Graduate Level Courses
Number 
Course Name 
33650  General Relativity 
Fall Semester  9 Units 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 spacetimes 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. 

33652  Introduction to String Theory 
Spring Semester  9 Units 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. 

33755  Quantum Mechanics I 
Fall Semester  12 Units This course is the first semester of a twosemester 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", volume 1, by CohenTannoudji, "Modern Quantum Mechanics" by J.J. Sakurai, "Quantum Physics" by Michel Le Bellac. 

33756  Quantum Mechanics II 
Spring Semester  12 Units This course is the second semester of a twosemester Quantum Mechanics sequence for graduate students. It focuses on qualitative methods and approximations in quantum mechanics, including timeindependent and timedependent 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", volume 2, by CohenTannoudji, "Modern Quantum Mechanics" by J.J. Sakurai, "Quantum Physics" by Michel Le Bellac. 

33758  Quantum Computation and Information (web page) 
Spring Semester  12 Unit 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. The course includes a weekly seminar. Typical Textbook(s): "Quantum Computation and Quantum Information" by Nielsen and Chuang. 

33759  Introduction to Mathematical Physics 
Fall Semester  12 Units This course covers mathematical physics at a firstyear graduate level. Familiarity with topics in advanced undergraduate physics (E&M, Quantum Mechanics, Statistical Mechanics, Classical Mechanics) will be assumed. The theme of the course is to examine the mathematical methods that are used in these physics subject areas including 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. Studying them as purely mathematical subjects should make you familiar with their use when you encounter them again in your physics courses. Facility with practical applications of mathematics will be emphasized. Typical Textbook(s): "Mathematical Physics" by S. Hassani, "Mathematical Methods of Physics" by J. Mathews and R.L. Walker, "Mathematical Methods for Physicists" by G.B. Arfken and H.J. Weber. 

33761  Classical Electrodynamics I 
Fall Semester  12 Units This course is the first semester of a twosemester Electricity and Magnetism sequence for physics graduate students. The class discusses static and dynamic properties of classical electrodynamics at the graduate level. Among the topics emphasized are solutions of Laplace's, Poisson's and wave equations, effects of boundaries, multipole expansions, propagation of electromagnetic radiation, response of dielectrics to electromagnetic fields and special relativity. Typical Textbook(s): Textbook: "Classical Electrodynamics" by J.D. Jackson. 

33762  Classical Electrodynamics II 
Spring Semester  12 Units The second part of the sequence in electrodynamics introduces selected topics of classical electricity and magnetism at the graduate level including solutions to boundary conditions using Green's functions, wave equations, retarded solutions, theory of wave guides, relativistic particles and electromagnetic fields or radiation by moving charges. Typical Textbook(s): Textbook: "Classical Electrodynamics" by J.D. Jackson. 

33765  Statistical Mechanics 
Spring Semester  12 Units 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 paramagnetics and introduction to simple interacting systems. Typical Textbook(s): "Statistical Mechanics" by R.K. Pathria, "Statistical and Thermal Physics" by Reif. 

33767  Biophysics: From Basic Concepts to Current Research (web page) 
Fall Semester  12 Units In this course students will gain a deeper appreciation of the fact that very basic physical principles underly many central life processes. Life is not only compatible with the laws of physics, it exploits them in ingenious ways. Students will be able to name examples of such situations for which they can provide a coherent line of reasoning outlining the physicsbiology connection. Ideally, they should be able to explain key experiments by which these connections either have been found or are nowadays routinely established, and outline simple backoftheenvelope estimates by which one can convince oneself of either the validity or inapplicability of certain popular models and ideas. Topics include membranes, protein or DNA. Typical Textbook(s): Chapters from various textbooks will be used. 

33769  Quantum Mechanics III: Many Body and Relativistic Systems 
Fall Semester  12 Units This course introduces the path integral formulation of quantum mechanics and deals with applications of quantum mechanics to selected manybody problems in atomic, nuclear, and condensed matter physics. Electromagnetic radiation (photons) is studied, and the Dirac equation is introduced and applied to the hydrogen atom. Superconductivity and superfluids are studied. Typical Textbook(s): Chapters from various textbooks will be used. 

33770  Quantum Field Theory I 
Fall Semester  12 Units This is a first course in relativistic quantum field theory. Topics include canonical and path integrals, quantization of fields, the KleinGordon and Dirac equation, as well as photon fields, Feynman diagram techniques, calculation of scattering cross section, methods of renormalization, and quantum electrodynamics. Typical Textbook(s): "An Introduction to Quantum Field Theory" by M. Peskin and D. Schroeder. 

33771  Quantum Field Theory II 
Spring Semester  12 Units Modern techniques and recent developments in relativistic field theory are discussed. The topics include theory of renormalization, renormalization group equation, quantization of nonAbelian 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, Chapters from various other textbooks or articles will be used. 

33775  Introduction to Research I 
Fall Semester  2 Units This is the first part of introducing students to the research activities in the department. In the first semester, students will gain a complete overview of the research in the department through colloquium style lectures given by various faculty on their research work. 

33776  Introduction to Research II 
Spring Semester  6 Units In the second part of this course students participate in active research by working with a research group of their choice. This course will help students to choose a research area for thesis research. 

33777  Introductory Astrophysics 
Spring Semester, 12 units Astrophysics is an application of physics to astronomy. This course covers all main branches of modern astrophysics and provides current understanding in astronomy based on physical explanations of observational data. Some of the basic physical tools used in astronomy are reviewed before an introduction to the physics of stars, galaxies, and the universe. Topics covered in this course include the physics of solar system objects, the structure, formation and evolution of stars and galaxies, the large scale structure of the universe and cosmology discussing the origin, evolution and fate of the universe. Typical Textbook(s): "An Introduction to Modern Astrophysics" by B.W. Carroll and D.A. Ostlie, "Modern Cosmology" by Scott Dodelson. 

33779  Introduction to Nuclear and Particle Physics 
Fall Semester  12 Units An introduction to the physics of atomic nuclei and elementary particles. This introductory treatment of nuclear and particle physics will touch on the basic physics concepts used in studying subatomic systems. Nuclear physics is largely nonrelativistic, and the approach owes a strong debt to atomic physics, nonrelativistic quantum mechanics and classical electromagnetic field theory. Particle physics is completely relativistic and breaks new conceptual ground in generalizing nonrelativistic quantum concepts. We will introduce only the most general aspects of nuclei in the first week before plunging into the phenomenology and calculational methods of high energy systems in which the number of particles can change in an interaction. That immediately takes us outside the realm of the Schroedinger equation and into relativistic quantum fields. This course is suitable as a onesemester course for students not specializing in this area and also provides an introduction to further work in particle physics. Typical Textbook(s): "Introduction to High Energy Physics" by Perkins, "Quarks and Leptons" by Halzen and Martin. 

33780  Nuclear and Particle Physics II 
Spring Semester  12 Units This course covers the phenomenology of weak interactions, group theory and quark model, parton model for the deep inelastic scattering, and an introduction to gauge theories of weak and strong (QCD) interactions. Various topics of current interest in particle physics will also be discussed. Typical Textbook(s): "Introduction to High Energy Physics" by Perkins, "Gauge Theory of Elementary Particle Physics" by Chang and Li. 

33783  Solid State Physics 
Fall Semester  12 Units The goal of this course is to prepare graduate students in physics and related fields to apply their knowledge of solid state physics in their research areas. This course includes two components: First, an overview of the basic concepts and phenomena of solid state physics, with readings covered in standard texts, and second, an introduction to the current solid state physics literature. The literature component serves several purposes: students learn to approach journal articles, which unlike textbooks will not contain a lot of background information; they gain experience in analyzing the scientific content of journal articles, and practice in synthesizing new information with their solid state physics background; and finally, they learn more about some of the problems and issues of greatest interest to solid state physicists today. Typical Textbook(s): "Condensed Matter Physics" by Michael P. Marder. 

33791  Group Theory with Physics Applications 
Spring Semester  12 Units The basic concepts and terminology of group theory will be discussed, along with a certain number of applications to physical problems, in particular those connected with quantum theory. Linear representations of groups will be a major focus. The time available obviously limits the number of topics that can be taken up, and the instructor welcomes suggestions. No prior knowledge of group theory will be assumed, but students should be familiar with basic concepts of quantum theory and the linear algebra of finitedimensional complex vector spaces. Typical Textbook(s): Chapters from various textbooks or articles will be used. 

33792  Special Topics in Quantum Physics: Quantum Optics 
Fall Semester  9 Units Quantum theory of light and its coupling to atoms. Classical, semiclassical, and fully quantum mechanical views of the atomfield interaction. Coherent states, number states, and other field states. Lasers. Modern experimental paradigms: cavity QED, resonance fluorescence. Open systems and quantum stochastic processes. Quantum measurements. Quantum information and communication. Tests of quantum foundations using quantum optics. Typical Textbook(s): "Introductory Quantum Optics" by Gerry and Knight 

33794  Colloquium 
Fall and Spring Semester  1 Unit The Physics Colloquium, held jointly with the University of Pittsburgh Physics Department, provides an opportunity for all physics faculty and students to hear invited lectures and discuss problems of current interest in physics. The talks are intended for physicists from all areas, and thereby constitute a unifying element for the department. Also, on occasion, talks of broad cultural interest are presented for the entire university community. Weekly onehour lectures alternate between Carnegie Mellon and the University of Pittsburgh. 

33795  Graduate Seminar in Quantum Computation and Information 
Fall and Spring Semester  2 Units  
33796  Graduate Seminar in Nuclear Physics 
Fall and Spring Semester  3 Units  
33797  Graduate Seminar in High Energy Physics 
Fall and Spring Semester  3 Units  
33798  Graduate Seminar in Condensed Matter Physics 
Fall and Spring Semester  3 Units  
338xx  Supervised Reading in Various Areas 
Fall and Spring Semester  Various Units  
33997  Graduate Laboratory 
Fall and Spring Semester  Various Units  
33998  Thesis Research 
Fall and Spring Semester  Various Units 
 All graduate courses at the University of Pittsburgh qualify for credit in our program.