Graduate Course Descriptions

This page describes the contents of graduate level physics courses offered at Carnegie Mellon University. Links to the web sites of these courses can be found here. Undergraduate physics courses are described in this link.

33-650
General Relativity
Spring Semester - 9 Units

33-658
Quantum Computation and Information
Spring Semester - 10 Units

See the description under 33-758.

33-755
Quantum Mechanics I
Fall Semester - 12 Units

This course introduces fundamental concepts of quantum mechanics.  Applications are made to quantum computing, the harmonic oscillator, the hydrogen atom, electron spin and addition of angular momentum. 3hrs. lecture. Typical Text: Cohen-Tannoudji Quantum Mechanics, volume 1.

33-756
Quantum Mechanics II
Spring Semester - 12 Units

This course focuses on qualitative and approximation methods in quantum mechanics, including time-independent and time-dependent perturbation theory, scattering and semiclassical methods.  Applications are made to atomic, molecular and solid matter. Systems of identical particles are treated including many electron atoms and the Fermi gas.  Prerequisite: 33-755, Quantum Mechanics I; 33-759 Theoretical Physics. 3 hrs. lecture. Typical Text: Cohen-Tannoudji Quantum Mechanics, volume 2.

33-757
Classical Mechanics
Fall Semester - 12 Units

This course includes a full treatment of Lagrange's equations with application to systems of particles, motion under central forces, charged particles in electric and magnetic fields, and nonlinear systems. Variational principles are discussed and Hamilton's theory developed, including Hamilton's equations, canonical transformations and invariants, infinitesimal contact transformations, symmetries and conservation laws, and the Hamilton-Jacobi method. Current topics in mechanics, including "chaotic" motion, will be introduced. 3 hrs. lecture. Typical Text: Goldstein, Classical Mechanics.

33-758
Quantum Computation and Information
Spring Semester - 12 Units

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 textbook is Nielsen and Chuang, Quantum Computation and Quantum Information. 3 hrs. lecture plus weekly seminar. A 10 unit version of the course, 33-658, does not include the seminar.

33-759
Introduction to Mathematical Physics
Fall Semester - 12 Units

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 Text: G. Arfken, Mathematical Methods for Physicists.

33-761
Classical Electrodynamics I
Fall Semester - 12 Units

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 Text: Jackson, Classical Electrodynamics, 2nd Ed.

33-762
Classical Electrodynamics II
Spring Semester - 12 Units

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 Text: Jackson, Classical Electrodynamics. 2nd Ed.

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 paramagnetics and introduction to simple interacting systems. 3 hrs. lecture, 1 hr. recitation. Typical Texts: Reif, Statistical and Thermal Physics; Pathria, Statistical Mechanics.

33-766
Special Topics in Statistical Mechanics
Spring Semester - 12 Units

The principles developed in 33-765 are applied to the statistical mechanics of interacting systems. Phase transitions and critical phenomena are discussed. The statistical principles relevant to linear transport properties are developed. More general non-equilibrium phenomena are discussed in the context of fluid mechanics of continuous media. Prerequisite: 33-765. 3 hrs. lecture.

33-769
Quantum Mechanics III
Fall Semester - 12 Units

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. Prerequisite: 33-756, 33-76l. 3 hrs. lecture.

33-770
Quantum Mechanics IV
Spring Semester (Fall 2002) - 12 Units

This course gives systematic studies of the relativistic field theories. Topics included are canonical quantization of fields, LSZ reduction formula, Feynman diagram techniques, application to quantum electrodynamics and the discussion of the methods of renormalization. Prerequisite: 33-769. 3 hrs. lecture.

33-772
Many-Body Physics
Fall or Spring Semester - 12 Units

This course is designed to serve as an introduction to the many-body problems which arise in both solid-state and nuclear physics. Topics covered include diagrammatic perturbation methods, Green's functions, various techniques for dealing with collective phenomena and renormalization-group theory. These methods will be developed in connection with their applications to real gases, normal and super-conducting many-fermion systems, nuclear structure, critical phenomena and other problems of current interest. Prerequisite: 33-765, 33-769. 3 hrs. lecture. Offered when there is sufficient demand.

33-789
Quantum Field Theory
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). 3 hrs. lecture.

33-775
Introduction to Research I
Fall Semester - 6 Units

33-776
Introduction to Research II
Spring Semester - 6 Units

Both semesters are designed to give the student opportunity to gain experience in modern experimental techniques either through participation in research laboratories or through formal instruction, depending on the student's background. In the first semester, the student will also learn of the research of the department through lectures by the faculty on their work. All students are required to take the first semester, but those with post-graduate or unusual laboratory experience may not be required to take the second. However, it should be noted that for the M.S. degree, 12 units of laboratory are required.

33-779
Intro. to Nuclear & Particle Physics
Fall Semester - 12 Units

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, 33-78l. Topics included are symmetry principles of strong and weak interactions, quark model, classification of particles and nuclear forces. Prerequisite: 33-769 (or con-currently). 3 hrs. lecture. Typical Text: Perkins, Introduction to High Energy Physics, plus notes and reading.

33-780
Particle Physics
Spring Semester - 12 Units

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. Prerequisite: 33-779, 33-770 (or concurrently). 3 hrs. lecture.

33-781
Nuclear Structure Physics
Fall or Spring Semester - 12 Units

This course is intended for students of experimental or theoretical nuclear physics. Many-body methods are applied to complex nuclei. Properties of nuclear states and transitions, nuclear reaction mechanisms and elementary particle interactions in nuclei are treated. 3 hrs. lecture.

33-782
Special Topics in Nuclear & Particle Physics
Fall or Spring Semester - 12 Units

Various topics of current interest not covered in 33-779, 780, 781 will be discussed. Offered when there is sufficient demand. 3 hrs. lecture.

33-783
Condensed Matter Physics I
Fall Semester - 12 Units

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. Prerequisite: 33-756. 3 hrs. lecture. Typical Text: Ashcroft and Mermin, Solid State Physics.

33-784
Condensed Matter Physics II
Spring Semester - 12 Units

The second semester is devoted to special topics in condensed matter physics. Among the subjects recently treated are magnetism, magnetic resonance, low temperature phenomena, superconductivity, icosahedral crystals, morphological stability during phase transformations, turbulence and chaos. Prerequisite: 33-756. 3 hrs. lecture.

33-785
Special Topics in Solid State Physics
Fall or Spring Semester - 12 Units

Various topics of current interest in solid state physics will be included. Offered when there is sufficient demand. 3 hrs. lecture.

33-777
Introductory Astrophysics
Fall Semester, 12 units

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.

33-786
Astronomical Techniques
Spring Semester - 12 units

Observational techniques used in astronomy at all wavelengths will be discussed. Lectures will generally cover instruments, detector systems, and methods from x-ray and gamma-ray wavelengths to radio wavelengths. For this course Pitt and CMU astronomy faculty will be scheduled to give lectures related to their main fields of expertise. Topics will include x-ray/gamma-ray astronomy, uv/optical photometry & spectroscopy, astrometry, polarimetry & spectropolarimetry, infrared astronomy, and radio astronomy, including measurements of the cosmic microwave background radiation. Data collection and analysis methods used in large astronomical projects like the Sloan Digital Sky Survey will also be discussed.

33-787
Radiative Processes in Astrophysics
Spring: 12 units

Electromagnetic radiation is our key to understanding the Universe. This course focuses on the physics of radiative processes in their application to astrophysical problems. The topics that will be covered include fundamentals of radiative transfer, basic theory of radiation fields, bremsstrahlung, synchrotron radiation and Compton scattering, atomic structure and radiative transitions. A basic background in electromagnetic theory, special ralativity, and some quantum mechanics and statistical mechanics is required. Brief reviews of the prerequisite materials will be given during the course.

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.

33-796
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
Various Units

33-997
Graduate Laboratory
Various Units

33-998
Thesis Research
Various Units