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This course will introduce students to how to observe and understand a variety of phenomena in the daytime and nighttime sky. The lecture portion of the course will focus on the history of our understanding of the universe and how observations of celestial phenomena provided clues at each stage of this journey, which continues to this day. The nighttime laboratory portion of the course will focus on naked-eye, telescopic, and photographic observations of the sky. The course will make use of Amherst’s on-campus observatory on the roof of the new science center.

Limited to 36 students, divided into two sections, with 24 seats reserved for first-year students. Omitted 2021-22.

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. Spring semester. Visiting Professor Sharon.

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. Omitted 2021-22.

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. Omitted 2021-22.

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 116 or 123, or permission of instructor . Fall semester. Professor Loinaz.

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: ASTR 228 is a prerequisite for 337 and consent of instructor. ASTR 228 maybe taken concurrently with ASTR 337 subject to consent of instructor. Fall semester. Instructor Robinson.

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 or use a online commercial telescope service (depending on the state of the pandemic) to 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. Instructor Robinson.

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. Spring semester. Visiting Professor Sharon.

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. Fall semester. The Department.

(Offered as PHYS 102 and MATH 102) On January 27th, 1921, Albert Einstein gave a lecture titled “Geometry and Experience" at the Prussian Academy of Science. In this lecture he reflects on the interdependence of geometry and physics. To commemorate the centenary of such an inspiring event, this course will explore the natural connections between geometry (axioms, the notions of space and time, dimension and curvature) and relativity (the relativity principle, simultaneity, thought experiments). No background in physics or mathematics (besides basic high school algebra and trigonometry) will be assumed.

The course is designed for students who do not intend to major in mathematics or physics. Omitted 2021-22. Professor Jagannathan.

The course is designed for students who do not intend to major in mathematics or physics. Omitted 2021-22. Professor Jagannathan.

(Offered as MUSI 108 and PHYS 108) Appreciating music requires no special scientific or mathematical ability. Yet science and mathematics have a lot to tell us about how we make music and build instruments, what we consider harmonious, and how music is processed by the ear and brain. This course will delve into the fundamentals of music theory, perceptual psychology, and physics in exploring such topics as scales and tunings, the physical properties of sound, Fourier analysis, organizing principles of musical forms, fundamentals of instrument construction, vocal sound production, and elements of sound recording and music production. We will consider ways in which science can be part of the creative process as well as the role creativity plays in scientific discovery. The course will include laboratories during the usual class times that cover a variety of topics ranging from basic acoustics to the formants of vowel sounds. The semester will culminate in an artistic or scientific project located at the crossroads of music and science. No background in music or physics is required. Students are expected to be well versed in high-school-level mathematics, but no knowledge of calculus will be assumed.

Spring semester. Limited to 20 students. Professors Sawyer and Friedman

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.

The course is designed as an in-person course with active lab work.

Requisite: A working knowledge of high-school algebra, geometry and trigonometry. Limited to 20 students. Omitted 2021-22. 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. Omitted 2021-22. Professor Carter.

We live in a moment of great advances in astronomy and fundamental physics that are changing our understanding of the physical world, from the microscopic realm of elementary particles to the large-scale structure of the universe. This course will explore the ideas of quantum theory and relativity that underpin our models of the universe. It will emphasize our present understanding of these models, the experimental and observational basis for them, and the many open questions under active investigation. Quantitative reasoning in the course will focus on probability, proportional reasoning, and reasonableness of answers rather than lengthy calculations. Fall semester: Professor Hanneke.

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 hour of discussion and three-hour laboratory per week.

Requisite: MATH 111. Fall semester: Professor Friedman and Dr. Moyer and Spring Semester: Department.

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 Carter and Instructor Moyer. Spring semester: 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. 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; Professor Hanneke

Phenomena that repeat over regular intervals of time and space play a fundamental role in physics and its applications. This course explores oscillations and waves in contexts from a simple mass on a spring to mechanical waves in solids, liquids, and gasses as well as electromagnetic waves. It emphasizes broadly applicable phenomena including superposition, boundary effects, interference, diffraction, coherence, normal modes, and the decomposition of arbitrary wave amplitudes into normal modes, as with Fourier analysis. The laboratory experiments on oscillations, mechanical waves and optics provide hands-on experience of the concepts discussed in the rest of the course. Two hours of lecture 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. Professor Hanneke and Jagannathan.

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 or equivalent or consent of the instructor. 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, instrumentation, and/or computational methods. 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: Professor Hunter.

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 CHEM 161/CHEM165 and PHYS 117/PHYS 124 and MATH 121. Recommended: MATH 211. Spring semester: Professor Carter.

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 2021-22.

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 116/123 PHYS 125, MATH 211 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 117/124, PHYS 125, MATH 211 or consent of the instructor. Fall semester. Professor Loinaz.

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: MATH 211 and PHYS 225 or consent of the instructor. Spring semester: Professor Jagannathan.

Quantum Mechanics is well known for its counterintuitive and seemingly paradoxical predictions. Despite its failure to give us a clear, intuitive picture of the world, the theory is remarkably successful at predicting the outcomes of experiments, although those predictions are probabilistic rather than deterministic. Because of its unparalleled success, the thorny issues about the theory’s foundations were often ignored during its first fifty years. Recent advances in both theory and experiment have again brought these issues to the fore. This course will review some of the most interesting and intriguing facets of quantum mechanics and its potential applications to information and computing. Topics to be covered will include the Schrödinger cat paradox and the quantum measurement problem; Bell’s inequalities, entanglement, and related phenomena that establish the “weirdness” of quantum mechanics; secure communication using quantum cryptography; and how quantum computers (if built) can solve certain problems much more efficiently than classical ones. We will also explore recent experiments in which quantum phenomena appear on the macroscopic scale, as well as technological progress towards building a large-scale, general-purpose quantum computer.

Requisite: Physics 225. Omitted 2021-2022.

(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 161/165, 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 and modern cosmology. 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 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 then discuss modern cosmology, including an introduction to the particle physics needed to describe the thermal history of the universe just after the Big Bang.

Requisite: PHYS 225 and MATH 211; or consent of the instructor. Omitted 2021-22.

Independent reading course.

Fall and spring semester.

Individual, independent work on some problem, usually in experimental physics. Reading, consultation and seminars, and laboratory work. Designed for honors candidates, but open to other advanced students with the consent of the department.

Fall semester. The Department.