Graduate Level Courses-Dept of Physics - Carnegie Mellon University

Graduate Level Courses

Number

Course Name

33-650 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 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.
33-652 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.
33-755 Quantum Mechanics I (web page)
Fall Semester - 12 Units
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", volume 1, by Cohen-Tannoudji,
"Modern Quantum Mechanics" by J.J. Sakurai,
"Quantum Physics" by Michel Le Bellac.
33-756 Quantum Mechanics II
Spring Semester - 12 Units
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", volume 2, by Cohen-Tannoudji,
"Modern Quantum Mechanics" by J.J. Sakurai,
"Quantum Physics" by Michel Le Bellac.
33-758 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.
33-759 Introduction to Mathematical Physics
Fall Semester - 12 Units
This course covers mathematical physics at a first-year 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.
33-761 Classical Electrodynamics I
Fall Semester - 12 Units
This course is the first semester of a two-semester 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.
33-762 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.
33-765 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 para-magnetics and introduction to simple interacting systems.
Typical Textbook(s):
"Statistical Mechanics" by R.K. Pathria,
"Statistical and Thermal Physics" by Reif.
33-767 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 physics-biology 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 back-of-the-envelope 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.
33-769 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 many-body 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.
33-770 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 Klein-Gordon 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.
33-771 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 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,
Chapters from various other textbooks or articles will be used.
33-775 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.
33-776 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.
33-777 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.
33-779 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 non-relativistic, and the approach owes a strong debt to atomic physics, non-relativistic quantum mechanics and classical electromagnetic field theory. Particle physics is completely relativistic and breaks new conceptual ground in generalizing non-relativistic 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 one-semester 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.
33-780 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.
33-783 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.
33-791 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 finite-dimensional complex vector spaces.
Typical Textbook(s):
Chapters from various textbooks or articles will be used.
33-792 Special Topics in Quantum Physics: Quantum Optics
Fall Semester - 9 Units
Quantum theory of light and its coupling to atoms. Classical, semi-classical, and fully quantum mechanical views of the atom-field 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
33-794 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 one-hour lectures alternate between Carnegie Mellon and the University of Pittsburgh.
33-795 Graduate Seminar in Quantum Computation and Information
Fall and Spring Semester - 2 Units
33-796 Graduate Seminar in Nuclear Physics
Fall and Spring Semester - 3 Units
33-797 Graduate Seminar in High Energy Physics
Fall and Spring Semester - 3 Units
33-798 Graduate Seminar in Condensed Matter Physics
Fall and Spring Semester - 3 Units
33-8xx Supervised Reading in Various Areas
Fall and Spring Semester - Various Units
33-997 Graduate Laboratory
Fall and Spring Semester - Various Units
33-998 Thesis Research
Fall and Spring Semester - Various Units