## Department of Physics

#### Chair

Lyman A. Page Jr.

#### Associate Chair

Steven S. Gubser

Herman L. Verlinde

#### Departmental Representative

Christopher G. Tully

#### Director of Graduate Studies

Herman L. Verlinde

#### Professor

Michael Aizenman, also Mathematics

Robert H. Austin

William Bialek, also Lewis-Sigler Institute for Integrative Genomics

Frank P. Calaprice

Curtis G. Callan Jr.

Cristiano Galbiati

Steven S. Gubser

F. Duncan Haldane

M. Zahid Hasan

David A. Huse

Igor R. Klebanov

Elliott H. Lieb, also Mathematics

Daniel R. Marlow

Kirk T. McDonald

Peter D. Meyers

James D. Olsen

Nai Phuan Ong

Lyman A. Page Jr.

Jason R. Petta

Alexander M. Polyakov

Frans Pretorius

Michael V. Romalis

A. J. Stewart Smith

Shivaji L. Sondhi

Suzanne T. Staggs

Paul J. Steinhardt

Christopher G. Tully

Herman L. Verlinde

Ali Yazdani

#### Associate Professor

Bogdan A. Bernevig

Thomas Gregor, also Lewis-Sigler Institute for Integrative Genomics

Joshua Shaevitz, also Lewis-Sigler Institute for Integrative Genomics

#### Assistant Professor

Waseem S. Bakr

Simone Giombi

William C. Jones

Mariangela Lisanti

Silviu S. Pufu

#### Senior Lecturer

Katerina Visnjic

#### Associated Faculty

Ravindra N. Bhatt, Electrical Engineering

Roberto Car, Chemistry

Garnet Kin-Lic Chan, Chemistry

Mihalis C. Dafermos, Mathematics

Andrew A. Houck, Electrical Engineering

Mansour Shayegan, Electrical Engineering

Yakov G. Sinai, Mathematics

David N. Spergel, Astrophysical Sciences

David W. Tank, Molecular Biology, Princeton Neuroscience Institute

Salvatore Torquato, Chemistry

Ned S. Wingreen, Molecular Biology

#### Information and Departmental Plan of Study

The physics department offers a comprehensive program with the flexibility to accommodate students with a range of interests. Those students wishing to maximize their preparation for graduate school can choose from a variety of advanced-level courses. The requirements of the core curriculum, however, are such that students with diverse interests can take a considerable course load outside the department. Thus, in addition to those students planning to enter graduate school in physics, the department encourages students with career goals in such areas as engineering physics, biophysics, law, medicine, materials science, and teaching.

#### Advanced Placement

An A.B. student who receives a score of 5 on the Physics B Advanced Placement Examination qualifies for two units of advanced placement credit. Any admission to advanced courses is contingent upon approval by the department. Advanced placement credit via the Physics B Advanced Placement Examination does not lead to admission to courses higher than 103.

The Physics C Advanced Placement Examination consists of two parts. A student with a 5 in both Parts I and II will receive two units of advanced placement credit and may, if desired, satisfy the B.S.E. physics requirement at entrance. Students with advanced placement credit who wish to enroll in a physics course usually take 105, but under exceptional circumstances may be eligible to enroll in 205 upon permission of the instructor. They are expected to take 106 in the spring.

#### Prerequisites

Students entering the department are encouraged to complete PHY 205 or 207, and 208 as well as linear algebra and multivariable calculus by the end of their sophomore year (MAT 203-204 is preferred, but MAT 201-202 is adequate). This means that students planning to major in physics should take 103-104 or 105-106 (101-102 may work in special cases) in their first year. The only routes into 200-level physics courses are to fulfill the prerequisites by taking the above-mentioned 100-level physics courses, or to pass the appropriate entrance exams offered at the beginning of the term. Students who do not discover their interest in physics until the sophomore year, and hence have only taken only the introductory-level courses, can still complete the physics program. Such students should meet with the departmental representative as early as possible.

#### Early Concentration

Early concentration enables the qualified student to exploit upperclass courses and independent work more effectively. Early concentration may be accomplished in any of several ways, depending on the particular abilities and background of the individual student. In certain cases a sophomore may be offered an opportunity to undertake independent work during the spring term by writing the first junior paper.

#### Program of Study

The department expects every student majoring in physics to have a basic knowledge of:

1. Mechanics

2. Electromagnetism and wave phenomena

3. Quantum mechanics and its application in simple atomic physics

4. Kinetic theory, thermodynamics, and statistical mechanics

5. Experimental physics

Proficiency in these areas is indicated by the student's performance in the courses listed below, or their equivalents. A physics major would normally take 103-104 (or 105-106), (or 205 or 207), and 208 in the first two years, and 301, 304, 305, and 312 before graduation. The core curriculum should also include at least two 300-level mathematics courses, one of which should stress complex analysis (MAT 330, MAT 335, or MAE 306). The department also offers a pair of optional sophomore seminars (209-210) that give hands-on experience with modern experimental and computational techniques.

Beyond the basic requirements described above, the only specific course requirement is one 300-level or above physics course or an appropriate cognate. In principle, any additional course at the 300 level or above can count as a cognate with the permission of the departmental representative. Students who have completed the basic requirements have a wide variety of options from which to choose. The 400-level physics courses include a sampling of many of the important areas of current research in physics. PHY 405 and 406 are frequent choices and provide the student with a good introduction to condensed matter and subatomic physics, respectively. Courses in astrophysics, biophysics, computer science, engineering, geophysical science, materials science, and mathematics, some of which are cross-listed as physics courses at the 300 or 400 level, are also appropriate areas to be considered depending on the interests of the student. Graduate courses may also be taken with permission from both the instructor and the departmental representative.

Concentrators may not take departmental courses on a pass/D/fail basis except with special permission of the departmental representative.

#### Independent Work

**Junior Year. **In addition to the coursework carried out during the junior year, the student is required to complete two junior papers, each of which is on a research topic of current interest. The purpose of the papers is to give students exposure to how physics research is actually performed by immersing them in journal, as opposed to textbook, literature. Each paper is written in close consultation with a faculty adviser, who is typically performing research in the subject area of the paper. A junior paper may serve as a preliminary investigation of a senior thesis topic.

The department feels strongly that experimental work is an essential ingredient of the undergraduate physics program. Experimental Physics (PHY 312) is therefore required for the physics concentrator. This course is normally taken in the spring term of the junior year, but it may be elected by advanced placement sophomores who have already completed two courses at the 200 level. Junior independent work may also be satisfied with a short experimental project.

**Senior Year. **In the senior year, in addition to coursework, students write a senior thesis based on their own research. The topic might be chosen from one of the active experimental or theoretical research fields of the physics department, or might be suggested by a faculty member with some subsidiary interest. A student could also choose a topic relating physics and another field, such as biophysics, geophysics, the teaching of physics, history of science, or engineering physics. In fact, almost any area connected to a student's interest in physics can generate a thesis topic. Students working in such areas should seek out two advisers: one from the physics faculty and one from the other department of interest. After the thesis has been read by two faculty members, the student takes an oral examination administered by the readers and a member of the senior committee. This examination also serves the role of senior departmental examination.

#### Senior Departmental Examination

As described above, an oral examination based on the student's senior thesis serves as the senior departmental examination.

#### Integrated Science Sequence

An alternative path into the department is through the integrated science curriculum of the Program in Quantitative and Computational Biology (QCB). ISC/CHM/COS/MOL/PHY 231-234 can be taken in the freshman year, instead of PHY 103-104 or PHY 105-106. For full course descriptions and more information, see the integrated science website.

**Certificate Programs in Engineering Physics, Biophysics, and Quantitative and Computational Biology. **For those students with an interest in such topics as solid-state devices, optics, fluid mechanics, engineering design, control theory, computer applications, or other applied disciplines, the Program in Engineering Physics provides an opportunity for close contact with the School of Engineering and Applied Science. Physics students enrolled in this program must take a coordinated program of at least five engineering courses. Upon completion of these courses with a grade average of at least B-, an engineering physics certificate is awarded at graduation. Further information on this program appears in the Program in Engineering Physics section.

The department also offers the opportunity for concentrators to participate in the biophysics certificate program. Interested students should discuss the program with the director and their departmental representative. Upperclass courses taken in the program count as cognates in the Department of Physics.

The Program in Quantitative and Computational Biology is designed for students with a strong interest in multidisciplinary and systems-level approaches to understanding molecular, cellular, and organismal behavior. The required courses provide a strong background in modern methodologies in data analysis, interpretation, and modeling.

**Physics Department Facilities. **The research laboratories in Jadwin Hall (the main physics building) are open to undergraduates to conduct supervised research for their junior papers, senior theses, and summer jobs. There is a "student shop" that offers a (noncredit) course in the use of machine tools. Students with an experimental bent are encouraged to take this course and are then able to participate actively in the construction of experimental apparatus. There is a graduate course in electronics (PHY 557) open to undergraduates that prepares students to design and build the sophisticated electronics required in modern experiments.

### Courses

PHY 101 Introductory Physics I Fall STL

A course in fundamental physics that covers classical mechanics, fluid mechanics, basic thermodynamics, sounds, and waves. Meets premedical requirements. One lecture, three classes, one three-hour laboratory.
* Staff*

PHY 102 Introductory Physics II Spring STL

Continuation of 101. A course in fundamental physics that covers electricity, magnetism, and an introduction to the quantum world. Meets premedical requirements. Two 90-minute lectures, one preceptorial, and one three-hour laboratory.
* Staff*

PHY 103 General Physics I Fall STL

The physical laws that govern the motion of objects, forces, and forms of energy in mechanical systems are studied at an introductory level. Calculus-based, primarily for engineering and science students, meets premedical requirements. Some preparation in physics and calculus is desirable; calculus may be taken concurrently. One demonstration lecture, three classes, one three-hour laboratory.
* Staff*

PHY 104 General Physics II Spring STL

Continuation of 103. Electromagnetism from electrostatics, DC and AC circuits to optics, and topics of modern physics are treated at an introductory level. Some preparation in physics and calculus is desirable; calculus may be taken concurrently. Calculus-based, primarily for engineering and science students, meets premedical requirements. One demonstration lecture, three classes, one three-hour laboratory.
* Staff*

PHY 105 Advanced Physics (Mechanics) Fall STL

This course parallels 103 at a level that assumes a good preparation in physics and calculus. The material is treated in more depth and with more mathematical sophistication than in 103. Students interested in 105 should enroll in 103. After three weeks, the course will reorganize with those students who qualify and are interested in entering 105 for the remainder of the term. Either course can lead to a major in physics. One demonstration lecture, three classes, one three-hour laboratory.
* Staff*

PHY 106 Advanced Physics (Electromagnetism) Spring STL

Parallels 104 at a more sophisticated level, emphasizing the unification of electric and magnetic forces and electromagnetic radiation. To enter this course, students must have done well in 103 or 105. 103 students must attend the lectures on special relativity given in reading period as part of 105. Three lectures, one class, one three-hour laboratory.
* Staff*

PHY 111 Contemporary Physics Not offered this year STL

Designed for students in the humanities and social sciences, the presentation stresses concepts over formulas and intuition over formalism. However, some proficiency in algebra and trigonometry is assumed. Offered both terms, this course does not satisfy requirements for science majors, premedical students, architects, or engineers. Two lectures, one class, one three-hour laboratory.
* Staff*

PHY 115A Physics for Future Leaders (also STC 115A) Fall STN

What do future leaders of our society need to know about physics and technology? The course is designed for non-scientists who will someday become our influential citizens and decision-makers. Whatever the field of endeavor, they will be faced with important decisions in which physics and technology play an important role. The purpose of this course is to present the key principles and the basic physical reasoning needed to interpret scientific and technical information and to make the best decisions. Topics include energy and power, atomic and subatomic matter, wave-like phenomena and light, and Einstein's theory of relativity.
* Staff*

PHY 115B Physics for Future Leaders (also STC 115B) Fall STL

What do future leaders of our society need to know about physics and technology? The course is designed for non-scientists who will someday become our influential citizens and decision-makers. Whatever the field of endeavor, they will be faced with important decisions in which physics and technology play an important role. The purpose of this course is to present the key principles and the basic physical reasoning needed to interpret scientific and technical information and to make the best decisions. Topics include energy and power, atomic and subatomic matter, wave-like phenomena and light, and Einstein's theory of relativity.
* Staff*

PHY 191 An Integrated Introduction to Engineering, Mathematics, Physics (see EGR 191)

PHY 192 An Integrated Introduction to Engineering, Mathematics, Physics (see EGR 192)

PHY 203 Classical Mechanics A Not offered this year STN

Classical mechanics, with emphasis on the Lagrangian method. The underlying physics is Newtonian, but with more sophisticated mathematics introduced as needed to understand more complex phenomena. Topics include the formalism of Lagrangian mechanics, central-force motion, small oscillations, coupled oscillations, and waves. The course differs from 205 in that it assumes less preparation, omitting some material in favor of a more pedagogical treatment of the ideas and techniques needed for 208. Prerequisites: 103-104, or 105-106, or permission of instructor; MAT 201 or 203 recommended. Two 90-minute lectures.
* Staff*

PHY 205 Classical Mechanics B Fall STN

Classical mechanics, with emphasis on the Lagrangian method. The underlying physics is Newtonian, but with more sophisticated mathematics introduced as needed to understand more complex phenomena. Topics in this intensive course include the formalism of Lagrangian mechanics, central-force motion and scattering, rigid body motion and noninertial forces, small oscillations, coupled oscillations, and waves. Prerequisite: 103-104, or 105-106 (recommended), or permission of instructor; prior completion of MAT 201 or 203 recommended. Two 90-minute lectures.
* Staff*

PHY 207 Mechanics and Waves Fall STN

Covers the basics of analytical mechanics, but shifts the emphasis to wave phenomena before moving on to aspects of quantum mechanics and quantum statistical mechanics. Special relativity is given greater weight than it usually is in PHY 205. Offers students a path toward the physics concentration that is less intensive than PHY 205 and more accessible to students with less mathematical background. Prerequisites: PHY103-104, or PHY105-106; one 200-level math course; or permission of instructor. Two 90-minute lectures.
* Staff*

PHY 208 Principles of Quantum Mechanics Spring STN

An introduction to quantum mechanics, the physics of atoms, electrons, photons, and other elementary particles. Topics include state functions and the probability interpretation, the Schrödinger equation, the uncertainty principle, the eigenvalue problem, operators and their algebras, angular momentum and spin, perturbation theory, and the hydrogen atom. Prerequisites: PHY 106, PHY 205, or PHY 207 and MAT 203 or MAT 217, and MAT 204 or MAT 218 (MAT 204/MAT 218 can be taken concurrently); or instructor's permission. Two 90-minute lectures.
* Staff*

PHY 209 Computational Physics Seminar Fall STL

Introductory course in the application of computers to physics research. Two main themes are numerical analysis methods and the computer-based techniques for implementing them. Methods discussed include least-squares fitting, numerical integration, and Monte Carlo simulation. Techniques include scientific programming, spreadsheets, symbolic-manipulation programs, statistical and plotting packages, and computer graphics. Examples are drawn from various fields of physics, including elementary particle physics and astrophysics. Prerequisites: 104 or 106 or permission of instructor. One 90-minute seminar, one three-hour laboratory.
* Staff*

PHY 210 Experimental Physics Seminar Spring STL

This seminar introduces students to the basic techniques of electronics and instrumentation used to conduct experiments in the physical sciences. The course begins by teaching a foundation in analog and digital circuits including programmable digital logic devices using an iPad interface for data acquisition. Students develop measurement techniques in a wide range of experimental areas. Prerequisites: PHY 102, 104, 106 or 304. One three-hour seminar.
* Staff*

PHY 231 An Integrated, Quantitative Introduction to the Natural Sciences I (see ISC 231)

PHY 232 An Integrated, Quantitative Introduction to the Natural Sciences I (see ISC 232)

PHY 233 An Integrated, Quantitative Introduction to the Natural Sciences II (see ISC 233)

PHY 234 An Integrated, Quantitative Introduction to the Natural Sciences II (see ISC 234)

PHY 235 An Integrated, Quantitative Approach to Biochemistry and Neuroscience (see ISC 235)

PHY 236 An integrated, Quantitative Approach to Genetics and Genomics (see ISC 236)

PHY 301 Thermal Physics Fall STN

A unified introduction to the physics of systems with many degrees of freedom: thermodynamics and statistical mechanics, both classical and quantum. Applications will include phase equilibrium, classical and quantum gases, and properties of solids. Three lectures. Prerequisites: Any one of PHY 106, 205, 207 or 208, or instructor's permission.
* Staff*

PHY 304 Advanced Electromagnetism Spring STN

Extensions of electromagnetic theory including some important applications of Maxwell's equations. Solutions to Laplace's equation--boundary value problems. Retarded potentials. Electromagnetic waves and radiation. Special relativity. Mathematical tools developed as required. Two 90-minute lectures. Prerequisites: 104 or 106.
* Staff*

PHY 305 Introduction to the Quantum Theory Fall STN

A second course on the basic principles of quantum mechanics with emphasis on applications to problems from atomic and solid-state physics. Two 90-minute lectures. Prerequisites: 208.
* Staff*

PHY 309 Science and Technology of Nuclear Energy: Fission and Fusion (see AST 309)

PHY 312 Experimental Physics Spring STL

The course offers six different experiments from the advanced laboratory collection. Experiments include Josephson effect, ß-decay, holography, Mössbauer spectroscopy, optical pumping. Lectures stress modern experimental methods and devices. One lecture, one laboratory.
* Staff*

PHY 321 General Relativity (see AST 301)

PHY 371 Global Geophysics (see GEO 371)

PHY 401 Cosmology (see AST 401)

PHY 402 Stars and Star Formation (see AST 403)

PHY 403 Mathematical Methods of Physics (also MAT 493) Not offered this year QR

Mathematical methods and techniques that are essential for modern theoretical physics. Topics such as group theory, Lie algebras, and differential geometry are discussed and applied to concrete physical problems. Special attention will be given to mathematical techniques that originated in physics, such as functional integration and current algebras. Three classes. Prerequisite: MAT 330 or instructor's permission.
* Staff*

PHY 404 Selected Topics in Condensed Matter Theory

This course serves as an introduction to the rapidly growing field of topological insulators and superconductors. The course will present old topics such as band theory, insulators, metals, ferromagnets, superconductors, but emphasis will be on the new topological phenomena that these systems are now known to harbor. Many experts in this field are home-grown on Princeton soil, and this course provides a unique opportunity for students to interact with them. There are ample opportunities for research in both theory and experiments.
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B. Bernevig*

PHY 405 Modern Physics I: Condensed-Matter Physics Spring STN

An introduction to modern condensed-matter physics, this course builds on quantum and statistical mechanics to study the electronic properties of solids, including band theory. Metals, quantum Hall effects, semiconductors, superconductors and magnetism, as well as phase transitions in condensed systems and structure and dynamic of solids and liquid crystals. Two 90-minute lectures. Prerequisites: PHY 208, PHY 301, and PHY 305.
* Staff*

PHY 406 Modern Physics II: Nuclear and Elementary Particle Physics Fall STN

The basic features of nuclear and elementary particle physics are described and interpreted, primarily in the context of the "Standard Model." Problems of current interest are discussed. Two 90-minute lectures.
* Staff*

PHY 408 Modern Classical Dynamics Spring STN

The course discusses some of the most important and beautiful phenomena described by classical dynamics. This includes generalized Hamiltonian systems and variational principles, shock waves propagation, gravitational instabilities, simple solitons and vortices plus elementary exposition of the theories of turbulence and period doubling. Two 90-minute lectures. Prerequisite: PHY 205 or 207.
* Staff*

PHY 419 Physics and Chemistry of Earth's Interior (see GEO 419)

PHY 442 Geodynamics (see GEO 442)