Courses taught in the Physics Department
Undergraduate Level Courses
Number 
Course Name 
33100  Basic Experimental Physics 
This course provides students with a basic introduction to experimental physics. The content of the course and the particular experiments to be carried out are chosen to be especially useful for students who intend to work in the health sciences. Specific topics will range from mechanics to nuclear and atomic physics. Fall and Spring: 6 units 

33101  Physics First Year Seminar: Science and Science Fiction 
Various seminars are offered that introduce firstyear students to current topics of modern physics. These are mini courses that meet for half a semester. In the past, seminar topics have included: Science and Science Fiction, Astrophysics, Black Holes, Cosmology and Supernovae, Elementary Particles, and The Building Blocks of Matter. These seminars are open only to MCS first year students. Fall: Mini Session  3 units 

33104  Experimental Physics 
This course provides first year students and sophomores with an introduction to the methods of experimental physics. Particular emphasis is placed on three aspects of experimentation: laboratory technique, including both the execution and the documentation of an experiment; data analysis, including the treatment of statistical and systematic errors and computeraided analysis of experimental data; and written communication of experimental procedures and results. The concepts and skills for measurement and data analysis are acquired gradually through a series of experiments covering a range of topics from mechanics to nuclear and atomic physics. Fall and Spring: 9 units 

33106  Physics I for Engineering Students 
This is a first semester, calculusbased introductory physics course. Basic principles of mechanics and thermodynamics are developed. Topics include vectors, displacement, velocity, acceleration, force, equilibrium, mass, Newton's laws, gravitation, work, energy, momentum, impulse, temperature, heat, equations of state, thermodynamic processes, heat engines, refrigerators, first and second laws of thermodynamics, and the kinetic theory of gases. All Semesters: 12 units Prerequisites: Corequisites: 21120 

33107  Physics II for Engineering Students 
This is the second half of a twosemester calculusbased introductory physics sequence for engineering students. One fifth of the course covers waves, including standing and traveling waves, superposition, beats, reflection, and interference. Two fifths of the course covers electricity, including electrostatics and electric fields, Gauss' law, electric potential, and simple circuits. The remaining two fifths cover magnetism, including magnetic forces, magnetic fields, induction and electromagnetic radiation All Semesters: 12 units Prerequisites: 21120 and 33106 Corequisites: 21122 

33111  Physics I for Science Students 
This calculus based course combines the basic principles of mechanics with some quantum physics and relativity to explain nature on both a microscopic and macroscopic scale. The course will build models to describe the universe based on a small number of fundamental physics principles. Some simple computer modeling will be done to develop insight into the solving of problems using Newton's laws. Topics covered will include vectors, momentum, force, gravitation, oscillations, energy, quantum physics, center of mass motion, angular momentum, statistical physics, and the laws of thermodynamics. No computer experience is needed. Fall and Spring: 12 units Prerequisites: Corequisites: 21120 

33112  Physics II for Science Students 
This is the second semester course that follows 33111. Electricity and magnetism is developed, including the following topics: Coulomb's law, polarization, electric field, electric potential, DC circuits, magnetic field and force, magnetic induction, and the origins of electromagnetic waves. Fall and Spring: 12 units Prerequisites: 21120 and 33111 Corequisites: 21122 

33114  Physics of Musical Sound 
An introduction to the physics and psychophysics of musical sound. Elementary physics of vibrating systems. Propagation of sound: traveling waves, reflection, and diffraction. Addition of waves: interference and beats. Anatomy of the ear and the perception of sound: loudness, pitch, and timbre. Standing waves and natural modes. Qualitative description of general periodic systems by Fourier analysis: the harmonic series and complex musical tones. The acoustics of musical instruments including percussion instruments, such as drums, bars, and struck and plucked strings; and instruments exhibiting selfsustained oscillations, including bowed strings, blown pipes, reeds, brasses, and singing. Intervals and consonance, musical scales, tuning and temperament. Basic room and auditorium acoustics. There are no formal prerequisites, but an ability to read music and having some previous musical experience will be very useful. Spring: 9 units 

33115  Physics for Future Presidents 
Countless topics of social and political importance are intimately related to science in general and physics in particular. Examples include energy production, global warming, radioactivity, terrorism, and space travel. This course aims to provide key bits of knowledge based on which such issues can be discussed in a meaningful way, i.e., on the level of arguments and not just vague beliefs. We will cover an unusually wide range of topics, including energy, heat, gravity, atoms, radioactivity, chain reactions, electricity, magnetism, waves, light, weather, and climate. No calculus or algebra will be required. The course is open for all students at CMU. Fall: 10 units 

33120  Science and Science Fiction 
We will view and critique the science content in a selection of science fiction films, spanning more than 100 years of cinematic history, and from scifi TV shows from the past 50+ years. Guided by selected readings from current scientific literature, and aided by orderofmagnitude estimates and careful calculations, we will ponder whether the films are showing things which may fall into one of the following categories: Science fiction at the time of production, but currently possible, due to recent breakthroughs. Possible, in principle, but beyond our current technology. Impossible by any science we know. Topics to be covered include the future of the technological society, the physics of Star Trek, the nature of space and time, extraterrestrial intelligence, robotics and artificial intelligence, biotechnology and more. Success of this course will depend upon class participation. Students will be expected to contribute to discussion of assigned readings and problems, and to give brief presentations in class on assigned films. Summer: 9 units 

33121  Physics I for Science Students 
This calculusbased course combines the basic principles of mechanics with some quantum physics and relativity to explain nature on both a microscopic and macroscopic scale. The course will build models to describe the universe based on a small number of fundamental physics principles. Some simple computer modeling will be done to develop insight into the solving of problems using Newton's laws. Topics covered will include vectors, momentum, force, gravitation, oscillations, energy, quantum physics, center of mass motion, rotation, angular momentum, statistical physics, and the laws of thermodynamics. No computer experience is needed. Examples illustrating basic principles being presented will be taken from physics, chemistry, and biology. Fall and Spring: 12 units Corequisite: 21120 

33122  Physics II for Science Students 
This is the second course in the introductory physics sequence for chemistry and biological science majors. The course will consist of eight portions covering (1) electrostatics and dynamics, (2) electrical circuits, (3) magnetism, (4) waves, (5) optics, (6) diffusive motion, and (7) hydrostatic forces and flow. Emphasis will be put on the application of the underlying physical principles in the study of biology and chemistry. Fall and Spring: 9 units Prerequisites: (21120 and 33121) or 33151 or 33141 Corequisites: 21124 and 21122 

33124  Introduction to Astronomy 
Astronomy continues to enjoy a golden age of exploration and discovery. This course presents a broad view of astronomy, straightforwardly descriptive and without any complex mathematics. The goal of the course is to encourage nontechnical students to become scientifically literate and to appreciate new developments in the world of science, especially in the rapidly developing field of astronomy. Subjects covered include the solar system, stars, galaxies and the universe as a whole. The student should develop an appreciation of the everchanging universe and our place within it. Computer laboratory exercises will be used to gain practical experience in astronomical techniques. In addition, small telescopes will be used to study the sky. Fall: 9 units 

33126  Astronomy Lab 
This course is the laboratory source in science and astronomy. It overviews the scientific method, teaches how to obtain knowledge from data and to develop physicsbased models of natural phenomena, trains how to use astronomical instruments (telescope) to make observations and to explain these observations qualitatively, and explains how to apply of the stateofthe art professional software to study our universe. Astronomy is one of the oldest fields of science with at least 3000 years of recorded history. On the astronomy side, major topics of this laboratory course include an overview of the Solar system and the Universe. The goals of the laboratory course are to expand the student?s understanding of the motions of objects through the sky, to use astronomical techniques, such as telescope and simulated observations, and to obtain, analyze, and interpret data. Fall: 3 units 

33131  Matter and Interaction I 
A more challenging alternative to 33111, Physics I for Science Students. Students with particularly strong physics backgrounds may volunteer for this course. Modeling of physical systems, including 3D computer modeling, with emphasis on atomiclevel description and analysis of matter and its interactions. Momentum, numerical integration of Newton's laws, ballandspring model of solids, harmonic oscillator, energy, energy quantization, massenergy equivalence, multiparticle systems, collisions, angular momentum including quantized angular momentum, kinetic theory of gases, statistical mechanics (temperature, entropy, and specific heat of the Einstein solid, Boltzmann factor). Fall: 12 units Prerequisites: Corequisites: 21120 

33132  Matter and Interactions II 
A more challenging alternative to 33112, Physics for Science Students II. Emphasis on atomiclevel description and analysis of matter and its electric and magnetic interactions. Coulomb's law, polarization, electric field, plasmas, field of charge distributions, microscopic analysis of resistor and capacitor circuits, potential, macroscopic analysis of circuits, Gauss' law, magnetic field, atomic model of magnetism, Ampere's law, magnetic force, relativistic issues, magnetic induction with emphasis on nonCoulomb electric field, Maxwell's equations, electromagnetic radiation including its production and its effects on matter, reradiation, interference. Computer modeling and visualization; desktop experiments. Spring: 12 units Prerequisites: 21120 and 33131 Corequisites: 21122 

33141  Physics I for Engineering Students 
This is a first semester, calculusbased introductory physics course. Basic principles of mechanics and thermodynamics are developed. Topics include vectors, displacement, velocity, acceleration, force, equilibrium, mass, Newton's laws, gravitation, work, energy, momentum, impulse, torque and angular momentum, temperature, heat, equations of state, thermodynamic processes, heat engines, refrigerators, first and second laws of thermodynamics, and the kinetic theory of gases. Fall and Spring: 12 units Corequisite: 21120 

33142  Physics II for Engineering and Physics Students 
This is the second half of a twosemester calculusbased introductory physics sequence for engineering and physics students. Two fifths of the course covers electricity, including electrostatics and electric fields, Gauss' law, electric potential, and simple circuits. Two fifths cover magnetism, including magnetic forces, magnetic fields, induction and electromagnetic radiation. One fifth of the course covers mechanical waves (including standing and traveling waves, superposition, and beats) and electromagnetic waves (including mode of propagation, speed, and other properties). Fall and Spring: 12 units Prerequisites: (33121 and 21120) or 33141 or 33151 Corequisite: 21122 

33151  Matter and Interactions I 
A more challenging alternative to 33111, Physics for Science Students I. Students with particularly strong physics backgrounds may volunteer for this course. Modeling of physical systems, including 3D computer modeling, with emphasis on atomiclevel description and analysis of matter and its interactions. Momentum, numerical integration of Newton's laws, ballandspring model of solids, harmonic oscillator, energy, energy quantization, massenergy equivalence, multiparticle systems, collisions, angular momentum including quantized angular momentum, kinetic theory of gases, statistical mechanics (temperature, entropy, and specific heat of the Einstein solid, Boltzmann factor). Fall: 12 units Prerequisite: 21120 Corequisite: 21122 

33152  Matter and Interactions II 
A more challenging alternative to 33142, Physics II for Engineering and Physics Students. There is an emphasis on atomiclevel description and analysis of matter and its electric and magnetic interactions. Topics include: Coulomb's law, polarization, electric field, plasmas, field of charge distributions, microscopic analysis of resistor and capacitor circuits, potential, macroscopic analysis of circuits, Gauss' law, magnetic field, atomic model of magnetism, Ampere's law, magnetic force, relativistic issues, magnetic induction with emphasis on nonCoulomb electric field, Maxwell's equations, electromagnetic radiation including its production and its effects on matter, reradiation, interference. There will also be computer modeling, visualization and desktop experiments. Spring: 12 units Prerequisites: 21122 and 33151 Corequisite: 21259 

33201  Undergraduate Colloquium I 
This course (together with 33202) is designed to give students an overview of the field of Physics and to help students make knowledgeable choices in both their academic and professional careers. We discuss several of the subfields of Physics in order to give students an understanding of the types of activities, from research to industrial applications, in each. Over the two semesters, we typically discuss six subfields in some detail with the goal of providing a minimal literacy in the relevant concepts and language. The course consists of one classroom lecture per week plus roughly one hour per week of reading and/or problem solving. Fall: 2 units 

33202  Undergraduate Colloquium II 
This course (together with 33201) is designed to give students an overview of the field of Physics and to help students make knowledgeable choices in both their academic and professional careers. We discuss several of the subfields of Physics in order to give students an understanding of the types of activities, from research to industrial applications, in each. Over the two semesters, we typically discuss six subfields in some detail with the goal of providing a minimal literacy in the relevant concepts and language. The course consists of one classroom lecture per week plus roughly one hour per week of reading and/or problem solving. Spring: 2 units 

33211  Physics III: Modern Essentials 
Physics III is primarily for thirdsemester students of physics, including all physics majors, but is open to any qualified student who wants an introduction to the physics of the 20th century. The course will have a strong component of Special Relativity, dealing with kinematics and dynamics, but not electricity and magnetism. (See 33213 description.) It will introduce students to a conceptual theory, which is mathematically simple but (initially) nonintuitive. The course also provides a broad exposure to quantum phenomena and early quantum theory without getting overly mathematical. It leads into the more formal Quantum Physics course (33234). Fall and Spring: 10 units Prerequisites: 33112 or 33132 

33213  MiniCourse in Special Relativity 
This course spans the first six weeks of 33211, Physics III: Modern Essentials. It treats the Mechanics aspects of Special Relativity, including topics such as simultaneity, the Lorentz transformation, time dilation, length contraction, spacetime geometry, resolving some famous puzzles, and the momentum, mass, and energy relations. The Electricity and Magnetism portions of the subject are deferred until the junior/senior courses in E&M (33338/33339). Fall and Spring: Mini Session  4 units Prerequisites: 33112 or 33132 

33224  Stars, Galaxies and the Universe 
The study of astronomy has blossomed over the past few decades as a result of new groundbased and spacebased telescopes, and with the advantage of fast computers for analysis of the huge quantities of data. As our astronomical horizon expands, we are still able to use the laws of physics to make sense of it all. This course is for students who want to understand the basic concepts in astronomy and what drives astronomical objects and the universe. The course emphasizes the application of a few physical principles to a variety of astronomical settings, from stars to galaxies to the structure and evolution of the universe. Introductory classical physics is required, but modern physics will be introduced as needed in the course. The course is intended for science and engineering majors as well as students in other disciplines with good technical backgrounds. Computer lab exercises will be used to gain practical experience in astronomical techniques. In addition, small telescopes are available for personal signout for those who would like to use them, and outdoor observing sessions will be organized as weather permits. Fall: 9 units Corequisites: 33131 or 33111 or 33106 

33225  Quantum Physics and Structure of Matter 
This course introduces the basic theory used to describe the microscopic world of electrons, atoms, and photons. The duality between wavelike and particlelike phenomena is introduced along with the deBroglie relations which link them. We develop a wave description appropriate for quanta which are partially localized and discuss the interpretation of these wavefunctions. The wave equation of quantum mechanics is developed and applied to the hydrogen atom from which we extrapolate the structure of the Periodic Table. Other materialsrelated applications are developed, for example, Boltzmann and quantum statistics and properties of electrons in crystals. This course is intended primarily for nonphysics majors who have not taken 33211. Fall: 9 units Prerequisites: 33107 or 33112 or 33132 

33228  Electronics I (web page) 
An introductory laboratory and lecture course with emphasis on elementary circuit analysis, design, and testing. We start by introducing basic circuit elements and study the responses of combinations to DC and AC excitations. We then take up transistors and learn about biasing and the behavior of amplifier circuits. The many uses of operational amplifiers are examined and analyzed; general features of feedback systems are introduced in this context. Complex functions are used to analyze all of the above linear systems. Finally, we examine and build some simple digital integrated circuits. Spring: 10 units Prerequisites: 33107 or 33112 or 33132 

33231  Physical Analysis 
This course aims to develop analytical skills and mathematical modeling skills across a broad spectrum of physical phenomena, stressing analogies in behavior of a wide variety of systems. Specific topics include dimensional analysis and scaling in physical phenomena, exponential growth and decay, the harmonic oscillator with damping and driving forces, linear approximations of nonlinear systems, coupled oscillators, and wave motion. Necessary mathematical techniques, including differential equations, complex exponential functions, matrix algebra, and elementary Fourier series, are introduced as needed. Fall: 9 units Prerequisites: 21122 and (33112 or 33132) 

33232  Mathematical Methods of Physics 
This course introduces, in the context of physical systems, a variety of mathematical tools and techniques that will be needed for later courses in the physics curriculum. Topics will include, linear algebra, vector calculus with physical application, Fourier series and integrals, partial differential equations and boundary value problems. The techniques taught here are useful in more advanced courses such as Physical Mechanics, Electricity and Magnetism, and Advanced Quantum Physics. Spring: 9 units Prerequisites: 33231 

33234  Quantum Physics 
An introduction to the fundamental principles and applications of quantum physics. A brief review of the experimental basis for quantization motivates the development of the Schrodinger wave equation. Several unbound and bound problems are treated in one dimension. The properties of angular momentum are developed and applied to central potentials in three dimensions. The one electron atom is then treated. Properties of collections of indistinguishable particles are developed allowing an understanding of the structure of the Periodic Table of elements. A variety of mathematical tools are introduced as needed. Spring: 10 units Prerequisites: 33211 

33241  Introduction to Computational Physics 
The course emphasizes the formulation of physical problems for machine computation with exploration of alternative numerical methods. Work will be done on a range of computers from workstations to high performance computing platforms. Examples are drawn from Physics I and II, and Experimental Physics, as well as concurrent physics courses. Fall: 9 units Prerequisites: 15100 and 21122 and 33104 and (33112 or 33132) 

33301  Undergraduate Colloquium III 
Junior and senior Physics majors meet together for 1 hour a week to hear discussions on current physics research from faculty, undergraduate and graduate students, and outside speakers. Other topics of interest such as application to graduate school, areas of industrial research and job opportunities will also be presented. Fall: 1 unit 

33302  Undergraduate Colloquium IV 
Continuation of 33301. Spring: 1 unit 

33331  Physical Mechanics I 
Fundamental concepts of classical mechanics. Conservation laws, momentum, energy, angular momentum, Lagrange's and Hamilton's equations, motion under a central force, scattering, cross section, and systems of particles. Fall: 10 units Prerequisites: 21259 and 33232 

33332  Physical Mechanics II 
This is the second semester of a twosemester course on classical mechanics. The course will use the tools developed in 33331 to examine motion in noninertial reference frames; in particular, rotating frames. This then leads to the development of general rigid body motion, Euler's Equations. Finally, the course will cover coupled oscillations with particular emphasis on normal modes. Spring: 10 units Prerequisites: 33331 

33338  Intermediate Electricity and Magnetism I 
This course includes the basic concepts of electro and magnetostatics. In electrostatics, topics include the electric field and potential for typical configurations, work and energy considerations, the method of images and solutions of Laplace's Equation, multipole expansions, and electrostatics in the presence of matter. In magnetostatics, the magnetic field and vector potential, magnetostatics in the presence of matter, properties of dia, para and ferromagnetic materials are developed. Fall: 10 units Prerequisites: 21259 and 33232 

33339  Intermediate Electricity and Magnetism II 
This course focuses on electro and magnetodynamics. Topics include Faraday's Law of induction, electromagnetic field momentum and energy, Maxwell's equations and electromagnetic waves including plane waves, waves in nonconducting and conducting media, reflection and refraction of waves, and guided waves. Electromagnetic radiation theory includes generation and characteristics of electric and magnetic dipole radiation. The Special Theory of Relativity is applied to electrodynamics: electric and magnetic fields in different reference frames, Lorentz transformations, fourvectors, invariants, and applications to particle mechanics. Spring: 10 units Prerequisites: 33338 

33340  Modern Physics Laboratory (web page) 
Emphasis is on handson experience observing important physical phenomena in the lab, advancing the student's experimental skills, developing sophisticated data analysis techniques, writing thorough reports, and improving verbal communication through several oral progress reports given during the semester and a comprehensive oral report on one experiment. Students perform three experiments which are drawn from the areas of atomic, condensed matter, classical, and nuclear and particle physics. Those currently available are the following: Zeeman effect, light scattering, optical pumping, thermal lensing, Raman scattering, chaos, magnetic susceptibility, nuclear magnetic resonance, electron spin resonance, Xray diffraction, M�ssbauer effect, neutron activation of radioactive nuclides, Compton scattering, and cosmic ray muons. Spring: 10 units Prerequisites: 33234 and (33331 or 33338 or 33341) 

33341  Thermal Physics I 
The three laws of classical thermodynamics, which deal with the existence of state functions for energy and entropy and the entropy at the absolute zero of temperature, are developed along phenomenological lines. Elementary statistical mechanics is then introduced via the canonical ensemble to understand the interpretation of entropy in terms of probability and to calculate some thermodynamic quantities from simple models. These laws are applied to deduce relationships among heat capacities and other measureable quantities and then are generalized to open systems and their various auxiliary thermodynamic potentials; transformations between potentials are developed. Criteria for equilibrium of multicomponent systems are developed and applied to phase transformations and chemical reactions. Models of solutions are obtained by using statistical mechanics and are applied to deduce simple phase diagrams for ideal and regular solutions. The concept of thermodynamic stability is then introduced and illustrated in the context of phase transformations. Fall: 10 units Prerequisites: 33234 and 33232 

33342  Thermal Physics II 
This course begins with a more systematic development of formal probability theory, with emphasis on generating functions, probability density functions and asymptotic approximations. Examples are taken from games of chance, geometric probabilities and radioactive decay. The connections between the ensembles of statistical mechanics (microcanonical, canonical and grand canonical) with the various thermodynamic potentials is developed for single component and multicomponent systems. FermiDirac and BoseEinstein statistics are reviewed. These principles are then applied to applications such as electronic specific heats, Einstein condensation, chemical reactions, phase transformations, mean field theories, binary phase diagrams, paramagnetism, ferromagnetism, defects, semiconductors and fluctuation phenomena. Spring: 10 units Prerequisites: 33341 

33350  Undergraduate Research 
The student undertakes a project of interest under the supervision of one of the members of the faculty. Fall and Spring: 112 units 

33353  Intermediate Optics 
Geometrical optics: reflection and refraction, mirrors, prisms, lenses, apertures and stops, simple optical instruments, fiber optics. Scalar wave optics: wave properties of light, interference, coherence, interferometry, HuygensFresnel principle, Fraunhofer diffraction, resolution of optical instruments, Fourier optics, Fresnel diffraction. Laser beam optics: Gaussian beams. Vector wave optics: electromagnetic waves at dielectric interfaces, polarized light. The course will use complex exponential representations of electromagnetic waves. Fall Alternate Years: 12 units Prerequisites: 33112 

33355  Nanoscience and Nanotechnology 
This course will explore the underlying science behind nanotechnology, the tools used to create and characterize nanostructures, and potential applications of such devices. Material will be presented on a level intended for upperlevel science and engineering students. The course will start with a brief review of the physical principles of electric fields and forces, the nature of chemical bonds, the interaction of light with matter, and elastic deformation of solids. Characterization using electron microscopy, scanning probe methods, and spectroscopic techniques will then be described in detail. Fabrication using topdown and bottomup methods will be discussed, contrasting these approaches and providing examples of each. Nanotechnology methods will be compared with those used in the modern microelectronics industry. Finally, examples of nanoscale components and systems will be described, including quantum dots, selfassembled monolayers, molecular computing, and others. Standalone laboratory exercises will be included as an important element of the course. These will focus on the use of scanning probe methods to study the nmscale structure and atomic forces involved in various nanostructures. Students will sign up for these laboratory sessions and perform the exercises under the supervision of a teaching assistant. In addition to the prerequisites, students should have taken a prior laboratory course in a science or engineering department and should have some familiarity with differential equations at an elementary level. Fall Alternate Years: 9 units Prerequisites: (33107 or 33112 or 33132) 

33398  Special Topics 
This course is offered occasionally and focuses on a variety of different topics. Recent topics have included String Theory and Nanoscience and Nanotechnology. Fall Alternate Years: 9 units Prerequisites: (33107, 33112, or 33132) 

33441  Introduction to BioPhysics 
This course introduces the use of physical methods in the study of biological systems. The biological systems to which the methods are applied will be surveyed and current interpretations of their structure and function will be discussed. Biological systems that have been discussed in recent years include membranes, nerves, muscle, photosynthetic systems and visual systems; not all these topics can be treated, and the particular selection can be influenced by student interest. The treatment of biophysical methods will be based on physical principles, which will be treated with appropriate mathematics when necessary. The biophysical methods will be selected from among the techniques of xray and neutron diffraction, light scattering, birefringence, microscopy, Raman and IR spectroscopy, dielectric response and calorimetry. Fall: 10 units 

33444  Introduction to Nuclear and Particle Physics 
Description of our understanding of nuclei, elementary particles, and quarks, with equal emphasis on the nuclear and particle aspects of subatomic matter. We discuss the physics of accelerators, and how particle interactions with matter lead to various kinds of detector instrumentation. Then we discuss methods for measuring subatomic structure, symmetries and conservation laws, and the electromagnetic, weak, and strong interactions. We examine the quark model of the mesons and baryons, as well as several models of the atomic nucleus. Spring Alternate Years: 9 units Prerequisites: 33234 and 33338 

33445  Adv Quantum Physics I 
Mathematics of quantum theory, linear algebra and Hilbert spaces; review of classical mechanics; problems with classical mechanics; postulates of quantum theory; one dimensional applications; the harmonic oscillator; uncertainty relations; systems with N degrees of freedom, multiparticle states, identical particles; approximation methods. Fall: 9 units Prerequisites: 33234 Corequisites: 33331 

33446  Advanced Quantum Physics II 
Classical symmetries; quantum symmetries; rotations and angular momentum; spin; addition of angular momentum; the hydrogen atom; quantum "paradoxes" and Bell's theorem; applications. Spring: 9 units Prerequisites: 33445 

33448  Introduction to Solid State Physics 
This course gives a quantitative description of crystal lattices, common crystal structures obtained by adding a basis of atoms to the lattice, and the definition and properties of the reciprocal lattice. Diffraction measurements are studied as tools to quantify crystal lattices, including Bragg's law and structure factors. Diffraction from amorphous substances and liquids is also introduced. The various types of atomic bonding, e.g., Van der Waals, metallic, ionic, covalent and hydrogen are surveyed. Binding energies of some crystalline structures are calculated. Models of crystal binding are generalized to include dynamics, first for classical lattice vibrations and then for quantized lattice vibrations known as phonons. These concepts are used to calculate the heat capacities of insulating crystals, to introduce the concept of density of states, and to discuss phonon scattering. The band theory of solids is developed, starting with the free electron model of a metal and culminating with the properties of conductors and semiconductors. Magnetic phenomena such as paramagnetism and the mean field theory of ferromagnetism are covered to the extent that time permits. Spring: 9 units Prerequisites: (33234 or 33225) and 33341 

33451  Senior Research 
Open to all senior physics majors. May include research done in a research lab, extending the capabilities of a teaching lab, or a theoretical or computational physics project. The student experiences the less structured atmosphere of a research program where there is much room for independent initiative. Modern Physics Laboratory, 33340, should precede this course, though it is not required. A list of research projects will be available before preregistration in spring of the junior year so that student project pairings can be set. Reports on results are required at end of semester. Fall and Spring: 112 units 

33456  Advanced Computational Physics 
This course will emphasize application of practical numerical techniques to the types of problems that are encountered by practicing physicists. The student will be expected to understand the principles behind numerical methods such as SVD decomposition, chisquared minimization, and Fast Fourier Transforms and Monte Carlo simulation of experiments. Applications will include data analysis and eigenvalue problems. Emphasis will be placed on the ability to implement complex algorithms accurately by devising methods of checking results and debugging code. The students will be expected to become proficient in Fortran or C programming. Spring: 9 units Prerequisites: 33241 

33458  Special Problems in Computational Physics 
The student will work under the direction of a Department faculty member on a computational physics problem of mutual interest. Fall and Spring: 9 units Prerequisites: 33456 

33466  Extragalactic Astrophysics and Cosmology 
Starting from the expanding universe of galaxies, this course lays out the structure of the universe from the Local Group of galaxies to the largest structures observed. The observational pinnacle of the Big Bang theory, the microwave background radiation, is shown to provide us with many clues to conditions in the early universe and to the parameters which control the expansion and fate of the universe. Current theories for the development of galaxies and clusters of galaxies are outlined in terms of our current understanding of dark matter. Observational cosmology continues to enjoy a golden era of discovery and the latest observational results will be interpreted in terms of the basic cosmological parameters. Spring: 9 units Prerequisites: 33224 and 33234 

33467  Astrophysics of Stars and the Galaxy 
The physics of stars is introduced from first principles, leading from star formation to nuclear fusion to late stellar evolution and the end points of stars: white dwarfs, neutron stars and black holes. The theory of stellar structure and evolution is elegant and impressively powerful, bringing together all branches of physics to predict the life cycles of the stars. The basic physical processes in the interstellar medium will also be described, and the role of multiwavelength astronomy will be used to illustrate our understanding of the structure of the Milky Way Galaxy, from the massive black hole at the center to the halo of dark matter which emcompasses it. Fall: 9 units Prerequisites: 33224 and 33234 

33499  Supervised Reading 
The student explores a certain area of advanced physics under the supervision of a faculty member. Fall and Spring: 112 units 

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. 

33658  Quantum Computation and Information 
Spring Semester  9 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. 
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 
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 
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.