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 BA in physics includes a strong emphasis on 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 requiring a strong technical background (e.g., biophysics, medical physics, atmospheric and environmental sciences).

Students who are majoring in other fields of study may also complete a minor in physics. Information follows the description of the major.

The curriculum leading to the BA degree in physics is designed for maximum flexibility consistent with a thorough coverage of the essential principles of physics. Degree requirements include introductory and advanced physics and mathematics courses, as well as physics electives that allow students to pursue specific interests. Students intending to pursue graduate work in astrophysics should consider the program leading to a BA in physics with a specialization in astrophysics, which is described later.

Students who plan to major in physics are encouraged to start course work in their first year. However, the program can be completed in three years, so one could start physics in the second year without delaying graduation. Two of the physics and two of the mathematics courses can be designated as general education courses, with fifteen courses remaining to fulfill the major.

In general, students should take the most advanced courses for which they have the appropriate prerequisites. Entering students will be given a placement for either PHYS 13100 Mechanics or PHYS 14100 Honors Mechanics based on their mathematics and physics background. Students majoring in physics usually start their program with the honors sequence PHYS 14100-PHYS 14200-PHYS 14300; however, the PHYS 13100-PHYS 13200-PHYS 13300 sequence is an equally acceptable pathway to the degree.

In addition to specified course work, the physics major requires three electives. These electives may be selected from the following courses:

The sample programs below illustrate different paths for fulfilling requirements for the physics major. Electives are indicated by an asterisk (*).

In the following example, an Analysis sequence partially satisfies the physics elective requirements, while preserving the option of a second major in math. (If Analysis replaces PHYS 22100, then an additional elective must be taken.) The optional PHYS 29100-PHYS 29200-PHYS 29300 sequence allows for completion of a bachelor's thesis.

Progress through the physics program can be accelerated by "doubling up" on some of the required courses. For example, PHYS 23500 and PHYS 19700 may be taken concurrently in the third year, and PHYS 22500/PHYS 22700 may be concurrent with PHYS 18500/PHYS 23400 in the second year. This provides more options in the third and fourth year for electives (as well as research or graduate course work). Note that it is possible to complete all program requirements in three years.

Finally, the sample programs shown here are only meant to be illustrative. Students are encouraged to speak with the departmental counselors in planning individual programs, especially regarding selection of mathematics courses and program electives.

Students who took the Physics C Advanced Placement examinations prior to matriculation in the College may receive credit for some or all of PHYS 12100-PHYS 12200-PHYS 12300. Consult the section on Advanced Placement Credit in this catalog for more information.

All regular (nonresearch) physics courses must be taken for quality grades. All courses used to satisfy prerequisites must be taken for quality grades. The Department of Physics requires students to pass PHYS 13100-PHYS 13200-PHYS 13300/PHYS 14100-PHYS 14200-PHYS 14300, PHYS 15400, PHYS 18500, and PHYS 23400 with an average of 2.0 or higher to continue in the program.

The physics program offers unique opportunities for College students to become actively involved in the research being conducted by faculty of the department. Interested students are welcome to consult with the departmental counselors. The focus of much of the undergraduate research is structured around the Bachelor's Thesis (PHYS 29100-PHYS 29200-PHYS 29300). Alternatively, third- or fourth-year students majoring in physics may register for research for academic credit (PHYS 29700). In addition to these formal arrangements, students at any level may become involved in research by working in a faculty member's lab or research group on an extracurricular basis.

There are two routes to receiving a BA with honors. Both require a minimum GPA of 3.0 in the courses listed under Major in the preceding Summary of Requirements section. In the first route, the student must pass an approved sequence of three graduate courses, with a grade of B or higher in each. The recommended 30000-level sequence typically is PHYS 34100-PHYS 34200 and PHYS 35200; however, if approval is obtained from the program chair, this sequence may be replaced by another sequence of graduate courses. The second route to receiving a BA with honors is to register for PHYS 29100-PHYS 29200-PHYS 29300 and earn a grade of B or higher based on a bachelor's thesis describing an approved research project completed during the year.

The program leading to a BA in physics with a specialization in astrophysics is a variant of the BA 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 BA degree in physics, plus a two-quarter sequence in astrophysics (ASTR 24100 and ASTR 24200), plus either a third course in astrophysics (ASTR 28200 or ASTR 30500) or a senior thesis project in physics (PHYS 29100-PHYS 29200-PHYS 29300) on a topic in astrophysics. If the latter option is chosen, the thesis topic must be approved by the program chair. (This thesis may simultaneously fulfill part of the requirements for honors in physics.) A grade of at least *C-* must be obtained in each course.

The minor in physics is designed to present a coherent program of study to students with a strong interest in physics but insufficient time to pursue the major. The courses required for the minor are:

The mathematics requirement for the minor is identical to the requirement for the major; please consult the description of the major for more information, particularly regarding MATH 22000 and PHYS 22100. Note that MATH 22000 and PHYS 22100 may be replaced by equivalent courses, as approved by the undergraduate program chair. Note also that the PHYS 13300/PHYS 14300, PHYS 22100, and MATH 15300/MATH 16300/MATH 22000 requirements will be waived for those who must take these courses to satisfy the requirements of a major or another minor. Consequently, the number of additional courses needed for the minor will vary between five and eight.

Students who elect the minor program in physics must meet with the physics undergraduate program chair before the end of Spring Quarter of their third year to declare their intention to complete the minor. The approval of the program chair for the minor program should be submitted to a student's College adviser by the deadline above on a form obtained from the College adviser. Courses for the minor are chosen in consultation with the program chair.

Courses in the minor (1) may not be double counted with the student's major(s) or with other minors and (2) may not be counted toward general education requirements. Courses in the minor must be taken for quality grades, and students must have a GPA of 2.0 or higher in the minor. More than half of the requirements for the minor must be met by registering for courses bearing University of Chicago course numbers.

### Physics Courses

**PHYS 12100-12200-12300. General Physics I-II-III.**

This is a one-year sequence in the fundamentals of physics. Topics include classical mechanics, fluids, electricity and magnetism, wave motion, optics, and modern physics. Where appropriate, attention will be drawn to interdisciplinary applications, such as in biology. Calculus is used as needed. The first two courses meet the general education requirement in physical sciences. (L)

**PHYS 12100. General Physics I. 100 Units.**

Terms Offered: Autumn

Prerequisite(s): MATH 13100-13200-13300 or 15100-15200-15300 or 16100-16200-16300, and second-year standing.

**PHYS 12200. General Physics II. 100 Units.**

Terms Offered: Winter

Prerequisite(s): PHYS 12100

**PHYS 12300. General Physics III. 100 Units.**

Terms Offered: Spring

Prerequisite(s): PHYS 12200

**PHYS 13100-13200-13300. Mechanics; Electricity and Magnetism; Waves, Optics, and Heat.**

This is a one-year introductory sequence in physics for students in the physical sciences. Univariable calculus is used extensively. The first two courses meet the general education requirement in physical sciences. (L)

**PHYS 13100. Mechanics. 100 Units.**

Topics include particle motion, Newton's Laws, work and energy, systems of particles, rigid-body motion, gravitation, oscillations, and special relativity. (L)

Terms Offered: Autumn

Prerequisite(s): MATH 13100-13200-13300 or 15100-15200-15300 or 16100-16200-16300. (MATH 15100-15200-15300 or 16100-16200-16300 may be taken concurrently.)

**PHYS 13200. Electricity and Magnetism. 100 Units.**

Topics include electric fields, Gauss’ law, electric potential, capacitors, DC circuits, magnetic fields, Ampere's law, induction, Faraday's law, AC circuits, Maxwell's equations, and electromagnetic waves. (L)

Terms Offered: Winter

Prerequisite(s): PHYS 13100 or 14100

**PHYS 13300. Waves, Optics, and Heat. 100 Units.**

Topics include mechanical waves, sound, light, polarization, reflection and refraction, interference, diffraction, geometrical optics, heat, kinetic theory, and thermodynamics. (L)

Terms Offered: Spring

Prerequisite(s): PHYS 13200 or 14200

**PHYS 14100-14200-14300. Honors Mechanics; Honors Electricity and Magnetism; Honors Waves, Optics, and Heat.**

This is a one-year introductory sequence in physics for students in the physical sciences. A strong background in univariable calculus is assumed. Multivariable and vector calculus will be introduced and used extensively. The first two courses meet the general education requirement in physical sciences. (L)

**PHYS 14100. Honors Mechanics. 100 Units.**

Topics include particle motion, Newton's Laws, work and energy, systems of particles, rigid-body motion, gravitation, oscillations, and special relativity. (L)

Terms Offered: Autumn

Prerequisite(s): MATH 13100-13200-13300 or 15100-15200-15300 or 16100-16200-16300. (MATH 15100-15200-15300 or 16100-16200-16300 may be taken concurrently.)

**PHYS 14200. Honors Electricity and Magnetism. 100 Units.**

Topics include electric fields, Gauss’ law, electric potential, capacitors, DC circuits, magnetic fields, Ampere's law, induction, Faraday's law, AC circuits, Maxwell's equations, and electromagnetic waves. (L)

Terms Offered: Winter

Prerequisite(s): PHYS 14100

**PHYS 14300. Honors Waves, Optics, and Heat. 100 Units.**

Topics include mechanical waves, sound, light, polarization, reflection and refraction, interference, diffraction, geometrical optics, heat, kinetic theory, and thermodynamics. (L)

Terms Offered: Spring

Prerequisite(s): PHYS 14200

**PHYS 15400. Modern Physics. 100 Units.**

This course is an introduction to quantum physics. Topics include Einstein's quantum theory of light, the wave nature of particles, atomic structure, the Schrödinger equation, quantum mechanics in one and three dimensions, barrier penetration and tunneling, and the hydrogen atom. Applications to nuclear and solid-state physics are presented. (L)

Terms Offered: Autumn

Prerequisite(s): PHYS 14300, or PHYS 13300 and MATH 22000

**PHYS 18500. Intermediate Mechanics. 100 Units.**

Topics include a review of Newtonian mechanics, the calculus of variations, Lagrangian and Hamiltonian mechanics, generalized coordinates, canonical momenta, phase space, constrained systems, central-force motion, non-inertial reference frames, and rigid-body motion.

Terms Offered: Winter

Prerequisite(s): PHYS 13100 or 14100, and PHYS 22100 or MATH 20300

**PHYS 19700. Statistical and Thermal Physics. 100 Units.**

This course develops a statistical description of physical systems. Topics include elements of probability theory, equilibrium and fluctuations, thermodynamics, canonical ensembles, the equipartition theorem, quantum statistics of ideal gases, and kinetic theory.

Terms Offered: Autumn

Prerequisite(s): PHYS 23400, and PHYS 22100 or MATH 20500

**PHYS 21101-21102-21103. Experimental Physics I-II-III.**

This is a year-long laboratory sequence, offering experiments in atomic, molecular, solid-state, nuclear, and particle physics. Additional material, as needed, is presented in supplemental lectures. Content varies from quarter to quarter. P/F grading in Autumn. (L)

Note(s): Open only to students who are majoring in Physics.

**PHYS 21101. Experimental Physics I. 000 Units.**

Terms Offered: Autumn

Prerequisite(s): PHYS 23400

**PHYS 21102. Experimental Physics II. 100 Units.**

Terms Offered: Winter

Prerequisite(s): PHYS 21101

**PHYS 21103. Experimental Physics III. 100 Units.**

Terms Offered: Spring

Prerequisite(s): PHYS 21101

**PHYS 22100. Mathematical Methods in Physics. 100 Units.**

Topics include linear algebra and tensor analysis, ordinary and partial differential equations, calculus of variations, special functions, series solutions of differential equations, and integral transforms.

Terms Offered: Autumn

Prerequisite(s): PHYS 14300, or PHYS 13300 and MATH 22000

**PHYS 22500-22700. Intermediate Electricity and Magnetism I-II.**

Topics include electrostatics, magnetostatics, electromagnetic induction, electric and magnetic fields in matter, plane electromagnetic waves, reflection and refraction of electromagnetic waves, and electromagnetic radiation.

**PHYS 22500. Intermediate Electricity and Magnetism I. 100 Units.**

Terms Offered: Winter

Prerequisite(s): PHYS 13200 or 14200, and PHYS 22100 or MATH 20300

**PHYS 22700. Intermediate Electricity and Magnetism II. 100 Units.**

Terms Offered: Spring

Prerequisite(s): PHYS 22500

**PHYS 22600. Electronics. 100 Units.**

The goal of this hands-on experimental course is 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, we 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. (L)

Terms Offered: Spring

Prerequisite(s): PHYS 12200 or 13200 or 14200

**PHYS 23400-23500. Quantum Mechanics I-II.**

Quantum Mechanics I-II

**PHYS 23400. Quantum Mechanics I. 100 Units.**

A study of wave-particle duality leading to the basic postulates of quantum mechanics is presented. Topics include the uncertainty principle, applications of the Schrödinger equation in one and three dimensions, the quantum harmonic oscillator, rotational invariance and angular momentum, the hydrogen atom, and spin.

Terms Offered: Spring

Prerequisite(s): PHYS 15400, and PHYS 22100 or MATH 20400

**PHYS 23500. Quantum Mechanics II. 100 Units.**

A review of quantum mechanics is presented, with emphasis on Hilbert space, observables, and eigenstates. Topics include spin and angular momentum, time-independent perturbation theory, fine and hyperfine structure of hydrogen, the Zeeman and Stark effects, many-electron atoms, molecules, the Pauli exclusion principle, and radiative transitions.

Terms Offered: Autumn

Prerequisite(s): PHYS 23400

**PHYS 23600. Solid State Physics. 100 Units.**

Topics include a review of quantum statistics, crystal structure and crystal binding, lattice vibrations and phonons, liquid helium, the free-electron model of metals, the nearly-free-electron model, semi-conductors, and optical properties of solids.

Terms Offered: Winter

Prerequisite(s): PHYS 23500 and 19700

**PHYS 23700. Nuclei and Elementary Particles. 100 Units.**

This course 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.

Terms Offered: Spring

Prerequisite(s): PHYS 23500

**PHYS 23800. Modern Atomic Physics. 100 Units.**

This course is an introduction to modern atomic physics. Topics to be covered include atomic structure, fundamental symmetries in atoms, interactions of atoms with radiation, laser spectroscopy, trapping and cooling, Bose-Einstein condensates, and quantum information.

Terms Offered: Autumn

Prerequisite(s): PHYS 23500

**PHYS 24300. Advanced Quantum Mechanics. 100 Units.**

This course will include topics not normally covered in PHYS 23400-23500. Topics may include the following: symmetry in quantum mechanics; quantum mechanics and electromagnetism; adiabatic approximation and Berry phase; path integral formulation; scattering.

Terms Offered: Winter

Prerequisite(s): A grade of B or higher in PHYS 23500 or permission of the instructor

Note(s): This course cannot be used as an elective for the major. PHYS 24300-44300-44400 can be used as a graduate course sequence for Honors.

**PHYS 24600. Topics in Solid State Physics. 100 Units.**

Recent developments in condensed matter physics will be covered. Topics include superconductivity, magnetism, quantum Hall effect, mesoscopic and nanoscale systems, and topological materials.

Instructor(s): Staff Terms Offered: Spring

Prerequisite(s): Phys 23600

**PHYS 25000. Computational Physics. 100 Units.**

This course introduces the use of computers in the physical sciences. After an introduction to programming basics, we cover numerical solutions to fundamental types of problems, techniques for manipulating large data sets, and computer simulations of complex systems. Additional topics may include an introduction to graphical programming, with applications to data acquisition and device control. (L)

Terms Offered: Autumn

Prerequisite(s): PHYS 13300 or 14300 required; knowledge of computer programming not required

**PHYS 26400. Spacetime and Black Holes. 100 Units.**

This course introduces general relativity. After a review of special relativity and four-dimensional spacetime, the basic tools of physics in a curved spacetime are introduced. The Schwarzschild solution describing both black holes and the exteriors of stars and planets is presented, and the behavior of objects in a Schwarzschild spacetime is extensively studied. The course concludes by introducing the dynamical equations relating energy and momentum to spacetime curvature (Einstein's equations).

Terms Offered: Autumn

Prerequisite(s): PHYS 18500, and PHYS 22100 or MATH 20400 or consent of instructor

**PHYS 29100-29200-29300. Bachelor's Thesis.**

This yearlong 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 (e.g., astrophysics) leading to the writing of a bachelor’s thesis. A student who submits a satisfactory thesis, earns a grade of B or higher based on the project, and achieves a GPA of 3.0 or higher in the required undergraduate physics courses is eligible to receive a BA with honors. The project may be one suggested by the instructor or one proposed by the student and approved by the instructor. In either 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, the faculty adviser, post-docs, and graduate students are, of course, available for consultation.

**PHYS 29100. Bachelor's Thesis. 100 Units.**

Terms Offered: Autumn

Prerequisite(s): Open to students who are majoring in Physics with fourth-year standing and consent of instructor.

Note(s): 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 a quality grade in Spring Quarter.

**PHYS 29200. Bachelor's Thesis. 100 Units.**

Terms Offered: Winter

Prerequisite(s): PHYS 29100

Note(s): 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 a quality grade in Spring Quarter.

**PHYS 29300. Bachelor's Thesis. 100 Units.**

Terms Offered: Spring

Prerequisite(s): PHYS 29200

Note(s): 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 a quality grade in Spring Quarter.

**PHYS 29700. Participation in Research. 100 Units.**

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 29700 for as many quarters as they wish; students need not remain with the same faculty member each quarter. (L)

Terms Offered: Autumn, Winter, Spring, Summer

Prerequisite(s): Consent of instructor and departmental counselor. Open to students who are majoring in Physics with third- or fourth-year standing.

Note(s): Students are required to submit the College Reading and Research Course Form. May be taken for P/F grading with consent of instructor.