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. 