- Introduction
- About Amherst College
- Admission & Financial Aid
- Regulations & Requirements
- Amherst College Courses
- Five College Programs & Certificates
- Honors & Fellowships

- General Regulations (Summary)
- Terms and Vacations
- Conduct
- Attendance at College Exercises
- Records and Reports
- Pass/Fail Option
- Examinations and Extensions
- Withdrawals
- Readmission
- Deficiencies
- Housing and Meal Plans
- Degree Requirements (Summary)
- Degree Requirements
- Course Requirements
- The Liberal Studies Curriculum
- The Major Requirement
- Departmental Majors
- Interdisciplinary Majors
- Comprehensive Requirement
- Degree with Honors
- Independent Scholar Program
- Field Study
- Five College Courses
- Academic Credit from Other Institutions
- Cooperative Doctor of Philosophy
- Engineering Exchange Program with Dartmouth

- American Studies
- Anthropology and Sociology
- Architectural Studies
- Art and the History of Art
- Asian Languages and Civilizations
- Biochemistry and Biophysics
- Biology
- Black Studies
- Chemistry
- Classics
- Colloquia
- Computer Science
- Creative Writing
- Economics
- English
- Environmental Studies
- European Studies
- Film and Media Studies
- First Year Seminar
- French
- Geology
- German
- History
- Kenan Colloquium
- Latinx and Latin American Studies
- Law, Jurisprudence, and Social Thought
- Mathematics and Statistics
- Mellon Seminar
- Music
- Neuroscience
- Philosophy
- Physics and Astronomy
- Political Science
- Psychology
- Religion
- Russian
- Sexuality Wmn's & Gndr Studies
- Spanish
- Theater and Dance
- Courses of Instruction
- 01- Bruss Seminar
- 02- Kenan Colloquium
- 03- Linguistics
- 04- Mellon Seminar
- 05- Physical Education
- 06- Premedical Studies
- 07- Teaching
- 08- Five College Dance

Professors Friedman, Hunter‡, Hall, Jagannathan (Chair), and Loinaz†; Associate Professors Carter‡ and Hanneke*; Assistant Professor Follette; Visiting Assistant Professor Collett; Post-doctoral Fellow Ward-Duong.

Physics is the study of the natural world emphasizing an understanding of phenomena in terms of fundamental interactions and basic laws. As such, physics underlies all of the natural sciences and pervades contemporary approaches to the study of the universe (astronomy and astrophysics), living systems (biophysics and neuroscience), chemistry (chemical physics), and earth systems (geophysics and environmental science). In addition, the relationship of physics to mathematics is deep, complex and rich. To reflect the broad range of activities pursued by people with training in physics, the department has developed a curriculum that provides a solid background in the fundamentals of physics while allowing some flexibility, particularly at the upper level, for students’ interests in astronomy, biology, chemistry, computer science, geology, mathematics and neuroscience.

The core physics program provides a course of study for those who are interested in physics as a liberal arts major, with career plans in diverse fields such as engineering, law, medicine, business and education. The department also provides a number of upper-level electives to deepen the background of those students intending to pursue careers in physics and closely related technical fields.

*Major Program.* Students who wish to major in physics are required to complete the following coursework:

- A comprehensive introduction to the calculus: MATH 111, 121, and 211
- An introduction to the core physics concepts of mechanics (PHYS 123 or 116), electromagnetism (PHYS 124 or 117), oscillations and waves (PHYS 125), relativity and quantum mechanics (PHYS 225), and statistical mechanics (PHYS 230 or CHEM 361)
- One advanced course in laboratory or observational techniques (PHYS 226 or ASTR 337)
- Three advanced elective courses on physics, the application of physics in other disciplines, or techniques used in physics. These courses must be approved by the chair of the department in consultation with the faculty of the department. At least one must be a 300-level PHYS course. At most one may be counted towards a second major.

The Department web page has links to a handbook that contains a partial list of electives for the major. In addition to consulting the handbook, students are encouraged to discuss additional choices of electives which they may consider, and their paths through the major, with members of the faculty. Students interested in majoring in physics should take PHYS 123 and 124 early in their college career. Those who have taken PHYS 116 and 117 are also able to join the majors’ stream, but they should discuss the transition with a faculty member as early as they can. The general content of the two sequences is similar, but the mathematical levels are different. Students who have placed out of MATH 111, 121, 211 or PHYS 123 are excused from these requirements and do not need to replace them with other courses.

The comprehensive evaluation for Physics majors has two components: a satisfactory performance on an approved standardized test in general physics, and attendance at a minimum of nine public physics or astronomy lectures during the senior year.

*General Education Physics Courses*. The Physics Department offers a variety of courses for students not majoring in the sciences. Typically, these courses do not assume any background beyond high-school science and mathematics. In most years, the department teaches a few of these courses.

*Departmental Honors Program.* Students who wish to receive departmental Honors should enroll in PHYS 498 and 499D in addition to completing the other requirements for the major. To enter the Honors program, a student must attain an average grade of at least B- in all Physics courses taken through the end of the junior year or receive department approval. At the end of the first semester of the senior year the student’s progress on the Honors problem will determine the advisability of continuation in the Honors program.

The aim of Departmental Honors work in Physics is to provide the student an opportunity to pursue, under faculty direction, in-depth research into a project in experimental and/or theoretical physics. Current experimental areas of research in the department include atomic and molecular physics, precision measurements and fundamental symmetries, Bose-Einstein condensation, ultracold collisions, the quantum-classical frontier, nonlinear dynamics, optical trapping, ion trapping, cellular and molecular mechanics, and phase transitions. Theoretical work is primarily in the area of High Energy and Elementary Particle physics, but faculty members pursue studies in quantum computers, foundations of quantum mechanics, and classical gravitation theory. In addition to apparatus for projects closely related to the continuing experimental research activity of faculty members, facilities are available for experimental projects in many other areas. Subject to availability of equipment and faculty interest, Honors projects arising out of students’ particular interests are encouraged. Students must submit a written thesis on the Honors work a few weeks before the end of their final semester (in late April for spring graduation). Students give a preliminary presentation of their work during the first semester, and a final presentation at the end of the second semester. In addition, they take oral examinations devoted primarily to the thesis work.

Astronomy was the first science, and it remains one of the most exciting, data-driven, and active fields of scientific research. Opportunities exist to pursue studies both at the non-technical and advanced levels. Non-technical courses are designed to be accessible to every Amherst student; their goal is to introduce students to the roles of quantitative reasoning and observational evidence in modern astronomy, and to give a general introduction to the nature of the astronomical universe. These courses are often interdisciplinary in nature, including discussion of issues pertaining to Earth Sciences and Physics.

The Astronomy major is designed to introduce students to the computational techniques, statistical tools, instrumentation, and physical principles that underlie modern Astronomy. Computational and statistical techniques are introduced in the first course in the major sequence, ASTR 200 (Intro to Data Science with Astronomical Applications), and further honed in ASTR 228 (Introductory Astrophysics) and ASTR 352 (Advanced Astrophysics). ASTR 228 and 352 also draw on physical principles introduced in the three course required physics sequence (PHYS 123, 124 and 225).

A joint Five College Astronomy Department offers courses beyond those offered at Amherst. All required courses are taught at Amherst, but students are also encouraged to take elective courses at the four other institutions, Hampshire, Mount Holyoke and Smith Colleges and the University of Massachusetts (http://www.astro.umass.edu/about/fcad/). As a result of this five college partnership, students can enjoy the benefits of a first-rate liberal arts education while maintaining association with a research department of international stature. Students may pursue independent theoretical and observational work in association with any member of the Five College Astronomy Department, either during the academic year or the summer term. The facilities of all five institutions are available to departmental majors.

*Major Program.* The Astronomy major consists of eleven required courses: MATH 111, MATH 121, PHYS 123 (or 116), PHYS 124 (or 117), PHYS 225, ASTR200, ASTR 228, ASTR 352, and three electives (many of which are also offered at Amherst) from the list below. Those who have taken PHYS 116 and 117 are also able to join the majors’ stream, but they should discuss the transition with a faculty member as early as they can. In order to fulfill the college-wide comprehensive exam requirement, all Astronomy majors must make an oral presentation describing a recently-published result in the astronomy literature to department faculty in the second semester of their senior year, and must attend at least nine public astronomy lectures during the senior year.

Of the three elective courses, at least one elective must be in Astronomy, and at least one must be 300-level or higher. These electives include: ASTR 220, 223, 224, 225, 226, 301, 330, 335, 337, 339, 341, 444 and 445; CHEM 351 and 361; GEOL 331, 341 and 431; MATH 230, 260, 272, 284, 320 335, 360, 365, and 370; STAT 220, 225, 230, 240, or 495; PHYS 226, 227, 230, 343, 347, 348 and 490; COSC 201, 247, and 301. Elective courses not on this list may count toward the major with departmental approval.

All Astronomy majors must assemble an e-portfolio demonstrating their mastery of the core competencies of the major prior to the beginning of the second semester of the senior year. Students failing to do so must instead pass an alternate comprehensive examination in the second semester of the senior year. All Astronomy majors must also attend at least nine public astronomy lectures or seminars during the senior year. Many departmental seminars qualify as astronomy themed, as do all Five College astronomy colloquia and seminars.

*Departmental Honors Program.* Students who wish to receive departmental Honors should enroll in ASTR 498 and 499 in addition to completing the other requirements for the major. To enter the Honors program, a student must attain an average grade of at least B– in all required courses taken through the end of the junior year or receive department approval. At the end of the first semester of the senior year the student’s progress on the Honors problem will determine the advisability of continuation in the Honors program.

The aim of Departmental Honors work in Astronomy is to provide the student an opportunity to pursue, under faculty direction, in-depth research into a project in observational and/or theoretical astronomy. Current areas of research at Amherst direct imaging of extrasolar planetary systems, circumstellar disk imaging and computational modeling, adaptive optics instrumentation, and next generation telescope mission design. Additional opportunities within the Five College Astronomy Department include planetary science, star formation, molecular clouds, galactic structure, galaxy evolution and cosmology. Subject to availability of resources and faculty interest, Honors projects arising out of students’ particular interests are encouraged.

Students must submit a written thesis on the Honors work a few weeks before the end of their final semester (in late April for spring graduation). Students give a preliminary presentation of their work during the first semester, and a final presentation at the end of the second semester. In addition, they take oral examinations devoted primarily to the thesis work. The departmental recommendation for the various levels of Honors will be based on the student’s record, Departmental Honors work, Comprehensive Examination, and Oral Examination on the thesis.

*General Education Astronomy Courses. *The Astronomy Department also offers courses for students not majoring in Astronomy. These include ASTR 111 and 112 at Amherst. Students may search for Astronomy courses through the Five College online catalog. The Website is https://www.fivecolleges.edu/academics/courses.

*On leave 2018-19.

†On leave fall semester 2018-19.

‡ On leave spring semester 2018-19.

What is the shape of the universe? How do stars die? What happens when galaxies collide? This course will provide an introduction to the nature and evolution of stars, our Milky Way galaxy, other galaxies, and the origin, size, shape and fate of the universe itself. We will explore how the fields of extragalactic astronomy and cosmology emerged and continue to evolve, and will touch on many of the big unanswered questions in these fields. Our investigations of galactic and extragalactic phenomena will focus on understanding proportionalities, relative sizes, and visual representations of data, as well as evaluating the reasonableness of quantitative answers rather than on lengthy calculations.

Limited to 60 students (25 spots reserved for first-year students). Not open to advanced physical science majors. Omitted 2018-19.

How did our solar system form? Are planets like Earth typical or rare? When, where, and how might we find life elsewhere in the universe? This course will provide an introduction to the formation and evolution of solar systems, including an exploration of the geology, chemistry and biology of the planets in our own solar system. We will discuss the origins, successes and limitations of techniques being used to discover planets around other stars (exoplanets), and the nature of planetary habitability. Our investigations will focus on understanding proportionalities, relative sizes, and visual representations of data, as well as evaluating the reasonableness of quantitative answers rather than on lengthy calculations.

Limited to 45 students (25 spots reserved for first-year students). Preference to first-year students and seniors. Fall semester. Professor Follette.

The purpose of this course is to introduce data analysis and visualization techniques that will allow students to excel in further coursework in astronomy and other STEM majors. Students will be introduced to how to use the Python programming language to analyze and manipulate data; how to create, interpret, and present visualizations of those data; and how to apply statistical analysis techniques to data. We will sharpen these skills through the lens of astronomical data collection and analysis, though the skills themselves are applicable in many other fields.

Recommended requisite: ASTR 111 or 112 and COSC 111. Limited to 20 students. Spring semester. Professor Follette.

This course will explore humankind’s understanding of the sun throughout history, from archaeoastronomy to modern problems in solar astrophysics. Topics may include the alignment of ancient structures to solar and lunar motions, the importance of the sun in time-keeping, the study of sunspots, the development of the theory of the sun’s power source, the behavior of the solar magnetic field, the “neutrino problem” in twentieth century solar observations which led to changes in particle physics theory, and challenges of solar observing. The course will include an observing component outside of lecture, work with planetarium software, and discussion of historical work done by observers in the Five Colleges.

Requisite: PHYS 117/124 or equivalent and one astronomy course. Limited to 18 students. Omitted 2018-2019.

Cosmological models and the relationship between models and observable parameters. Topics in current astronomy that bear upon cosmological problems, including background electromagnetic radiation, nucleosynthesis, dating methods, determinations of the mean density of the universe and the Hubble constant, and tests of gravitational theories. Discussion of questions concerning the foundations of cosmology and its future as a science.

Requisites: MATH 111 and one course in the physical sciences. Omitted 2018-2019.

This course provides a quantitative introduction to the physical principles that govern the universe. The laws of gravity, thermal physics, atomic physics, and radiation will be applied to develop understanding of a variety of astrophysical phenomena. These include: the formation of stars and planets, the life cycle of stars, and the nature of the interstellar medium. This course is intended for students majoring in astronomy and serves as a gateway to the more complex topics covered in upper division astronomy classes. However, non-majors who are interested in a robust treatment of introductory astrophysics are welcome to participate in the course, and we will review the relevant physics and mathematics as we apply them to astrophysical problems

Requisite: MATH 121 and PHYS 124 or 117, concurrent enrollment acceptable. Fall semester. Professor Follette.

From “Hot Jupiters” to “Super Earths,” many of the extrasolar planets (exoplanets) being detected by astronomers today have markedly different physical properties than the planets in our own solar system. At the same time, the ever-increasing rate of detections has enabled statistical studies of exoplanet populations, allowing astronomers to make inferences about planet formation processes. This course will provide an overview of the field of exoplanet detection and characterization. We will review detection techniques, the physics of planetary atmospheres and interiors, the dynamical evolution of planetary systems, planet population statistics, definitions and constraints on habitability, and prospects for the detection of biosignatures with next-generation telescopes. Students will hone their skills in close reading of published scientific results and in summarizing those results to an audience of their peers.

Requisites: PHYS 116 or 123, MATH 211 or PHYS 227, or permission of the instructor. Omitted 2018-2019

The same basic laws describe stars and planets. We will learn about equations of state as well as radiative and convective heat transport in order to understand the steady-state structure of stellar and planetary interiors and atmospheres. We will then see how waves propagate through these bodies, producing stellar pulsations, earthquakes, and weather.

Requisite: MATH 121 and PHYS 124 or 117. Omitted 2018-2019.

An introduction to the techniques of observational astronomy, with emphasis on optical and infrared observations. Students will use the Python computing language to reduce real astronomical data. Topics covered include: astronomical software; observation planning; coordinate and time systems; telescope design and optics; instrumentation and techniques for imaging and photometry; astronomical detectors; digital image processing tools and techniques; and statistical techniques for making astronomical measurements.

Requisite: At least one of ASTR 200, 224, 225, 226 or 228, two PHYS courses, and one COSC course. Fall semester Post-doctoral Fellow Ward-Duong.

An immersive research experience in observational astrophysics for students who have completed ASTR 337. Students begin the semester with a January trip to the WIYN 0.9m telescope on Kitt Peak, AZ, where they collect data that they will use to design and carry out independent research projects. The semester is spent reducing and analyzing the data and preparing scientific results for presentation. Professional techniques of CCD imaging, photometry, astrometry and statistical image analysis are applied using research-grade software. Weekly class seminar meetings are supplemented by individual and team-based tutorial sessions.

Requisites: ASTR 337 and consent of the instructor. Limited to 12 students. Not open to first-year students or sophomores. Spring semester. Post-doctoral Fellow Ward-Duong.

This course applies physics to understand the astronomical phenomena related to galaxies. The structure and evolution of galaxies will be examined, exploring both the interrelationship of stars, gas, and dust in galaxies and the interaction of galaxies in groups or clusters. Concepts of stellar populations and the feedback between stars and galaxies through star formation and death will be used to understand the differences between elliptical, spiral, and irregular galaxies and their structure as seen using radio, optical, and high-energy telescopes. Galactic rotation and other motions will be studied to reveal evidence of dark matter as a significant constituent of the known universe, and to understand the source of spiral arms and bars in some galaxies. Evidence for massive black holes at the centers of galaxies will be discussed.

Requisite: ASTR 228 or ASTR 335, PHYS 117/124 or equivalent. Recommended requisite: PHYS 225. Omitted 2018-19.

Independent reading course.

Fall and spring semesters. The Department.

Opportunities for theoretical and observational work on the frontiers of science are available in cosmology, cosmogony, radio astronomy, planetary atmospheres, relativistic astrophysics, laboratory astrophysics, gravitational theory, infrared balloon astronomy, stellar astrophysics, spectroscopy, and exobiology. Facilities include the Five College Radio Astronomy Observatory, the Laboratory for Infrared Astrophysics, balloon astronomy equipment (16-inch telescope, cryogenic detectors), and modern 24- and 16-inch Cassegrain reflectors. An Honors candidate must submit an acceptable thesis and pass an oral examination. The oral examination will consider the subject matter of the thesis and other areas of astronomy specifically discussed in Astronomy courses.

Open to seniors. Required of Honors students. Spring semester. The Department.

We will develop the concept of energy from a Physics perspective. We will introduce the various forms that energy can take and discuss the mechanisms by which it can be generated, transmitted, and transformed. The law of conservation of energy will be introduced both as a useful tool, and as an example of a fundamental physical law. The environmental and financial costs and benefits of various methods of energy generation and consumption will be discussed. Demonstrations and hands-on laboratory experiences will be an integral part of the course. The course is intended for non-science majors and not for students who have either completed or intend to complete the equivalent of PHYS 117 or CHEM 110.

Requisite: A working knowledge of high-school algebra, geometry and trigonometry. Limited to 20 students. Omitted 2018-19. Professor Hunter.

The aim of the course is to foster an understanding of and intuition for the modern-day electronic devices and circuits that are central to many aspects of our research, work, and play. A practical hands-on approach serves this aim well. After investigating the electrical characteristics of electronic components, including discrete semiconductor devices and integrated circuits (ICs), we go on to build and analyze both analog and digital circuits in order to gain insight into electronic control devices, data acquisition systems, and computers. Brief introductory lecture/discussion periods will be followed by experiments to help students understand new concepts. While the course is elementary, experienced students will be able to explore more complex circuitry and will be encouraged to apply some of their newly developed electronics knowledge and creativity to ongoing research projects in other fields. Two eighty-minute meetings per week of Lecture/Discussion/Laboratory.

Limited to 20 students. Fall semester. Professor Carter.

This course will begin with a description of the motion of particles and introduce Newton’s dynamical laws and a number of important force laws. We will apply these laws to a wide range of problems to gain a better understanding of the laws and to demonstrate the generality of the framework. The important concepts of work, mechanical energy, and linear and angular momentum will be introduced and the unifying idea of conservation laws will be discussed. Additional topics may include, the study of mechanical waves, fluid mechanics and rotational dynamics. Three hours of lecture and one three-hour laboratory per week.

Requisite: MATH 111. Limited to 48 students. Fall semester: Visiting Assistant Professor Collette. Spring semester: Professor Friedman.

Most of the physical phenomena we encounter in everyday life are due to the electromagnetic force. This course will begin with Coulomb’s law for the force between two charges at rest and introduce the electric field in this context. We will then discuss moving charges and the magnetic interaction between electric currents. The mathematical formulation of the basic laws in terms of the electric and magnetic fields will allow us to work towards the unified formulation originally given by Maxwell. His achievement has, as a gratifying outcome, the description of light as an electromagnetic wave. Laboratory exercises will emphasize electrical circuits and electronic measuring instruments. Three hours of lecture and discussion and one three-hour laboratory per week.

Requisite: PHYS 116 or 123. Limited to 48 students. Fall semester: Professor Hall. Spring semester: The Department.

The idea that the same simple physical laws apply equally well in the terrestrial and celestial realms, called the Newtonian Synthesis, is a major intellectual development of the seventeenth century. It continues to be of vital importance in contemporary physics. In this course, we will explore the implications of this synthesis by combining Newton’s dynamical laws with his Law of Universal Gravitation. We will solve a wide range of problems of motion by introducing a small number of additional forces. The concepts of work, kinetic energy, and potential energy will then be introduced. Conservation laws of momentum, energy, and angular momentum will be discussed, both as results following from the dynamical laws under restricted conditions and as general principles that go well beyond the original context of their deduction. Newton’s laws will be applied to a simple continuous medium to obtain a wave equation as an approximation. Four hours of lecture and discussion and one three-hour laboratory per week.

Requisite: MATH 111. Admission with consent of the instructor. Limited to 24 students. Fall semester. Professor Hunter.

In the mid-nineteenth century, completing nearly a century of work by others, Maxwell developed an elegant set of equations describing the dynamical behavior of electromagnetic fields. A remarkable consequence of Maxwell’s equations is that the wave theory of light is subsumed under electrodynamics. Moreover, we know from subsequent developments that the electromagnetic interaction largely determines the structure and properties of ordinary matter. This course will begin with Coulomb’s Law but will quickly introduce the concept of the electric field. Students will explore moving charges and their connection with the magnetic field, study currents and electrical circuits, and discuss Faraday’s introduction of the dynamics of the magnetic field and Maxwell’s generalization. Laboratory exercises will concentrate on circuits and electronic measuring instruments. Four hours of lecture and discussion and one three-hour laboratory per week.

Requisite: MATH 121 and PHYS 116 or 123. Limited to 24 students. Spring semester. The Department.

Phenomena that repeat over regular intervals of time and space play a fundamental role in many areas of physics and its applications. This course begins with a review of periodic oscillations of a simple harmonic oscillator, and proceeds to a discussion of a damped, driven, linear oscillator. Both mechanical and electrical oscillators will be discussed within a single mathematical framework. The course then turns to waves, including mechanical waves in solid, liquid, or gas media as well as electromagnetic waves. Classes of waves are distinguished, such as longitudinal and transverse as well as traveling and standing. General wave phenomena are discussed, including superposition, interference, and diffraction. Discussion of ray optics as a limiting case of wave optics leads to a simple description of reflection and refraction at plane and curved interfaces and to an understanding of simple optical instruments as well as the eye. The laboratory experiments on oscillations, mechanical waves and optics provide hands-on experience of the concepts discussed in the rest of the course. Optional topics include coupled oscillators and normal modes using matrix methods, and Fourier series and Fourier Transforms as tools for examining arbitrary signals and waves in terms of their harmonic components. Four hours of lectures and discussion and one three-hour laboratory per week.

Requisite: PHYS 116/123 and MATH 121 or consent of the instructor. Limited to 24 students. Fall semester. Professors Carter and Jagannathan.

Makers are doers, inventors, builders, or creators who learn as they go. Here we will take that approach with optics in this project-based course. The semester will begin with discussions of the principles of optics and with exercises to improve students’ skills in computer-assisted design, laser alignment, data acquisition, and technical communication. At the same time, students will be creating their own optical system and testing their skills. In the second half of the semester, students will explore, design, and build a second optical system in either holography, interferometry, optical information processing, laser optics, fiber optics, or a topic of their choice. The class is open to both science and non-science majors. Two projects and a final paper. Two class meetings per week.

Requisite: PHYS 116. Limited to 12 students. Omitted 2018-2019. The Department.

The theories of relativity (special and general) and the quantum theory constituted the revolutionary transformation of physics in the early twentieth century. Certain crucial experiments precipitated crises in our classical understanding to which these theories offered responses; in other instances, the theories implied strange and/or counterintuitive phenomena that were then investigated by crucial experiments. After an examination of the basics of Special Relativity, the quantum theory, and the important early experiments, we will consider their implications for model systems such as a particle in a box, the harmonic oscillator, and a simple version of the hydrogen atom. We will also explore the properties of nuclei and elementary particles, and study other topics such as lasers, photonics, and recent experiments of interest in contemporary physics. Three class hours per week.

Requisites: MATH 121 and PHYS 117 or 124. Fall semester. Professor Friedman.

How do we gather information to refine our models of the physical world? This course is all about data: acquiring data, separating signals from noise, analyzing and interpreting data, and communicating results. Much – indeed nearly all – data spend some time as an electrical signal, so we will study analog electronics. In addition, students will become familiar with contemporary experimental techniques and instrumentation. Throughout, students will develop skills in scientific communication, especially in the written form. Six hours of laboratory work per week.

Requisite: PHYS 225 or consent of the instructor. Spring semester. The Department.

The basic laws of physics governing the behavior of microscopic particles are in certain respects simple. They give rise both to complex behavior of macroscopic aggregates of these particles, and more remarkably, to a new kind of simplicity. Thermodynamics focuses on the simplicity at the macroscopic level directly, and formulates its laws in terms of a few observable parameters like temperature and pressure. Statistical Mechanics, on the other hand, seeks to build a bridge between mechanics and thermodynamics, providing in the process, a basis for the latter, and pointing out the limits to its range of applicability. Statistical Mechanics also allows one to investigate, in principle, physical systems outside the range of validity of Thermodynamics. After an introduction to thermodynamic laws, we will consider a microscopic view of entropy, formulate the kinetic theory, and study several pertinent probability distributions including the classical Boltzmann distribution. Relying on a quantum picture of microscopic laws, we will study photon and phonon gases, chemical potential, classical and degenerate quantum ideal gases, and chemical and phase equilibria. Three class hours per week.

Requisite: PHYS 225 or consent of the instructor. Spring semester. The Department.

A two-level quantum system is one whose states are represented by unit rays in a two-dimensional vector space. Such a system is the simplest non-trivial quantum mechanical entity. Nevertheless, a two-level system or a collection of such systems exhibits all of the challenging and subtle features for which the quantum theory is notorious. Examples of two-level systems we will consider are the polarization states of a photon, the spin of an electron or similar particle, and any atomic system for which only two of its many energy levels are important in a given problem. After an overview of the current state of quantum mechanics, we will spend about three weeks on a synopsis of the concepts of pre-quantum (classical) physics. We will review complex numbers and matrix algebra mainly to establish a common notation. We then begin to explore quantum kinematics and dynamics of a two-level system in the language of matrices, as well as in the abstract language of vector spaces. We extend the theory to a collection of two-level systems and discuss *entanglement*, the devil at the heart of quantum conundrums. Discussions of the Uncertainty Principle, the Einstein-Podolsky-Rosen challenge, Schrodinger’s Cat, Bell’s theorem, the no-cloning theorem and quantum teleportation follow. The work in the course consists of regular problem sets, two midterm tests, and a final short project presentation and report. No college physics is presupposed. Two meetings per week.

Requisites: MATH 211 and MATH 271/272. Omitted 2018-19. The Department.

This course begins with the foundation of classical mechanics as formulated in Newton’s Laws of Motion. We then use Hamilton’s Principle of Least Action to arrive at an alternative formulation of mechanics in which the equations of motion are derived from energies rather than forces. This Lagrangian formulation has many virtues, among them a deeper insight into the connection between symmetries and conservation laws. From the Lagrangian formulation we will move to the Hamiltonian formulation and the discussion of dynamics in phase space, exploring various avenues for the transition from the classical to the quantum theory. We will study motion in a central force field, the derivation of Kepler’s laws of planetary motion from Newton’s law of gravity, two-body collisions, and physics in non-inertial reference frames. Other topics may include the dynamics of driven, damped oscillators, and non-linear dynamics of chaotic systems. Three class hours per week.

Requisite: PHYS 227 or consent of the instructor. Fall semester. Professor Jagannathan.

A development of Maxwell’s electromagnetic field equations and some of their consequences using vector calculus. Topics covered include: electrostatics, steady currents and static magnetic fields, time-dependent electric and magnetic fields, and the complete Maxwell theory, energy in the electromagnetic field, Poynting’s theorem, electromagnetic waves, and radiation from time-dependent charge and current distributions. Three class hours per week.

Requisite: PHYS 117 or 124 and PHYS 227 or consent of the instructor. Fall semester. Professor Friedman.

Wave-particle duality and the Heisenberg uncertainty principle. Basic postulates of Quantum Mechanics, wave functions, solutions of the Schroedinger equation for one-dimensional systems and for the hydrogen atom. Three class hours per week.

Requisite: PHYS 225 and 343 or consent of the instructor. Spring semester. The Department.

(Offered as PHYS 400, BIOL 400, BCBP 400, and CHEM 400) How do the physical laws that dominate our lives change at the small length and energy scales of individual molecules? What design principles break down at the sub-cellular level and what new chemistry and physics becomes important? We will answer these questions by looking at bio-molecules, cellular substructures, and control mechanisms that work effectively in the microscopic world. How can we understand both the static and dynamic shape of proteins using the laws of thermodynamics and kinetics? How has the basic understanding of the smallest molecular motor in the world, ATP synthase, changed our understanding of friction and torque? We will explore new technologies, such as atomic force and single molecule microscopy that have allowed research into these areas. This course will address topics in each of the three major divisions of Biophysics: bio-molecular structure, biophysical techniques, and biological mechanisms.

Requisite: CHEM 161, PHYS 116/123, PHYS 117/124, BIOL 191 or evidence of equivalent coverage in pre-collegiate courses. Spring semester. Professor Carter.

The course is an elementary introduction to Einstein's theory of gravity. After a brief review of the special theory of relativity, we will investigate vector and tensor fields in terms of their properties under changes of coordinates. We will study geometric ideas such as geodesics, parallel transport, and covariant differentiation, and present the Principle of Equivalence as the central physical principle behind Einstein's theory of gravity. After introducing the stress tensor, we will then state the field equations and obtain the simplest solutions to them, and derive the physical implications of the theory for the motion of planets and light in the vicinity of massive stars. We will round out the discussion of the subject with classical cosmology and gravitational radiation.

Requisite: PHYS 225, and either MATH 211 or PHYS 227; or consent of the instructor. Omitted 2018-19. Professor Loinaz.

Independent reading course.

Fall and spring semester.

Same description as PHYS 498. A double course.

Requisite: PHYS 498. Spring semester. The Department.

- Five College Courses
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- Ethnomusicology Certificate
- International Relations Certificate
- Latin American Caribbean Latino Studies Certificate
- Logic Certificate
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