Physics

Undergraduate Courses

33-100   Basic Experimental Physics

Fall and Spring:  6 units

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.

33-101   Physics First Year Seminar: Science and Science Fiction

Fall:  Mini Session -   3 units

Various seminars are offered that introduce first-year 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.

33-102   Concepts of Modern Physics

Spring:  9 units

This course is designed to provide non-technical students an opportunity to learn about some of the frontier areas of physics in which active research is now going on. Topics that may be covered include the current models of elementary particles, how the fundamental forces are understood in terms of quantum physics, Einstein's Special and General Theories of Relativity,  Astrophysics and Cosmology, or applications of Physics to current areas of technology. Although the emphasis is on concepts rather than mathematical methods, algebra and trigonometry are used in order to enable students to reach a deeper and more quantitative knowledge of the concepts. Students write brief reports about current topics in science and give a seminar on a topic of current interest in physics.

33-104   Experimental Physics

Fall and Spring:  9 units

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 computer-aided 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.

33-106   Physics I for Engineering Students

All Semesters:  12 units

This is a first semester, calculus-based 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.

Prerequisites:      Corequisites: 21-120

33-107   Physics II for Engineering Students

All Semesters:  12 units

This is the second half of a two-semester calculus-based 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

Prerequisites: 21120 and 33106     Corequisites: 21-122

33-111   Physics I for Science Students

Fall and Spring:  12 units

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.

Prerequisites:      Corequisites: 21-120

33-112   Physics II for Science Students

Fall and Spring:  12 units

This is the second semester course that follows 33-111. 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.

Prerequisites: 21120 and 33111     Corequisites: 21-122

33-114   Physics of Musical Sound

Spring:  9 units

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 self-sustained 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.

33-115   Energy and Environmental Issues

Fall:  10 units

An introduction to the fundamental principles and methodology of physics. The course will introduce and use the physics concepts of energy and the laws of thermodynamics to analyze environmental issues, such as fossil fuel use, nuclear power, solar power and others. Issues of risk assessment will also be discussed. This course is intended for students in the Colleges of H&SS and Fine Arts and does not require calculus, however, students are expected to have some facility with basic algebra.

33-124   Introduction to Astronomy

Fall:  9 units

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 non-technical 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 ever-changing 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.

33-131   Matter and Interaction I

Fall:  12 units

A more challenging alternative to 33-111, 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 atomic-level description and analysis of matter and its interactions. Momentum, numerical integration of Newton's laws, ball-and-spring model of solids, harmonic oscillator, energy, energy quantization, mass-energy 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).

Prerequisites:      Corequisites: 21-120

33-132   Matter and Interactions II

Spring:  12 units

A more challenging alternative to 33-112, Physics for Science Students II. Emphasis on atomic-level 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 non-Coulomb electric field, Maxwell's equations, electromagnetic radiation including its production and its effects on matter, re-radiation, interference. Computer modeling and visualization; desktop experiments.

Prerequisites: 21120 and 33131     Corequisites: 21-122

33-201   Undergraduate Colloquium I

Fall:  2 units

This course (together with 33-202) 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 sub-fields 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.

33-202   Undergraduate Colloquium II

Spring:  2 units

This course (together with 33-201) 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 sub-fields 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.

33-211   Physics III: Modern Essentials

Fall and Spring:  10 units

Physics III is primarily for third-semester 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 33-213 description.) It will introduce students to a conceptual theory, which is mathematically simple but (initially) non-intuitive. 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 (33-234).

Prerequisites: 33112 or 33132

33-213   Mini-Course in Special Relativity

Fall and Spring:  Mini Session -   4 units

This course spans the first six weeks of 33-211, Physics III: Modern Essentials. It treats the Mechanics aspects of Special Relativity, including topics such as simultaneity, the Lorentz transformation, time dilation, length contraction, space-time 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 (33-338/33-339).

Prerequisites: 33112 or 33132

33-224   Stars, Galaxies and the Universe

Fall:  9 units

The study of astronomy has blossomed over the past few decades as a result of new ground-based and space-based 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 sign-out for those who would like to use them, and outdoor observing sessions will be organized as weather permits.

Corequisites: 33-131 or 33-111 or 33-106

33-225   Quantum Physics and Structure of Matter

Fall:  9 units

This course introduces the basic theory used to describe the microscopic world of electrons, atoms, and photons. The duality between wave-like and particle-like 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 materials-related applications are developed, for example, Boltzmann and quantum statistics and properties of electrons in crystals. This course is intended primarily for non-physics majors who have not taken 33-211.

Prerequisites: 33107 or 33112 or 33132

33-228   Electronics I

Spring:  10 units

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.

Prerequisites: 33107 or 33112 or 33132

33-231   Physical Analysis

Fall:  9 units

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.

Prerequisites: 21122 and (33112 or 33132)

33-232   Mathematical Methods of Physics

Spring:  9 units

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.

Prerequisites: 33231

33-234   Quantum Physics

Spring:  10 units

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.

Prerequisites: 33211

33-241   Introduction to Computational Physics

Fall:  9 units

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.

Prerequisites: 15100 and 21122 and 33104 and (33112 or 33132)

33-301   Undergraduate Colloquium III

Fall:  1 units

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.

33-302   Undergraduate Colloquium IV

Spring:  1 units

Continuation of 33-301.

33-331   Physical Mechanics I

Fall:  10 units

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.

Prerequisites: 21259 and 33232

33-332   Physical Mechanics II

Spring:  10 units

This is the second semester of a two-semester course on classical mechanics. The course will use the tools developed in 33-331 to examine motion in non-inertial 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.

Prerequisites: 33331

33-338   Intermediate Electricity and Magnetism I

Fall:  10 units

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.

Prerequisites: 21259 and 33232

33-339   Intermediate Electricity and Magnetism II

Spring:  10 units

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 non-conducting 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, four-vectors, invariants, and applications to particle mechanics.

Prerequisites: 33338

33-340   Modern Physics Laboratory

Spring:  10 units

Emphasis is on hands-on 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, X-ray diffraction, Mössbauer effect, neutron activation of radioactive nuclides, Compton scattering, and cosmic ray muons.

Prerequisites: 33234 and (33331 or 33338 or 33341)

33-341   Thermal Physics I

Fall:  10 units

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.

Prerequisites: 33234 and 33232

33-342   Thermal Physics II

Spring:  10 units

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. Fermi-Dirac and Bose-Einstein 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.

Prerequisites: 33341

33-350   Undergraduate Research

Fall and Spring:  1-12 units

The student undertakes a project of interest under the supervision of one of the members of the faculty.

33-353   Intermediate Optics

Fall Alternate Years:  12 units

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, Huygens-Fresnel 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.

Prerequisites: 33112

33-398 Nanoscience and Nanotechnology

Fall Alternate Years: 9 units

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 upper-level 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 top-down and bottom-up methods will be discussed, contrasting these approaches and providing examples of each. Nanotechnology methods will be compared with those used in the modern micro-electronics industry. Finally, examples of nanoscale components and systems will be described, including quantum dots, self-assembled monolayers, molecular computing, and others. Stand-alone 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 nm-scale structure and atomic forces involved in various nanostructures. Students will sign up for these laboratory sessions and perform the exercises under the supervision of the Director of MCS Interdisciplinary Laboratories.

Prerequisites: (33-106, 33-111, or 33-131) and (33-107, 33-112, or 33-132)

33-401   Undergraduate Colloquium V

Fall:  1 units

A continuation of 33-301, 302 for seniors.

33-402   Undergraduate Colloquium VI

Spring:  1 units

A continuation of 33-301, 302 for seniors.

33-441   Introduction to BioPhysics

Fall:  10 units

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 x-ray and neutron diffraction, light scattering, birefringence, microscopy, Raman and IR spectroscopy, dielectric response and calorimetry.

33-444   Introduction to Nuclear and Particle Physics

Spring Alternate Years:  9 units

Description of our understanding of nuclei, elementary particles, and quarks, with equal emphasis on the nuclear and particle aspects of sub-atomic 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 sub-atomic 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.

Prerequisites: 33234 and 33338

33-445   Adv Quantum Physics I

Fall:  9 units

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, multi-particle states, identical particles; approximation methods.

Prerequisites: 33234     Corequisites: 33-331

33-446   Advanced Quantum Physics II

Spring:  9 units

Classical symmetries; quantum symmetries; rotations and angular momentum; spin; addition of angular momentum; the hydrogen atom; quantum "paradoxes" and Bell's theorem; applications.

Prerequisites: 33445

33-448   Introduction to Solid State Physics

Spring:  9 units

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.

Prerequisites: (33234 or 33225) and 33341

33-451   Senior Research

Fall and Spring:  1-12 units

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, 33-340, should precede this course, though it is not required. A list of research projects will be available before pre-registration in spring of the junior year so that student project pairings can be set. Reports on results are required at end of semester.

33-456   Advanced Computational Physics

Spring:  9 units

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, chi-squared 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.

Prerequisites: 33241

33-458   Special Problems in Computational Physics

Fall and Spring:  9 units

The student will work under the direction of a Department faculty member on a computational physics problem of mutual interest.

Prerequisites: 33456

33-466   Extragalactic Astrophysics and Cosmology

Spring:  9 units

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.

Prerequisites: 33224 and 33234

33-467   Astrophysics of Stars and the Galaxy

Fall:  9 units

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 multi-wavelength 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.

Prerequisites: 33224 and 33234

33-499   Supervised Reading

Fall and Spring:  1-12 units

The student explores a certain area of advanced physics under the supervision of a faculty member.

33-650   General Relativity

Fall:  9 units

General Relativity (GR) is the foundation upon which we build a theory for the universe. The course will outline GR and provide the students with a solid physical understanding of the elegant theory. The course will also use GR to explain the observable universe and students will get an appreciation of this theory through modern-day experiments.

Prerequisites: 33211 and 33339

33-652 An Introduction to String Theory

Spring: 9 units

The two triumphs  of 20th century physics, quantum mechanics and general relativity, are monuments to the progress of science, yet they have yet 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 intended as an introduction to this new field. The course will be self contained but general relativity, or some knowledge of differential geometry (tensor analysis) will be required.

Prerequisites: 33650 or permission of instructor

33-658   Quantum Computation and Quantum Information Theory

Spring:  10 units

This course provides an overview of 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; proposals for the physical realization of quantum devices, such as ions in traps, solid-state devices, and nuclear magnetic resonance. Linear algebra at the level of 21-241 or 21-341, or as taken up in 33-345, is a prerequisite; in addition, students who are not familiar with vector spaces over complex numbers, including unitary and Hermitian operators, will need to learn these topics on their own. Quantum mechanics is not a prerequisite, but some prior knowledge at the level of 33-234 or 33-445 will prove helpful. Algorithms and complexity theory are not prerequisites, but some prior knowledge at the level of 15-211, 15-251 or 15-451 will prove helpful. This course is also offered for 12 units as 33-758, which involves some additional work.

33-755   Quantum Mechanics I

Fall:  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.

Prerequisites: 33759

33-756   Quantum Mechanics II

Spring:  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 and Spring:  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 Quantum Information Theory

Spring:  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 I

Fall:  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:  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:  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:  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

Fall and Spring:  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:  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

Prerequisites: 33756 and 33761

33-770   Quantum Mechanics IV

Fall:  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.

33-771   Quantum Mechanics V

All Semesters:  12 units

33-775   Introduction to Research 1

Fall:  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.

33-776   Introduction to Research II

Spring:  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.

33-777   Introductory Astrophysics

Fall:  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.

33-779   Introduction to Nuclear and Particle Physics

Fall:  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.

Corequisites: 33-769

33-780   Nuclear and Particle Physics II

Spring:  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.

33-782   Special Topics in Nuclear and Particle Physics

Fall and Spring:  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   Theory of Solids I

Fall:  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.

Prerequisites: 33756

33-785   Special Topics in Condensed Matter Physics

Fall and Spring:  12 units

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

33-786   Astronomical Techniques

Spring:  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.

33-788   Special Topics in Astro Physics

All Semesters:  12 units

33-789   Quantum Field Theory I

Fall and Spring:  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.

33-794   Colloquium

Fall and Spring:  1 units

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.