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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). Fall semester. Visiting Professor Stage.

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

How do Astronomers gather information about the universe? What tools and techniques do they use to interpret that information? How does one tell sound results from questionable ones? The purpose of this course is to introduce computational and numerical reasoning techniques that will allow students to excel in further coursework in astronomy and/or other STEM majors. With a particular emphasis on how to clearly and honestly visualize real astrophysical data, students will be introduced to: how to use the Python programming language to analyze and manipulate data, how to read and interpret scientific publications, how to make and dissect data-driven arguments, and how to give an engaging scientific presentation. We will sharpen these skills through the lens of astronomical data collection and analysis, with a focus on how astronomers collect and analyze light, including types that are not visible to the human eye.

Recommended requisite: ASTR 111 or 112. Limited to 20 students. Omitted 2017-18. Professor Follette and Visiting Professor Stage.

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. Preference will be given to Amherst and Five College astronomy majors, then other Amherst physics/science majors, and finally by seniority.

Requisite: PHYS 117/124 or equivalent and one astronomy course. Limited to 18 students. Omitted 2017-18. Visiting Professor Stage.

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. Spring semester. Visiting Professor Stage.

A calculus-based introduction to the properties, structure, formation and evolution of stars and galaxies. The laws of gravity, thermal physics, and atomic physics provide a basis for understanding observed properties of stars, interstellar gas and dust. We apply these concepts to develop an understanding of stellar atmospheres, interiors, and evolution, the interstellar medium, and the Milky Way and other galaxies.

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

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. Fall semester. Professor TBA.

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.

Requisites: at least one of AST 200, 224, 225, 226 or 228, two physics courses, and one computer science course. Fall semester. Professor Follette and 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 permission 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. Spring semester. Visiting Professor Stage.

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.

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. Spring semester. Professor Hunter.

The 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. The study of mechanical waves permits a natural transition from the dynamics of particles to the dynamics of waves, including the interference of waves. Additional topics may include fluid mechanics and rotational dynamics. Three hours of lecture. Also one three-hour laboratory per week.

Requisite: MATH 111. Limited to 48 students. Fall semester: Professor Hunter. 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. The course will consider both ray-optics and wave-optics descriptions of light. Laboratory exercises will emphasize electrical circuits, electronic measuring instruments, optics and optical experiments. 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. Spring semester: Professor Hall.

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. Properties of mechanical waves will be discussed. 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 Hanneke.

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. The 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, electronic measuring instruments, and optics. 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 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. If over-enrolled, students will be asked to provide a paragraph stating why they would like to be in the course.

Requisite: PHYS 116. Limited to 12 students. Spring semester. Assistant Professor Carter.

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. Professor Hanneke.

The course will present the mathematical methods frequently used in theoretical physics. The physical context and interpretation will be emphasized. Topics covered will include vector calculus, complex numbers, ordinary differential equations (including series solutions), partial differential equations, functions of a complex variable, and linear algebra. Four class hours per week.

Requisite: MATH 121 and PHYS 117/124 or consent of the instructor. Fall semester. Professor Loinaz.

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. Professor Loinaz.

(Offered as PHYS 240 and BCBP 240) Why is ultrasound the most commonly used imaging technology used at clinics and hospitals? What happens at the biological level when ultrasound interacts with living matter? How can ultrasound be used for gentle imaging purposes, but also for disrupting cell membranes, bursting blood clots and breaking kidney stones? What other biological applications of ultrasound exist in modern research? We will answer these questions and more by first studying the theory and principles of acoustic waves at higher frequencies, including related phenomena such as acoustic streaming, acoustic radiation forces and cavitation, followed by a walk-through of modern biologically relevant applications of ultrasound. We will also introduce a novel research area called microscale acoustofluidics, where ultrasound is applied to microfluidic systems with applications in, for example, cellular separation, enrichment, isolation and tissue engineering.

Requisite: PHYS 116/123, PHYS 117/124, and MATH 111, or evidence of equivalent coverage in pre-collegiate courses. Fall semester. Stint Fellow Viklund.

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. Fall semester. Professor Jagannathan.

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 Loinaz.

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. Professor Hunter.

(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 prsent 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 instructor. Spring semester. Professor Loinaz.

Independent Reading Course. A full course.

Fall and spring semester.

Same description as PHYS 498. A double course.

Requisite: PHYS 498. Spring semester. The Department.