Physics

Physics is concerned with the study of matter, energy, forces, and their interaction in the world and universe around us. The undergraduate curriculum in the Department of Physics leading to the Bachelor of Arts in physics includes a strong emphasis on laboratory experiment and covers the broad fundamentals necessary for graduate study in theoretical physics, experimental physics, or astronomy and astrophysics, as well as some fields of engineering and many interdisciplinary specialties that require a strong technical background, such as biophysics, medical physics, or atmospheric and environmental sciences.

Courses. The curriculum leading to the B.A. degree in physics is designed for maximum flexibility consistent with a reasonably thorough coverage of the essential principles of physics. The minimum requirements consist of twelve physics courses and six mathematics courses, including the required general education sequences. The twelve required physics courses are General Physics I, II, III, followed by Physics 185, 186, 197, 225, 227, 234, 235, 236, and 237. The six required mathematics courses are a first-year calculus sequence and three additional intermediate or advanced mathematics courses.

Students who plan to concentrate in physics are encouraged to start physics courses in their first year. However, the concentration can be completed in three years, so one could start physics in the second year and still concentrate in physics. Two of the physics and two of the mathematics courses can be designated as general education courses so that fourteen courses remain to fulfill the concentration requirement.

In general, students should take the most advanced courses for which they have the appropriate prerequisites. Entering students planning to register for any of the introductory physics variants must take the optional physical sciences placement test during Orientation. Those wishing to take the honors sequence (Physics 141) must also take the optional calculus placement test. Students concentrating in physics usually start their physics program with Physics 141-142-143. However, students are placed into either Physics 141 or 131 on the basis of their scores on the physical sciences and calculus placement tests. Beginning the introductory sequence with Physics 131 allows a more gradual transition from high school physics to the honors-level college physics in Physics 142. Experience has shown that students following the Physics 131-142-143 route are not handicapped in intermediate-level courses. Another acceptable (but less preferable) route is to take the complete sequence of Physics 131-132-133 before the more advanced physics courses.

At least three mathematics courses at the 200-level (that is, beyond introductory calculus) are required to complete the physics concentration. One possible sequence, Mathematical Methods (Mathematics 200-201-202), introduces and develops practical mathematical tools that are particularly useful in physics. Those preferring a more rigorous presentation of advanced calculus may register for Analysis (Mathematics 203-204-205 or 207-208-209), though some of the most useful topics of the Mathematical Methods sequence are omitted. Other combinations of advanced mathematics courses and selected statistics courses (for example, Statistics 240) may also be used to fulfill the mathematics requirement. Students should discuss their choices thoroughly with their adviser and/or with the concentration chair for physics (KPTC 201).

Students are advised to include in their electives some of the following courses: Physics 226, 251; Astronomy and Astrophysics 241-242; Mathematics 250, 270, 273, 275; Biological Sciences 263; Statistics 240; and Chemistry 121-122-123, 261.

Students intending to pursue graduate work in astrophysics should consider the concentration program leading to a B.A. in physics with a specialization in astrophysics. This version of the B.A. in physics follows.

1	Phys 143†
1	1 Math 153 or 163†
2	Phys 185-186
1	Phys 225, 227
2	Phys 225, 227
4	Phys 234-235-236-237
3	mathematics courses at the 200 level
14

† Credit may be granted by examination.

NOTE: Entering students wishing to take Mathematics 200-201-202 after placing out of Mathematics 151-152 will have the Mathematics 153/163 concentration requirement waived.

Option A		Option B
3	Phys 341-342-343 or approved alternative graduate sequence	3	Phys 291-292-293

Sample Programs. The following sample programs show several paths for fulfilling the physics concentration requirements. As illustrated in the first example, the formal course requirements can be completed in three years, thereby allowing time in the fourth year for electives such as graduate courses or work on a bachelor's thesis. This particular example corresponds to honors option B.

Alternatively, the requirements can be satisfied over four years by postponing Physics 225, 227, and 234 until the third year and then completing the remainder of the concentration requirements during the fourth year, as shown in the next example. In most cases, this still allows the student to complete a bachelor's thesis.

Entering students who place out of Mathematics 151-152 can satisfy the physics concentration mathematics requirement with Mathematics 200-201-202 in the first year.

Introductory Course. The introductory course in physics is divided into three variants so students may learn with others who have comparable physics and mathematics backgrounds, or similar interdisciplinary interests. The minimum prerequisite for all three variants is previous or concurrent registration in a first-year calculus sequence (Mathematics 131-132-133, 151-152-153, or 161-162-163). The essential physics content of these variants is the same. Both Physics 131-132-133 and 141-142-143 prepare students for further courses in the Department of Physics.

The optional physical sciences placement test offered during Orientation is required of all entering students planning to register for any of the introductory physics variants. For Physics 141, the optional calculus placement test is required as well. Unless excused by satisfactory performance on the Advanced Placement physics test, first-year students are assigned to a variant of general physics based on the results of these calculus and physical sciences placement tests. Transfer students who have satisfactorily completed calculus-based introductory physics courses at another university may be granted appropriate transfer credit upon petition to and approval by the concentration chair. However, the procedures for obtaining credit for the laboratory portions of the courses, described in the following section on Advanced Placement, applies. Third- and fourth-year students are assigned to a variant based on their grade point average in previous mathematics and chemistry courses taken in the College. For entry into Physics 131, this grade point average must be above 2.5; for entry into Physics 141, it must be above 3.0. If any student is unhappy with the level of introductory physics placement, he or she may submit a petition in writing to the undergraduate program chair (KPTC 205).

Students who complete Physics 141 or 142 with a grade below C are normally required to move to Physics 132 or 133 the following quarter. Petitions for waiver of this requirement have to be presented to the undergraduate program chair before the second day of the succeeding

course. Students who receive As in Physics 131 or 132 are encouraged to move to Physics 142 or 143.

Advanced Placement. Students who took the C Advanced Placement examination in physics prior to matriculation in the College and received a grade of 4 or 5 are given credit for the lecture portions of Physics 121-122-123. The Department of Physics also administers accreditation examinations in Physics 121-122-123 and Physics 141-142-143 at the beginning of the corresponding quarter of each year. Students may receive credit for the lecture portion of one or more quarters of general physics on the basis of their performance on these examinations. All students who receive advanced standing on the basis of any of the above examinations or who receive transfer credit are interviewed by the undergraduate program chair to determine the extent of their laboratory experience. Those who have not completed the equivalent of the laboratory portions of the courses are asked to do some or all of the experiments when the relevant courses are offered.

Grading. All regular (nonresearch) physics courses must be taken for letter grades. The Department of Physics requires that all students achieve a minimum grade point average of 2.0 in the twelve required physics courses listed previously to graduate with a concentration in physics. In addition, the College requires that each student achieve a minimum grade point average of 2.0 in the courses designated for the concentration in the preceding Summary of Requirements section. Also, students concentrating in physics must pass General Physics I, II, and III and Physics 185, 186, and 197 with a grade point average of 2.0 or better. Any grade-conferring course credit may be counted toward the minimum grade point average requirements at the time of graduation. Incompletes are permitted only under exceptional circumstances.

Opportunities for Participation in Research. The physics program offers unique opportunities for College students to become involved actively in the research work being conducted by faculty and graduate students of the department. The focus of much of this undergraduate research is structured around the Bachelor's Thesis (Physics 291-292-293). Alternatively, third- or fourth-year students concentrating in physics may register for research for academic credit (Physics 297). There are other, more limited, openings for students at any level to become involved in research through regular part-time employment in a faculty member's laboratory or research group. Students concentrating in physics are encouraged to participate in research through one of these arrangements. In 1992, a participant in bachelor's thesis research was awarded the prestigious Apker Award of the American Physical Society for outstanding achievement in undergraduate research.

Honors Program. There are two alternative routes to a B.A. honors degree. Both require a minimum grade point average of 3.0 in the twelve required 100- and 200-level physics courses. In the first route, the student must pass an approved sequence of three graduate courses to become eligible for a B.A. honors degree. Normally, the recommended 300-level sequence is Physics 341-342-343; however, upon approval of the concentration chair, it may be replaced by another sequence of graduate courses in physics or graduate courses offered by the departments of astronomy, biophysics, chemistry, geophysical sciences, or mathematics. The second route to earning a B.A. honors degree is to register for Physics 291-292-293 (Bachelor's Thesis) and earn a grade of B or better based on a bachelor's thesis describing an approved research project completed during the year.

Degree Program in Physics with Specialization in Astrophysics. The concentration program leading to a B.A. in physics with a specialization in astrophysics is a version of the B.A. in physics. The degree is in physics with the designation "with specialization in astrophysics" included on the final transcript. Candidates are required to complete all requirements for the B.A. degree in physics, plus a two-quarter sequence in astrophysics (Astronomy 241-242), plus either a third course in astrophysics (Astronomy 280 or Astronomy 305) or a senior thesis project in physics (Physics 291-292-293) on a topic in astrophysics. If the latter option is chosen, the thesis topic must be approved by the concentration chair. (This thesis may simultaneously fulfill part of the requirements for an Honors Degree in physics.) A grade of at least C- must be obtained in each course.

Internet. For updated departmental and course information, consult the Department of Physics Web site (http://rainbow.uchicago.edu/physics).

In the following course descriptions, L refers to courses with laboratory.

121-122-123, 131-132-133, and 141-142-143. General Physics I, II, III. PQ: For all three variants, previous or concurrent registration in a first-year calculus sequence (Math 131-132-133, 151-152-153, or 161-162-163) and appropriate placement recommendation. Calculus is used in all three sequences. For entering students, the physical sciences placement test is required for all variants. The calculus placement test is required as well for Phys 141. Any of these course sequences fulfills the physical sciences requirement in general education. Although the essential physics content of these variants is similar, Phys 131-132-133 and 141-142-143 prepare students for further courses in the Department of Physics, while Phys 121-122-123 includes a broader emphasis on interdisciplinary applications, such as in biology. Two sections of Variant B (Phys 131-132-133) are offered. Labs for all three variants: Staff.

121-122-123. General Physics I, II, III (Variant A). PQ: Second-year standing. A one-year sequence in the fundamentals of physics. Topics include classical mechanics, electricity and magnetism, wave motion, optics, and an introduction to modern physics. W. Kang, Autumn; C. Covault, Winter; R. Winston, Spring. L.

131-132-133. General Physics I, II, III (Variant B). A one-year sequence in the fundamentals of physics. Topics include classical mechanics, electricity and magnetism, wave motion, optics, and an introduction to modern physics. This sequence is recommended for students with mathematical abilities and training beyond that required for the Phys 121-122-123 sequence. Section a: D. Grier, Autumn; E. Blucher, Winter; H. Jaeger, Spring. Section b: D. Müller, Autumn, S. Gazes, Winter; M. Oreglia, Spring. L.

141-142-143. General Physics I, II, III (Honors). A one-year sequence in the fundamentals of physics. Topics include classical mechanics, electricity and magnetism, wave motion, optics, and an introduction to modern physics. This sequence is recommended for physics concentrators who have a strong background in mathematics and have taken a good high school physics course. Multivariable and vector calculus is used. S. Swordy, Autumn; I. Abella, Winter; R. Ong, Spring. L.

185-186. Intermediate Mechanics. PQ: Phys 131 or 141, and concurrent registration in Math 200 or 203. A more sophisticated presentation of Newtonian mechanics, harmonic motion, central forces, systems of particles, and noninternal reference frames. Lagrange's equations, rigid bodies, and special relativity are also covered. Y. Wah, J. Pilcher. Autumn, Winter. L.

197. Thermal Physics. PQ: Phys 186 or consent of instructor. Elements of probability theory, statistical description of physical systems, thermodynamics, canonical ensembles, and kinetic theory are examined. W. Kang. Spring. L.

225, 227. Intermediate Electricity and Magnetism. PQ: Phys 132 and Math 200 or 203, or Phys 142 and concurrent registration in Math 200 or 203. Phys 225 and 227 must be taken in sequence. Topics include electrostatics, magnetostatics, electromagnetic induction, electric and magnetic fields in matter, plane electromagnetic waves, reflection and refraction of electromagnetic waves, and electromagnetic radiation. I. Abella, K. Levin. Autumn, Winter. L.

226. Electronics. PQ: Phys 122, 132, or 142; or equivalent. A hands-on experimental course to develop confidence, understanding, and design ability in modern electronics. This is not a course in the physics of semiconductors. In two lab sessions a week, students explore the properties of diodes, transistors, amplifiers, operational amplifiers, oscillators, field effect transistors, logic gates, digital circuits, analog-to-digital and digital-to-analog converters, phase-locked loops, and more. Lectures supplement the lab. S. Meyer. Spring. L.

234. Structure of Matter I: Introductory Quantum Mechanics and Atomic Physics. PQ: Phys 186 and 227, and concurrent registration in 197. This course examines the Bohr model of the atom, the crucial experiments leading to the formulation of quantum mechanics, fundamental concepts of wave mechanics, use of the Schrödinger equation to describe simple systems including the hydrogen atom, time-independent perturbation theory, the Pauli principle and the construction of the periodic table of the elements, optical spectra of the atoms, angular momentum, and properties of atoms in magnetic fields. S. Coppersmith. Spring.

235. Structure of Matter II: Introductory Quantum Mechanics and Atomic and Molecular Physics. PQ: Phys 234. Topics include spin operators and eigenfunctions, fine structure, nuclear magnetic moments, hyperfine structure, the Pauli exclusion principle, X-ray spectra, radiative transitions, ionic and covalent chemical bonding, van der Waals forces, hybridization, rotational and vibrational states of molecules, and Raman and infrared spectra. J. Harvey. Autumn. L.

236. Structure of Matter III: Solid State Physics. PQ: Phys 235. Topics include crystal structure and crystal binding, Boltzmann, Bose-Einstein, and Fermi-Dirac statistics, lattice vibrations and phonons, liquid helium, the free-electron model of a metal, the nearly free-electron model, semiconductors, and optical properties of solids. D. Grier. Winter. L.

237. Structure of Matter IV: Nuclei and Elementary Particles. PQ: Phys 235. This class covers topics such as nuclear structure, processes of transformation, observables of the nucleus, passage of nuclear radiation through matter, accelerators and detectors, photons, leptons, mesons, and baryons, hadronic interactions, and the weak interaction. J. Rosner. Spring. L.

251. Chaos, Complexity, and Computers (=ComSci 279, Math 292, Phys 251). PQ: One year of calculus and two quarters of physics at any level. Knowledge of computer programming not required. In this course we use the computer to investigate the question of how patterns and complexity arise in nature. The systems studied are drawn from physics, biology, and other areas of science. This course also is intended to be an introduction to the use of computers in the physical sciences. T. Witten. Winter. L.

291-292-293. Bachelor's Thesis. PQ: Open to physics concentrators with fourth-year standing and consent of instructor. Students are required to submit the College Reading and Research Course Form in autumn quarter. Students receive a grade in each quarter of registration: P/F grading in autumn and winter quarters, and letter grading in spring quarter. This year-long sequence of courses is designed to involve the student in current research. Over the course of the year, the student works on a research project in physics or a closely related field, for example, astrophysics, leading to the writing of a bachelor's thesis. A student who submits a satisfactory thesis, earns a grade of B or better based on the project, and achieves a grade point average of 3.0 or higher in the required undergraduate physics courses is awarded a B.A. with honors degree. The project may be one suggested by the instructor or one proposed by the student and approved by the instructor. Most work is done within the research groups of faculty members, but some experimental projects are done in the student project lab. In every case, all phases of the project (including the literature search, design and construction of the experiments, and analysis) must be done by the student. The instructor, faculty adviser, postdocs, and graduate students are, of course, available for consultation. S. Nagel, J. Pilcher. Autumn, Winter, Spring.

297. Participation in Research. PQ: Consent of instructor and departmental counselor. Open to physics concentrators with third- or fourth-year standing. Students are required to submit the College Reading and Research Course Form. Available for either Pass, or for P/N or letter grading with consent of instructor. By mutual agreement, students work in a faculty member's research group. Participation in research may take the form of independent work, with some guidance, on a small project or of assistance in research to an advanced graduate student or research associate. A written report must be submitted at the end of the quarter. Students may register for Phys 297 for as many quarters as they wish; students need not remain with the same faculty member each quarter. Staff. Summer, Autumn, Winter, Spring. L.

311. Introduction to Structured Fluids (=BchMB 321, Phys 311). PQ: Phys 197 or Chem 262. This course presents an overview of the fundamental physical concepts governing the behavior of the major categories of structured fluids: colloids, polymers, and surfactant assemblies. This course discusses how the characteristic spatial dimensions (response times and interaction energies of chain molecules, colloids, and membranes) scale with the number of atoms in these structures. Phys 311 and 312 are intended for students of physical and biological science who wish to understand the statistical-mechanics underlying structure and motion in these liquids. T. Witten. Autumn.

312. Nonlinear Response in Structured Fluids (=BchMB 322, Phys 312). PQ: Phys 197 or Chem 262. May be taken in sequence with Phys 311 or individually. This course explores distinctive responses that can occur when these structures are driven out of thermodynamic equilibrium by, for example, an oscillating electric field or chemical reaction. The focus of this course is the harnessing of free energy. It emphasizes general principles of reaction rate theory and driven diffusion and applies these concepts to study how disequilibrium in such reactions can be made to drive motion of, for example, colloidal particles. Staff. Winter.

316. Advanced Classical Mechanics. PQ: Phys 186. This course begins with variational formulation of classical mechanics of point particles, including discussion of the principle of least action, Poisson brackets, and Hamilton-Jacobi theory. These concepts are generalized to continuous systems with infinite number of degrees of freedom, including a discussion of the transition to quantum mechanics. The course also includes detailed treatment of the theory of classical relativistic fields. Staff. Autumn.

321-322-323. Advanced Electrodynamics and Optics I, II, III. PQ: Phys 227 and 235. Topics include electrostatics boundary-value problems, electrostatics of continuous media, magnetostatics, electromagnetic waves, radiation, relativistic electrodynamics, Lorentz theory of electrons, and theoretical optics. We study the mathematical methods behind the develop-ment of the physics of these problems. Staff. Autumn, Winter, Spring.

331. Mathematical Methods of Physics. PQ: Phys 227. This course is structured to provide mathematical background to complement the regular first-year graduate course content. It deals with complex variables, first- and second-order linear differential equations and their singularities, special functions, and generalized wave and diffusion equations. Included among the topics are eigenvalue problems, Green's functions, integral transforms, asymptotic methods, and perturbation theory. Staff. Winter.

341-342-343. Quantum Mechanics I, II, III. PQ: Phys 235 and Math 273. This course covers wave functions and their physical content, one-dimensional systems, WKB method, operators and matrix mechanics, angular momentum and spin, two- and three-dimensional systems, the Pauli principle, perturbation theory, Born approximation, scattering theory, the Dirac equation, elementary quantum field theory, and Feynman path integrals. Staff. Autumn, Winter, Spring.

352. Statistical Mechanics. PQ: Phys 197 and 341. This course covers principles of statistical mechanics and their applications to physics and chemistry. Staff. Spring.

361. Solid State Physics. PQ: Phys 236, 342, and 352. This course includes an introduction to the one-electron approximation and effective mass concept in solids. Other topics include optical properties of solids, with emphasis on the role of imperfections, ferromagnetism, and transport phenomena. Staff. Autumn.

362. Nuclear Physics. PQ: Phys 237 and 342. Course topics include general nuclear properties, the two-body problem, the symmetry principle, nuclear forces, nuclear reactions, interaction of nuclei with E-M radiation, and beta decay. Staff. Winter.

363. Particle Physics. PQ: Phys 237 and 342. This course covers the following topics: the properties of elementary particles; strong, weak, and electromagnetic interactions; CPT symmetries; SU(3) symmetry; hadronic structure and interactions in terms of quark and gluon substructure; CP violation and KM mixing of quark fields; introduction to electroweak theory; quark and lepton interaction at high energy; current experiments; and detectors in high-energy physics. Staff. Spring.