# Physics

**Director of undergraduate studies:** Simon Mochrie, 68C SPL, 436-4809, [F]; Reina Maruyama, Wright Lab 209, 432-3362, [Sp]; dus.physics@yale.edu; physics.yale.edu/academics/undergraduate-studies

The overarching goal of the physics program is to train students—majors and non-majors alike—to think like a physicist, the hallmarks of which include: striving for fundamental explanations that have broad predictive power; appreciating that quantitative analysis is necessary for proper understanding; simplifying physical situations to their essentials to enable the development of mathematical models to explain and predict experimental data; and comparing experimental data from the natural world to theory.

To achieve this goal, we offer courses for physics majors who intend to further their study of physics or any STEM field in graduate school, as well as those physics majors who intend to go into law, consulting, financial services, technology industries, teaching, or any number of fields. Many students enroll in our introductory courses as a compulsory requirement of their STEM major; to satisfy a requirement for admission into medical school; or because they appreciate the quantitative training and intrinsic value offered by a basic understanding of modern physics. The director of undergraduate studies can help students prepare for graduate school in physics by recommending appropriate electives to supplement the core courses. Research experience (PHYS 469, 470, 471, and 472) is an important aspect of preparing for graduate school.

The department offers two majors in Physics: the B.S. and the B.S. intensive major. Students in either program acquire advanced training in physics, mathematics, and related topics through the core courses. They use electives to design individualized programs with more depth or breadth, depending on their interests. Both degree programs require some research experience. PHYS 469 and PHYS 470, introductory research courses, are open to all students. Juniors and seniors, as part of the senior requirement, are required to enroll in PHYS 471 and 472—one term for the B.S. degree and two terms for the B.S. degree, intensive major. Combined majors are available in Mathematics and Physics; Astrophysics; Physics and Philosophy; and Physics and Geosciences.

#### COURSES NONMAJORS AND MAJORS

A guide to selecting physics courses is available to aid in course selection. Questions about placement should be addressed to the DUS.

**Introductory courses with no calculus requirement **Physics courses numbered 120 or below and are for students with little or no previous experience in physics who do not plan to major in the natural sciences. Many of these courses fulfill the science and/or quantitative reasoning distributional requirements. These courses have no college-level mathematics requirement and do not satisfy the medical school requirement.

**Introductory calculus-based lecture sequences**

- PHYS 170, 171 is aimed at students who are interested in the biological sciences or medicine. Knowledge of differential and integral calculus at the level of MATH 112 or equivalent is a prerequisite. MATH 115 should be taken concurrently with PHYS 171. PHYS 170 is a prerequisite for PHYS 171.
- PHYS 180, 181 is aimed at students who plan to major in the physical sciences or engineering. Calculus at the level of MATH 112 is a prerequisite; MATH 115 and 120 should be taken concurrently. PHYS 180 or PHYS 200 is a prerequisite for PHYS 181.
- PHYS 260, 261 is intended for students who have had excellent prior training in mathematics and a solid foundation in physics. One of MATH 120, ENAS 151, PHYS 301, or MATH 230, 231 or equivalent should be taken concurrently with PHYS 260, 261.

**Introductory laboratories **Two different introductory laboratory sequences are offered: PHYS 165L, 166L, and PHYS 205L, 206L. Each of these laboratory courses earns one-half course credit. Students normally take the laboratory courses associated with the introductory physics sequence in which they are enrolled.

- PHYS 165L, 166L is an introductory laboratory sequence aimed at students interested in engineering, the life sciences, and medicine. Related lecture courses are PHYS 170, 171, and PHYS 180, 181.
- PHYS 205L, 206L is for students who plan to major in the physical sciences or engineering. Related lecture courses are PHYS 180, 181; PHYS 200, 201; and PHYS 260, 261. Students who take the lecture courses in their first year are advised to start this laboratory sequence with PHYS 205L in the spring of their first year or in the fall of sophomore year.

**Advanced electives **A series of 340-level electives explores special topics of interest to both majors and nonmajors. The electives are open to any student in Yale College who has completed a year of introductory calculus-based physics (PHYS 170, 171; or 180, 181; or 200, 201; or 260, 261). The offerings for 2018-2019 include PHYS 341, PHYS 343, and PHYS 344.

#### Prerequisites

**B.S. degree program** The prerequisites are an introductory lecture course sequence with a mathematics sequence equivalent to, or more advanced than, the corequisite of the physics sequence. The following options are appropriate: PHYS 170, 171 with MATH 112, 115; or PHYS 180, 181 with MATH 115, 120; or PHYS 200, 201 with MATH 120 and either 222 or 225; or PHYS 260, 261 with MATH 120, ENAS 151, PHYS 301, or MATH 230, 231 or equivalent. In addition, the laboratory sequence PHYS 205L, 206L or PHYS 165L, 166L is required. Students who take these physics and mathematics courses starting in their first year may satisfy the prerequisites by the middle of their sophomore year. Students who begin taking physics courses in their sophomore year may also complete either the standard or the intensive major. Students are advised to take mathematics courses throughout their first year at the appropriate level.

**B.S. degree program, intensive major **The prerequisites for the B.S. degree with an intensive major are the same as for the standard program.

#### Requirements of the Major

**B.S. degree program** Eight courses are required beyond the prerequisites, including the senior project. Students must take a mathematics course at the level of, or more advanced than, PHYS 301. Three courses at the core of the major, PHYS 401, 402, and PHYS 440 or 439, involve advanced study of fundamental topics common to all branches of physics. PHYS 401 and 402 pertain to advanced classical physics (mechanics, statistical physics and thermodynamics, and electromagnetism), while the third, PHYS 439 or 440 covers quantum mechanics. PHYS 401 must be taken before PHYS 402, 440, or 439.

Three advanced elective courses are also required. Suitable advanced courses include the PHYS 340-level electives, an advanced laboratory such as PHYS 382L, and 400-level courses in Physics. Students may also find suitable advanced courses in other departments in the sciences, engineering, and mathematics. Courses taken to satisfy these requirements must be approved by the DUS. In order to pursue their individual interests in sufficient depth, many students choose to take more than the required number of advanced courses.

**B.S. degree program, intensive major **Ten courses are required beyond the prerequisites, including the senior project. Students must take a mathematics course at the level of, or more advanced than, PHYS 301. Five courses at the core of the major involve advanced study of fundamental topics common to all branches of physics. Three of the courses pertain to advanced classical physics: mechanics (PHYS 410), statistical physics and thermodynamics (PHYS 420), and electromagnetism (PHYS 430). Two other courses incorporate quantum mechanics (PHYS 440 and 441). Because the ideas build progressively: PHYS 410 must precede PHYS 440, and PHYS 440 must precede 441, 420, and 430.

Because experiment is at the heart of the discipline, the intensive major requires one term of advanced laboratory (PHYS 382L or equivalent) and at least two terms of independent research (PHYS 471, 472 or equivalent). One advanced elective course is required to complete the program. Suitable advanced courses include the PHYS 340-level electives and 400-level courses in Physics. Students may also find suitable advanced courses in other departments in the sciences, engineering, and mathematics. Courses taken to satisfy these requirements must be approved by the DUS. In order to pursue their individual interests in sufficient depth, many students choose to take more than ten advanced courses.

**Credit/D/Fail courses **Courses taken Credit/D/Fail may not be counted toward the requirements of either major.

**Roadmap **See visual roadmap of the requirements.

#### Senior Requirement

**B.S. degree program **The senior requirement for the standard B.S. degree is fulfilled by receiving a passing grade on a one-term research project in PHYS 471 or 472 or equivalent. Students should consult the DUS for further information.

**B.S. degree program, intensive major **The senior requirement for the intensive major is fulfilled by receiving a passing grade on a two-term research project in PHYS 471, 472 or equivalent. Students should consult the DUS for further information.

#### Advising

All Physics majors in the sophomore, junior, and senior classes must have their programs approved by the DUS. First-year students and undeclared sophomores who are interested in Physics or related majors are encouraged to meet with the DUS to discuss their questions and proposed programs.

For both the standard B.S. degree and the B.S. degree with an intensive major, students are advised to begin the program in their first year to allow the greatest amount of flexibility in course selection. It is possible, however, to complete either program in a total of six terms, as illustrated below.

A program for a student completing the Physics B.S. in three years might be:

First-Year or Sophomore | Sophomore or Junior | Senior |
---|---|---|

PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261 | PHYS 206L | PHYS 439 or PHYS 440 |

PHYS 205L | PHYS 301 | PHYS 471 or 472 |

Mathematics corequisites | PHYS 401 | Two advanced electives |

PHYS 402 | ||

One advanced elective |

A program for a student completing the intensive major in three years might be:

First-Year or Sophomore | Sophomore or Junior | Senior |
---|---|---|

PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261 | PHYS 206L | PHYS 441 |

PHYS 205L | PHYS 301 | PHYS 420 |

Mathematics corequisites | PHYS 410 | PHYS 430 |

PHYS 440 | PHYS 471 | |

PHYS 382L | PHYS 472 | |

One advanced elective |

**REQUIREMENTS OF THE MAJOR**

**B.S. DEGREE**

**Prerequisites **PHYS 170, 171 or 180, 181 or 200, 201 or 260, 261, with appropriate math coreqs; PHYS 205L, 206L or PHYS 165L, 166L

**Number of courses **8 term courses beyond prereqs (incl senior req)

**Specific courses required **PHYS 301 or other advanced math course; PHYS 401, 402, and either PHYS 439 or 440, in sequence

**Distribution of courses **3 advanced electives approved by DUS

**Senior requirement **PHYS 471 or 472 or equivalent

**B.S. DEGREE, INTENSIVE MAJOR**

**Prerequisites **PHYS 170, 171 or 180, 181 or 200, 201 or 260, 261, with appropriate math coreqs; PHYS 205L, 206L or PHYS 165L, 166L

**Number of courses** 10 term courses beyond prereqs (incl senior req)

**Specific courses required **PHYS 301 or other advanced math course; PHYS 410, 440, 441, 420, 430, in sequence; PHYS 382L

**Distribution of courses **1 advanced elective approved by DUS

The overarching goal of the physics program is to train students—majors and non-majors alike—to think like a physicist, the hallmarks of which include: striving for fundamental explanations that have broad predictive power; appreciating that quantitative analysis is necessary for proper understanding; simplifying physical situations to their essentials to enable the development of mathematical models to explain and predict experimental data; and comparing experimental data from the natural world to theory.

To achieve this goal, we offer courses for physics majors who intend to further their study of physics or any STEM field in graduate school, as well as those physics majors who intend to go into law, consulting, financial services, technology industries, teaching, or any number of fields. Many students enroll in our introductory courses as a compulsory requirement of their STEM major; to satisfy a requirement for admission into medical school; or because they appreciate the quantitative training and intrinsic value offered by a basic understanding of modern physics. The director of undergraduate studies can help students prepare for graduate school in physics by recommending appropriate electives to supplement the core courses. Research experience (PHYS 469, 470, 471, and 472) is an important aspect of preparing for graduate school.

## Courses with No Calculus Requirement

These courses are designed for non–science students with little or no background in physics. None have a college-level mathematics requirement. Each course may count toward the distributional requirements in science and/or quantitative reasoning. Expected offerings for 2018–2019 include:

#### Course List

PHYS 100 , Energy Technology and Society

PHYS 112 , Practical Electronics

PHYS 120 , Quantum Physics and Beyond

## Calculus-Based INTRODUCTORY Physics Lecture Courses

The four introductory physics course sequences listed below are calculus-based. Students should have the appropriate background in mathematics to take these courses. Completion of an introductory sequence also prepares students for a series of 340-level electives, which cover special topics of interest to both majors and non-majors.

For more details, please see the Guide to Selecting the Best Physics Course for You.

- PHYS 170 and PHYS 171 are for students who are interested in the medical and biological sciences. Knowledge of differential and integral calculus at the level of MATH 112 , or equivalent is a prerequisite for PHYS 170 and PHYS 171 . PHYS 170 is a prerequisite for PHYS 171. MATH 115 should be taken concurrently with PHYS 171 .
- PHYS 180 and PHYS 181 are for students with some previous background in physics and mathematics who plan to major in the physical sciences. Calculus at the level of MATH 112 is a prerequisite; PHYS 180 or PHYS 200 is a prerequisite for PHYS 181. MATH 115 and MATH 120 , should be taken concurrently.
- PHYS 200 and PHYS 201 are for students with a strong background in mathematics and physics who plan to major in the physical sciences. Calculus at the level of MATH 115 is presumed; MATH 120 and either MATH 225 or MATH 222 , are generally taken concurrently.
- PHYS 260 and PHYS 261 are for students who have excellent training in physics and mathematics and a flair for mathematical methods and quantitative analysis. One of the following: MATH 120 , ENAS 151 , PHYS 301 , or MATH 230 and MATH 231 or the equivalent should be taken concurrently.

## Laboratory Courses

- PHYS 165L and PHYS 166L do not require a strong high school physics laboratory preparation. Related lecture courses are PHYS 170 , PHYS 171 or PHYS 180 , PHYS 181 .
- PHYS 205L and PHYS 206L are for students who plan to major in the physical sciences or engineering. The related lecture courses are PHYS 180 , PHYS 181 , or PHYS 200 , PHYS 201 , or PHYS 260 , PHYS 261 . Students are advised to start this laboratory sequence in the spring of the first year or the fall of the sophomore year.

The following table summarizes some important information about the lecture and laboratory courses described above.

Meets Medical School Requirement | Acceptable for Physics Major | Math Taken Concurrently | |
---|---|---|---|

PHYS 050 - PHYS 120 | no | no | none |

PHYS 170, PHYS 171 | yes | yes | MATH 115 |

PHYS 180, PHYS 181 | yes | yes | MATH 115, MATH 120 |

PHYS 200, PHYS 201 | yes | yes | MATH 120, and MATH 225 or MATH 222 |

PHYS 260, PHYS 261 | yes | yes | One of MATH 120, ENAS 151, MATH 230 or MATH 231, or PHYS 301 |

PHYS 165L, PHYS 166L | yes | yes | |

PHYS 205L, PHYS 206L | yes | yes |

Questions about placement should be addressed to the director of undergraduate studies (DUS) at a meeting in the fall for all first-year students interested in the Physics major. Details will be listed in the *Calendar for the Opening Days*. Further information about undergraduate physics at Yale can be found on the departmental website.

#### FACULTY OF THE DEPARTMENT OF PHYSICS

**Professors **†Charles Ahn, Yoram Alhassid, Thomas Appelquist, †Charles Bailyn, O. Keith Baker, Charles Baltay, Sean Barrett, †Hui Cao, Richard Casten (*Emeritus*), †Paolo Coppi, David DeMille, †Michel Devoret, †Debra Fischer, Bonnie Fleming, †Marla Geha, Steven Girvin, Leonid Glazman, John Harris, Karsten Heeger, †Victor Henrich, †Jonathon Howard, Francesco Iachello, †Sohrab Ismail-Beigi, Steven Lamoreaux, Simon Mochrie, Vincent Moncrief, †Priyamvada Natarajan, Peter Parker (*Emeritus*), †Daniel Prober, Nicholas Read, Jack Sandweiss (*Emeritus*), †Peter Schiffer, †Robert Schoelkopf, Ramamurti Shankar, Witold Skiba, †A. Douglas Stone, †Hong Tang, Paul Tipton (*Chair*), C. Megan Urry, †Pieter van Dokkum, †John Wettlaufer, Michael Zeller (*Emeritus*)

**Associate Professors **†Murat Acar, Helen Caines, Sarah Demers, †Thierry Emonet, Walter Goldberger, Jack Harris, Reina Maruyama, Daisuke Nagai, †Corey O'Hern, Nikhil Padmanabhan, David Poland

**Assistant Professors **†Eric Michael Brown, Meng Cheng, †Damon Clark, †Liang Jiang, Benjamin Machta, David Moore, †John Murray, †Michael Murrell, Nir Navon, Laura Newburgh, †Peter Rakich

**Senior Lecturer **Sidney Cahn

**Lecturers **Stephen Irons, Rona Ramos, Adriane Steinacker

†A joint appointment with primary affiliation in another department.

### Courses

*** PHYS 040a / ASTR 040, Expanding Ideas of Time and Space** C. Megan Urry

Discussions on the nature of time and space. Topics include the shape and contents of the universe, special and general relativity, dark and light matter, and dark energy. Observations and ideas fundamental to astronomers' current model of an expanding and accelerating four-dimensional universe. Enrollment limited to first-year students. Preregistration required; see under First-Year Seminar Program. SC

TTh 11:35am-12:50pm

*** PHYS 045b, Physics Meets the Arts** Agnes Mocsy

This seminar provides an opportunity to acquire a basic understanding of fundamental and contemporary physics topics curated as stories infused with the arts, emphasis is placed on science as a process rather than an outcome. Enrollment limited to first-year students. Preregistration required; see under First-Year Seminar Program.

T 1:30pm-3:20pm

*** PHYS 050a / APHY 050a, Science of Modern Technology and Public Policy** Daniel Prober

Examination of the science behind selected advances in modern technology and implications for public policy, with focus on the scientific and contextual basis of each advance. Topics are developed by the participants with the instructor and with guest lecturers, and may include nanotechnology, quantum computation and cryptography, renewable energy technologies, optical systems for communication and medical diagnostics, transistors, satellite imaging and global positioning systems, large-scale immunization, and DNA made to order. Enrollment limited to first-year students. Preregistration required; see under First-Year Seminar Program. SC RP

MW 2:30pm-3:45pm

*** PHYS 100b / APHY 100b / ENAS 100b / EVST 100b / G&G 105b, Energy Technology and Society** Daniel Prober, Michael Oristaglio, and Julie Paquette

The technology and use of energy. Impacts on the environment, climate, security, and economy. Application of scientific reasoning and quantitative analysis. Intended for non–science majors with strong backgrounds in math and science. QR, SC

MW 1pm-2:15pm

*** PHYS 107b / EDST 107b / MB&B 107b, Being Human in STEM** Helen Caines, Andrew Miranker, Sarah Demers, Katherine Schilling, and Agnes Mocsy

A collaboratively-designed, project-oriented course that seeks to examine, understand, and disseminate how diversity of gender, race, religion, sexuality, economic circumstances, etc. shape the STEM experience at Yale and nationally, and that seeks to formulate and implement solutions to issues that are identified. Study of relevant peer-reviewed literature and popular-press articles. Implementation of a questionnaire and interviews of STEM participants at Yale. Creation of role-play scenarios for provoking discussions and raising awareness. Design and implementation of group interventions. SO

F 2:30pm-4:20pm

*** PHYS 120b, Quantum Physics and Beyond** John Harris

Current topics in modern physics, beginning with quantum physics and continuing through subatomic physics, special and general relativity, cosmology, astrophysics, and string theory. SC

M 3:30pm-5:20pm

**PHYS 151a or b / APHY 151a or b / ENAS 151a or b, Multivariable Calculus for Engineers** Staff

An introduction to multivariable calculus focusing on applications to engineering problems. Topics include vector-valued functions, vector analysis, partial differentiation, multiple integrals, vector calculus, and the theorems of Green, Stokes, and Gauss. Prerequisite: MATH 115 or equivalent. QR RP

HTBA

**PHYS 165La and PHYS 166Lb, General Physics Laboratory** David DeMille, Rona Ramos, Oliver Baker, and Laura Newburgh

A variety of individually self-contained experiments are roughly coordinated with the lectures in PHYS 170, 171, and 180, 181 and illustrate and develop physical principles covered in those lectures. SC ½ Course cr per term

HTBA

*** PHYS 170a and PHYS 171b, University Physics for the Life Sciences** Simon Mochrie

An introduction to classical physics with special emphasis on applications drawn from the life sciences and medicine. Fall-term topics include vectors and kinematics, Newton's laws, momentum, energy, random walks, diffusion, fluid mechanics, mathematical modeling, and statistical mechanics. Spring-term topics include oscillations, waves, sound, electrostatics, circuits, Maxwell's equations, electromagnetic waves, gene circuits, and quantum mechanics. Essential mathematics are introduced and explained as needed. Completion of MATH 112 or equivalent is prerequisite for PHYS 170. Completion of PHYS 170 is a prerequisite for PHYS 171. MATH 116 (or MATH 115) is recommended prior to or concurrently with PHYS 171. QR, SC

MW 11:35am-12:50pm

**PHYS 180a and PHYS 181b, University Physics** Adriane Steinacker

A broad introduction to classical and modern physics for students who have some previous preparation in physics and mathematics. Fall-term topics include Newtonian mechanics, gravitation, waves, and thermodynamics. Spring-term topics include electromagnetism, special relativity, and quantum physics. Concurrently with MATH 115 and 120 or equivalents. See comparison of introductory sequences and laboratories in the YCPS. May not be taken for credit after PHYS 170, 171. QR, SC

HTBA

**PHYS 200a and PHYS 201b, Fundamentals of Physics** Sarah Demers

A thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis on problem solving and quantitative reasoning. Fall-term topics include Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves. Spring-term topics include electromagnetism, geometrical and physical optics, and elements of quantum mechanics. Prerequisite: MATH 115 or equivalent. MATH 210 and either MATH 225 or MATH 222, are generally taken concurrently. See comparison of introductory sequences and laboratories in the YCPS. QR, SC

MW 11:35am-12:50pm

**PHYS 205La or b and PHYS 206La or b, Modern Physical Measurement** Staff

A two-term sequence of experiments in classical and modern physics for students who plan to major in Physics. In the first term, the basic principles of mechanics, electricity, and magnetism are illustrated in experiments designed to make use of computer data handling and teach error analysis. In the second term, students plan and carry out experiments illustrating aspects of wave and quantum phenomena and of atomic, solid state, and nuclear physics using modern instrumentation. May be begun in either term. SC ½ Course cr per term

HTBA

*** PHYS 210a, Electronics for the Physicist** Stephen Irons and Steve Lamoreaux

Hands-on investigation of electronics topics of particular interest to the experimental physicist. Students learn the about electronic circuits, equipment and devices that are commonly used in modern experimental laboratories. Topics covered include, but are limited to: basic theory of circuits, test equipment, passive and active components, amplifiers, filters and noise, sensors and feedback, prototyping and circuit construction, and programmable microprocessors. There will be weekly hands-on activities and a final project. Prerequisites: PHYS 170 and 171, or PHYS 180 and 181, or PHYS 200 and 201, or PHYS 260 and 261; and MATH 115 or equivalent. SC

Th 9am-12pm

*** PHYS 260a and PHYS 261b, Intensive Introductory Physics** Steven Girvin

The major branches of physics—classical and relativistic dynamics, gravitation, electromagnetism, heat and thermodynamics, statistical mechanics, quantum physics—at a sophisticated level. For students majoring in the physical sciences, Mathematics, and Philosophy who have excellent training in and a flair for mathematical methods and quantitative analysis. Concurrently with MATH 230 and 231, or PHYS 301, or equivalent. QR, SC

MW 11:35am-12:50pm

**PHYS 293a / APHY 293a, Einstein and the Birth of Modern Physics** A. Douglas Stone

The first twenty-five years of the 20th century represent a turning point in human civilization as for the first time mankind achieved a systematic and predictive understanding of the atomic level constituents of matter and energy, and the mathematical laws which describe the interaction of these constituents. In addition, the General Theory of Relativity opened up for the first time a quantitative study of cosmology, of the history of the universe as a whole. Albert Einstein was at the center of these breakthroughs, and also became an iconic figure beyond physics, representing scientist genius engaged in pure research into the fundamental laws of nature. This course addresses the nature of the transition to modern physics, underpinned by quantum and relativity theory, through study of Einstein’s science, biography, and historical context. It also presents the basic concepts in electromagnetic theory, thermodynamics and statistical mechanics, special theory of relativity, and quantum mechanics which were central to this revolutionary epoch in science. Prerequisites: Two terms of PHYS 170, 171, or PHYS 180, 181, or PHYS 200, 201, or PHYS 260, 261, or one term of any of these course with permission of instructor. QR, SC

TTh 1pm-2:15pm

**PHYS 295b / ASTR 255b, Research Methods in Astrophysics** Marla Geha

The acquisition and analysis of astrophysical data, including the design and use of ground- and space-based telescopes, computational manipulation of digitized images and spectra, and confrontation of data with theoretical models. Examples taken from current research at Yale and elsewhere. Use of the Python programming language. A background in high school calculus and physics. No previous programming experience required. QR, SC RP

MWF 9:25am-10:15am

**PHYS 301a, Introduction to Mathematical Methods of Physics** Vincent Moncrief

Topics include multivariable calculus, linear algebra, complex variables, vector calculus, and differential equations. Designed to give accelerated access to 400-level courses by providing, in one term, the essential background in mathematical methods. Recommended to be taken concurrently with PHYS 401 or 410. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor. QR

TTh 11:35am-12:50pm

**PHYS 341b, Biological Physics** Simon Mochrie

An introduction to the physics of biological structures and life processes, and to the burgeoning field of biological physics. Related concepts from probability theory and statistical physics are developed as needed. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor. QR, SC

TTh 1pm-2:15pm

**PHYS 343b / ASTR 343b, Gravity, Astrophysics, and Cosmology** Laura Newburgh

Introduction to frontier areas of research in astrophysics and cosmology exploring ideas and methods. In-depth discussion of the physics underlying several recent discoveries including extrasolar planets—their discovery, properties, and issues of habitability; black holes—prediction of their properties from GR, observational signatures, and detection; and the accelerating universe—introduction to cosmological models and the discovery of dark energy. Prerequisites: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor. QR, SC

TTh 11:35am-12:50pm

**PHYS 344b, Quantum and Nanoscale Physics** Sean Barrett

An introduction to cutting-edge developments in physics involving quantum information and/or nanotechnology. Background concepts in quantum mechanics, electromagnetism, and optics are introduced as necessary. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor. PHYS 301 or other advanced mathematics course recommended. QR, SC

TTh 9am-10:15am

**PHYS 353a / BENG 353a, Introduction to Biomechanics** Michael Murrell

An introduction to the biomechanics used in biosolid mechanics, biofluid mechanics, biothermomechanics, and biochemomechanics. Diverse aspects of biomedical engineering, from basic mechanobiology to the design of novel biomaterials, medical devices, and surgical interventions. Prerequisites: PHYS 180, 181, MATH 115, and ENAS 194. QR

TTh 9am-10:15am

*** PHYS 382Lb, Advanced Physics Laboratory** Reina Maruyama, Sidney Cahn, Steve Lamoreaux, and Nir Navon

Laboratory experiments with some discussion of theory and techniques. An advanced course focusing on modern experimental methods and concepts in atomic, optical, nuclear, and condensed matter physics. Intended to prepare students for independent research. For majors in the physical sciences. After or concurrently with PHYS 439 or 440, or with permission of instructor. PHYS 206L WR, SC

TTh 1:30pm-4:30pm

**PHYS 401a and PHYS 402b, Advanced Classical Physics from Newton to Einstein** Nikhil Padmanabhan

Advanced physics as the field developed from the time of Newton to the age of Einstein. Topics include mechanics, electricity and magnetism, statistical physics, and thermodynamics. The development of classical physics into a "mature" scientific discipline, an idea that was subsequently shaken to the core by the revolutionary discoveries of quantum physics and relativity. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261. Concurrently with PHYS 301 or other advanced mathematics course. QR, SC

MW 11:35am-12:50pm

**PHYS 410a, Classical Mechanics** Charles Baltay

An advanced treatment of mechanics, with a focus on the methods of Lagrange and Hamilton. Lectures and problems address the mechanics of particles, systems of particles, and rigid bodies, as well as free and forced oscillations. Introduction to chaos and special relativity. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261. Concurrently with PHYS 301 or other advanced mathematics course. QR, SC

MW 11:35am-12:50pm

*** PHYS 420a / APHY 420a, Thermodynamics and Statistical Mechanics** Nir Navon

This course is subdivided into two topics. We study thermodynamics from a purely macroscopic point of view and then we devote time to the study of statistical mechanics, the microscopic foundation of thermodynamics. Prerequisites: PHYS 301, 410, and 440 or permission of instructor. QR, SC

MW 9am-10:15am

**PHYS 428a / AMTH 428a / E&EB 428a / G&G 428a, Science of Complex Systems** Jun Korenaga

Introduction to the quantitative analysis of systems with many degrees of freedom. Fundamental components in the science of complex systems, including how to simulate complex systems, how to analyze model behaviors, and how to validate models using observations. Topics include cellular automata, bifurcation theory, deterministic chaos, self-organized criticality, renormalization, and inverse theory. Prerequisite: PHYS 301, MATH 247, or equivalent. QR, SC

MWF 10:30am-11:20am

**PHYS 430b, Electromagnetic Fields and Optics** David Moore

Electrostatics, magnetic fields of steady currents, electromagnetic waves, and relativistic dynamics. Provides a working knowledge of electrodynamics. Prerequisites: PHYS 301 and 410 or equivalents. QR, SC

MW 11:35am-12:50pm

**PHYS 439a / APHY 439a, Basic Quantum Mechanics** Liang Jiang

The basic concepts and techniques of quantum mechanics essential for solid-state physics and quantum electronics. Topics include the Schrödinger treatment of the harmonic oscillator, atoms and molecules and tunneling, matrix methods, and perturbation theory. Prerequisites: PHYS 181 or 201, PHYS 301, or equivalents, or permission of instructor. QR, SC

TTh 1pm-2:15pm

**PHYS 440b, Quantum Mechanics and Natural Phenomena I** Ramamurti Shankar

The first term of a two-term sequence covering principles of quantum mechanics with examples of applications to atomic physics. The solution of bound-state eigenvalue problems, free scattering states, barrier penetration, the hydrogen-atom problem, perturbation theory, transition amplitudes, scattering, and approximation techniques. Prerequisite: PHYS 410 or 401. QR, SC

TTh 11:35am-12:50pm

**PHYS 441a, Quantum Mechanics and Natural Phenomena II** Witold Skiba

Continuation of PHYS 440. Prerequisite: PHYS 440. QR, SC

MW 11:35am-12:50pm

**PHYS 442b, Introduction to Nuclear and Elementary Particle Physics** Charles Baltay

Fundamental concepts in nuclear and particle physics, including the discovery of radioactivity, the Dirac equation, antimatter, Feynman diagrams, hadron resonances, quarks and gluons, fundamental symmetries, the weak interaction, beta decay, quantum chromodynamics, neutrino oscillation, unification, and particle theories for dark matter. Prerequisite: two term courses in quantum mechanics. QR, SC

MW 1pm-2:15pm

**PHYS 448a / APHY 448a, Solid State Physics I** Sohrab Ismail-Beigi

The first term of a two-term sequence covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structure, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonances, phase transitions, dielectrics, magnetic materials, and superconductors. Prerequisites: APHY 322, 439, PHYS 420. QR, SC

TTh 1pm-2:15pm

**PHYS 449b / APHY 449b, Solid State Physics II** Vidvuds Ozolins

The second term of the sequence described under APHY 448. QR, SC

TTh 1pm-2:15pm

**PHYS 458a / APHY 458a, Principles of Optics with Applications** Hui Cao

Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, and nanostructure physics. Topics include propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence. Prerequisite: PHYS 430. QR, SC

TTh 11:35am-12:50pm

**PHYS 460a, Mathematical Methods of Physics** Nicholas Read

Survey of mathematical techniques useful in physics. Physical examples illustrate vector and tensor analysis, group theory, complex analysis (residue calculus, method of steepest descent), differential equations and Green's functions, and selected advanced topics. Prerequisite: PHYS 301 or other advanced mathematics course. QR

MW 9am-10:15am

*** PHYS 469a and PHYS 470b / PHYS 470b, Independent Research in Physics** David Moore

Each student works on an independent project under the supervision of a member of the faculty or research staff. Students participate in a series of seminar meetings in which they present a talk on their project or research related to it. A written report is also required. For students with a strong background in physics coursework. This course may be taken multiple times for pass/fail credit. Suggested for first years and sophomores.

HTBA

*** PHYS 471a and PHYS 472b, Independent Projects in Physics** David Moore

Each student works on an independent project under the supervision of a member of the faculty or research staff. Students participate in a series of seminar meetings in which they present a talk on their project or research related to it. A written report is also required. Registration is limited to junior and senior physics majors. This course may be taken up to four times for a letter grade.

HTBA