar | 2019-2020 | Spring - 12 units | Download |

Modern techniques and recent developments in relativistic field theory are discussed. The topics include theory of renormalization, renormalization group equation, quantization of non-Abelian gauge theories, quantum chromodynamics (QCD), gauge theories of weak and electromagnetic interactions, and grand unification theory (GUT). | |||

Typical Textbook(s): |
An Introduction to Quantum Field Theory by M. Peskin and D. Schroeder |

## 33-777: Introductory Astrophysics |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Tina Kahniashvili | 2020-2021 | Spring - 12 units | Download |

Introductory Astrophysics will explore the applications of physics to the following areas: (i) celestial mechanics and dynamics, (ii) the physics of solar system objects, (iii) the structure, formation and evolution of stars and galaxies, (iv) the large scale structure of the universe of galaxies, (v) cosmology: the origin, evolution and fate of the universe. |

## 33-778: Introduction to Cosmology |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Rachel Mandelbaum, Scott Dodelson | 2020-2021 | Fall - 12 units | Download |

An introduction to modern cosmology that includes detailed description of the smooth expanding universe (e.g., nucleosynthesis, the cosmic microwave background, and dark matter) and the perturbations that translate into the large scale structure of the universe. | |||

Prerequisites: |
33-232 and 33-234 |

## 33-779: Introduction to Nuclear and Particle Physics |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Brian Quinn | 2020-2021 | Fall - 12 units | Download |

An introduction to the physics of atomic nuclei and elementary particles. This course is suitable as a one-semester course for students not specializing in this area and also provides an introduction to further work in 33-780, 33-781. Topics included are symmetry principles of strong and weak interactions, quark model, classification of particles and nuclear forces. | |||

Typical Textbook(s): |
Introduction to High Energy Physics by Perkins |
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Prerequisites: |
33-769 (or concurrently) |

## 33-780: Nuclear and Particle Physics II |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Ira Rothstein | 2016-2017 | Spring - 12 units | N/A |

This course covers the phenomenology of weak interactions, parton model for the deep inelastic scattering, and introduction to gauge theories of weak and electromagnetic interactions. Various topics of current interest in particle physics will also be included. | |||

Prerequisites: |
33-779 and 33-770 (or concurrently) |

## 33-783: Solid State Physics |
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Professor |
Academic Year |
Course Semester |
Sample Syllabus |

Sara Majetich | 2020-2021 | Fall - 12 units | Download |

This course is designed to give advanced graduate students a fundamental knowledge of the microscopic properties of solids in terms of molecular and atomic theory, crystal structures, x-ray diffraction of crystals and crystal defects, lattice vibration and thermal properties of crystals; free-electron model, energy bands, electrical conduction and magnetism. | |||

Typical Textbook(s): |
Solid State Physics by Ashcroft and Mermin |
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Prerequisites: |
33-756 |

## 33-795: Graduate Seminar in Quantum Computation and Information |
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Fall and Spring Semester - 2 units |

## 33-796: Graduate Seminar in Nuclear Physics |
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Fall and Spring Semester - 3 units |

## 33-797: Graduate Seminar in High Energy Physics |
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Fall and Spring Semester - 3 units |

## 33-798: Graduate Seminar in Condensed Matter Physics |
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Fall and Spring Semester - 3 units |

## 33-8xx: Supervised Reading in Various Areas |
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Fall and Spring Semester - Various units |

## 33-996: Practicum in Physics |
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Fall and Spring Semester - Various units |

## 33-997: Graduate Laboratory |
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Fall and Spring Semester - Various units |

## 33-998: Thesis Research |
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Fall and Spring Semester - Various units |