Physics Jump To: Jump To: Program Offerings A.B. Offering type A.B. 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 majors with career goals in such areas as engineering physics, law, medicine, materials science and teaching. Goals for Student Learning As a discipline, physics addresses the material Universe at its most fundamental level. A surprisingly small number of physical laws are sufficient to describe natural phenomena from subatomic to cosmological scales. The goals of physics are to push to ever deeper levels of understanding of the physical world, and to push upward, extending our understanding to more complicated systems, including molecules, fluids, solids, galaxies and living things.Majoring in physics will not only teach you about the structure of physical law; it will allow you to take part in its discovery. In the process you will acquire universally valuable skills, including analytic problem-solving, methods of estimation and approximation, and reasoning both inductively and from first principles. Furthermore, you will build your intuition for how the physical world works, from electricity, the phases of matter, forms of energy, to the quantum realm.Physics majors are prepared not only for a career in physics, but many other fields as well. Physics alumni may be found in academic and industrial physics research positions as well as consulting, medicine, law, teaching, biotechnology, university leadership and engineering.A unique aspect of your experience at Princeton is the degree of involvement in contemporary physics through your own independent research. Each of two junior papers provides an opportunity to explore, in depth, an active area of current research.The senior thesis is the capstone of the physics major and an opportunity for intellectual exploration broader than courses can afford. It is a year-long collaboration with a faculty member that is intended to actually contribute to current research in an area that is of greatest interest to you. Whether your thesis is on gravity and cosmology, condensed matter or string theory, it invariably represents your highest effort to come to grips with science as a living, breathing subject. Advanced Placement Students can take requirement fulfillment exams administered by the physics department to satisfy the basic physics requirements of the biological sciences (PHY 101-102) or SEAS (PHY 103-104). Passing the department-administered exams is the only way to receive advanced placement, although these will not satisfy the prerequisite requirements for any 200-level physics course. A separate exam is offered to place into PHY 207, which does serve to fulfill the departmental and course prerequisite requirements of the PHY 103/104 and PHY 105/106 course sequences. Prerequisites Prerequisites for a major in physics are the following five courses: PHY 103-104, PHY 207, and MAT 201-202 or 203-204. These five courses should be completed by the end of sophomore year. PHY 103 may be replaced by PHY 105. PHY 104 may be replaced by PHY 106. The PHY 109/110 (spring/summer) sequence is fully equivalent to PHY 104. Students with a particular interest in formal mathematics may instead satisfy the MAT 203-204 prerequisite with either the MAT 215-217 or the MAT 216-218 sequence. Prerequisites for majoring in physics cannot be taken on a pass/D/fail basis.It is possible to major in physics starting with 100-level physics courses in sophomore year. Interested students should meet with the director of undergraduate studies as early as possible. Program of Study Upon completion of the prerequisites described above, courses required for majoring in physics are as follows:One semester of quantum mechanics: PHY 208.One semester of thermodynamics and statistical mechanics: PHY 301.One semester of experimental physics: PHY 312.One course on complex analysis or on differential equations chosen from the following list: APC 350MAE 305MAE 306MAT 330MAT 335MAT 427One additional course in physics (not including cross-lists) at the 300 level or above.One additional course in physics at the 300 level or above, including cross-lists.One additional course in either physics or math at the 300 level or above, including cross-lists.One elective course at the 300 level or higher, as detailed below.All eight courses must be taken for a letter grade, not pass/D/fail. Note that this excludes any pass/D/fail–only courses from counting as one of the eight.The elective course can be any physics department course (including cross-lists) at 300 level or above. 400-level physics courses are particularly recommended. Courses in astrophysics, biology, chemistry, computer science, engineering, geophysical science, materials science, plasma physics and mathematics may also be appropriate, depending on the interests of the student. Courses from these departments may be approved on a case-by-case basis by the director of undergraduate studies. Graduate courses may also be taken with permission from both the instructor and the director of undergraduate studies. Independent Work Early Major Students who complete the prerequisites for the major before the end of sophomore year may declare an early major in physics. They may be offered an opportunity to undertake independent work during the spring term by writing the first junior paper. Students interested in this option must do so with the advice and consent of the physics department and the residential college director of studies.Junior YearIn addition to the coursework carried out during 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. Junior independent work may also be satisfied with a short experimental project.Senior YearIn 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 to physics and another field, such as geophysics, the teaching of physics, history of science or engineering physics. Students whose main adviser is outside the physics department must also have a co-adviser who is a faculty member in the physics department. Senior Departmental Examination An oral examination conducted by a departmental committee at the end of senior year serves as the senior departmental examination. Additional Information Physics Department FacilitiesThe 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 are graduate courses in electronics (PHY 557 and PHY 558) open to undergraduates that prepare students to design and build the sophisticated electronics required in modern experiments. Certificate ProgramsFor 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. Specific requirements for the engineering physics certificate can be found in the section of this announcement on the Program in Engineering 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. Faculty Chair James D. Olsen Associate Chair Waseem S. Bakr Simone Giombi Director of Undergraduate Studies Waseem S. Bakr Director of Graduate Studies Simone Giombi Professor Dmitry Abanin Michael Aizenman Robert H. Austin Waseem S. Bakr Bogdan A. Bernevig William Bialek Jo Dunkley Cristiano Galbiati Simone Giombi Thomas Gregor Frederick D. Haldane M. Zahid Hasan David A. Huse William C. Jones Igor R. Klebanov Mariangela Lisanti Daniel R. Marlow James D. Olsen Nai Phuan Ong Lyman A. Page Frans Pretorius Silviu S. Pufu Michael V. Romalis Shinsei Ryu Peter Schiffer Joshua W. Shaevitz Suzanne T. Staggs Paul J. Steinhardt Christopher G. Tully Herman L. Verlinde Ali Yazdani Associate Professor Andrew M. Leifer Assistant Professor Saptarshi Chaudhuri Lawrence W. Cheuk Biao Lian Isobel R. Ojalvo Gautam Reddy Sanfeng Wu Associated Faculty Ravindra N. Bhatt, Electrical & Comp Engineering Roberto Car, Chemistry Mihalis Dafermos, Mathematics Andrew A. Houck, Electrical & Comp Engineering Leslie M. Schoop, Chemistry Mansour Shayegan, Electrical & Comp Engineering David N. Spergel, Astrophysical Sciences David W. Tank, Princeton Neuroscience Inst Jeffrey D. Thompson, Electrical & Comp Engineering Salvatore Torquato, Chemistry Ned S. Wingreen, Molecular Biology Nathalie P. de Leon, Electrical & Comp Engineering Professor Emeritus (teaching) Peter D. Meyers Senior Lecturer Grace Bosse Katerina Visnjic Lecturer Steven J. Benton Justin G. DeZoort Aurelien A. Fraisse Norman C. Jarosik Shengkai Li Katharine Moran Jason L. Puchalla Andi Tan Visiting Lecturer with Rank of Professor Stephen L. Adler Nima Arkani-Hamed Juan M. Maldacena Nathan Seiberg For a full list of faculty members and fellows please visit the department or program website. Courses PHY 101 - Introductory Physics I Fall SEL 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 SEL 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 SEL 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 SEL 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 SEL PHY105 is an advanced first year course in classical mechanics, taught at a more sophisticated level than PHY103. Care is taken to make the course mathematically self contained, and accessible to the motivated physics student who may not have had exposure to an introductory college level physics course. The approach of PHY105 is that of an upper-division physics course, with more emphasis on the underlying formal structure of physics than PHY103, including an introduction to modern variational methods (Lagrangian dynamics), with challenging problem sets due each week and a mini-course in Special Relativity held over reading period. Staff PHY 106 - Advanced Physics (Electromagnetism) Spring SEL 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 108 - Physics for the Life Sciences SEL A new one semester physics course designed specifically for life science majors. Selected topics in physical theory and experiment will be presented and highlighted using a range of examples. J. Puchalla PHY 115A - Physics for Future Leaders (also STC 115A) Fall SEN 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 SEL 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 205 - Classical Mechanics Not offered this year SEN 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 - From Classical to Quantum Mechanics Fall SEN 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 SEN 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 SEL Introduction to Python coding and its application to data collection, analysis and statistical inference. The course consists of weekly hands-on labs that introduce the students to the Linux coding environment with Jupyter and Python modules. Labs involve configuring a Raspberry Pi to interface with hardware sensors to collect interrupt-driven measurements. Multivariate discriminators and confidence levels for hypothesis testing will be applied to data samples. Labs are drawn from different forms of sensors data from accelerometers and photodetectors to external sources including radio-astronomy and XRF analysis of Art Museum paintings. Staff PHY 210 - Experimental Physics Seminar Spring SEL This seminar introduces fundamental techniques of electronics and instrumentation. The course consists of weekly hands-on labs that introduce the students to the fascinating world of electronics. We begin with learning how to build circuits and probe their behavior and then explore what can be done to create instrumentation and make measurements. We start with analog electronics and then proceed with programmable digital logic with FPGAs. The final project involves Machine Learning implemented in FPGAs, a glimpse of what modern electronics can do. Staff PHY 301 - Thermal Physics Fall SEN 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 SEN 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 SEN 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 312 - Experimental Physics Fall/Spring SEL 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 403 - Mathematical Methods of Physics (also MAT 493) Not offered this year QCR 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 405 - Modern Physics I: Condensed-Matter Physics Not offered this year SEN 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 Not offered this year SEN 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 Fall SEN 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 AST 301 - General Relativity (also PHY 321) Not offered this year SEN This is an introductory course in general relativity for undergraduates. Topics include the early universe, black holes, cosmic strings, worm holes, and time travel. Designed for science and engineering majors. Two 90-minute lectures. Prerequisites: MAT 201 and 202, OR MAT 203 and 204. Also PHY 205 or 207. PHY 304 is recommended. J. Goodman AST 309 - The Science of Fission and Fusion Energy (also ENE 309/MAE 309/PHY 309) Spring SEN We develop the scientific ideas behind fission and fusion energy. For fission we move from elementary nuclear physics to calculations of chain reactions, understanding how both reactors and nuclear weapons work. We examine safety and waste concerns, as well as nuclear proliferation. We look at new reactor concepts. For fusion we address the physics of confining hot, ionized gases, called plasmas. We address the control of large-scale instabilities and small-scale turbulence. We examine progress and prospects, as well as challenges, for the development of economically attractive fusion power. R. Goldston AST 401 - Cosmology (also PHY 401) Not offered this year QCR or SEN Topics include the properties and nature of galaxies, quasars, clusters, superclusters, the large-scale structure of the universe, dark matter, dark energy, the formation and evolution of galaxies and other structures, microwave background radiation, and the evolution of the universe from the Big Bang to today. Two 90-minute lectures. Prerequisites: MAT 201, 202; PHY 207, 208. Designed for science and engineering majors. N. Bahcall AST 403 - Stars and Star Formation (also PHY 402) Spring SEN Stars form from the interstellar medium (ISM), and the nuclear fusion that powers stars is also the main energy source in the ISM. This course discusses the structure and evolution of the ISM and stars. Topics include: physical properties and methods for studying ionized, atomic, and molecular gas in the ISM; dynamics of magnetized gas flows and turbulence; gravitational collapse and star formation; structure of stellar interiors; radiation transport; production of energy by nucleosynthesis; stellar evolution and end states; effects of stars on interstellar environment. Prerequisites: MAT 201, 202; PHY 208, 301 or permission of instructor. E. Ostriker EGR 191 - An Integrated Introduction to Engineering, Mathematics, Physics (also MAT 191/PHY 191) Not offered this year SEL Taken concurrently with EGR/MAT/PHY 192. An integrated course that covers the material of PHY 103 and MAT 201 with the emphasis on applications to engineering. Physics topics include: mechanics with applications to fluid mechanics, wave phenomena, and thermodynamics. The lab revolves around a single project to build, launch, and analyze the flight dynamics of water-propelled rockets. One lecture, three preceptorials, one three-hour laboratory. P. Meyers EGR 192 - An Integrated Introduction to Engineering, Mathematics, Physics (also APC 192/MAT 192/PHY 192) Not offered this year QCR Taken concurrently with EGR/MAT/PHY 191. An integrated course that covers the material of PHY 103 and MAT 201 with the emphasis on applications to engineering. Math topics include: vector calculus; partial derivatives and matrices; line integrals; simple differential equations; surface and volume integrals; and Green's, Stokes's, and divergence theorems. One lecture, two preceptorials. C. Kelleher GEO 371 - Global Geophysics (also PHY 371) Fall SEN An introduction to the fundamental principles of global geophysics. Taught on the chalkboard, in four parts, the material builds up to form a final coherent picture of (how we know) the structure and evolution of the solid Earth: gravity, magnetism, seismology, and geodynamics. The emphasis is on physical principles including the mathematical derivation and solution of the governing equations. Prerequisites: MAT 201 or 203, PHY 103/104 or PHY 105/106. Two 90-minute lectures. F. Simons GEO 419 - Physics and Chemistry of Earth's Interior (also PHY 419) Not offered this year The Earth is a physical system whose past and present state can be studied within the framework of physics and chemistry. Topics include current concepts of geophysics and the physics and chemistry of Earth materials; origin and evolution of the Earth; and nature of dynamic processes in its interior. One emphasis is to relate geologic processes on a macroscopic scale to the fundamental materials properties of minerals and rocks. Three lectures. Prerequisites: one year of college-level chemistry or physics (preferably both) and calculus. Offered alternately with 424. T. Duffy GEO 442 - Geodynamics (also PHY 442) Not offered this year An advanced introduction to setting up and solving boundary value problems relevant to the solid Earth sciences. Topics include heat flow, fluid flow, elasticity and plate flexure, and rock rheology, with applications to mantle convection, magma transport, lithospheric deformation, structural geology, and fault mechanics. Prerequisites: MAT 201 or 202. Two 90-minute lectures. A. Rubin ISC 231 - An Integrated, Quantitative Introduction to Life Sciences I (also CHM 231/MOL 231/PHY 231) Fall QCR or SEL The four-course sequence ISC 231-234 integrates introductory topics in calculus-based physics, chemistry, molecular biology, and scientific computing with Python, with an emphasis on laboratory experimentation, quantitative reasoning, and data-oriented thinking. It best suits students interested in complex problems in living organisms and prepares them for interdisciplinary research in the life sciences. The fall courses ISC 231 and 232 must be taken together. See ISC website for details on course equivalencies and recommended academic paths from ISC. M. Wühr, T. Gregor, B. Zhang ISC 232 - An Integrated, Quantitative Introduction to Life Sciences I (also CHM 232/MOL 232/PHY 232) Fall QCR or SEL The four-course sequence ISC 231-234 integrates introductory topics in calculus-based physics, chemistry, molecular biology, and scientific computing with Python, with an emphasis on laboratory experimentation, quantitative reasoning, and data-oriented thinking. It best suits students interested in complex problems in living organisms and prepares them for interdisciplinary research in the life sciences. The fall courses ISC 231 and 232 must be taken together. See ISC website for details on course equivalencies and recommended academic paths from ISC. B. Adamson, M. Skinnider, J. Gadd-Reum
