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Professors Friedman, Hunter, Hall†, Jagannathan (Chair), and Loinaz; Assistant Professors Carter, Follette, and Hanneke; Visiting Professor and STINT Fellow Viklund; Visiting Assistant Professor Stage; Post-doctoral Fellow Ward-Duong.

†On leave fall semester 2017-18.

Physics

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 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.

The sequence PHYS 116, 117 may be taken by students who require two semesters of physics with laboratory. MATH 111 is a requisite for PHYS 116. There is no additional mathematics requirement for PHYS 117. 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. MATH 121 is a requisite for PHYS 124, but not for PHYS 117. Hence, students who wish to major after completing PHYS 117 should complete MATH 121.

*Major Program. *Students who wish to major in physics are required to take MATH 111 and 121, and PHYS 123, 124 (or PHYS 116, 117, but see above), 225, 226, 227, 230 (or CHEM 361), 343, 347 and 348. Students may petition the Department to substitute an upper-level course in a related discipline for a required upper level departmental course. Students planning a career in physics should seriously consider taking one or more electives in physics or a cognate field. Electives offered vary year to year.

All Physics majors must demonstrate satisfactory performance on an approved standardized test in general physics 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 Physics majors must also attend at least nine public physics 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 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. 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.

Astronomy

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 (Practical Astronomy), 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.

*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

Energy

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.

Introductory Physics I: Mechanics and Wave Motion

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.

Introductory Physics II: Electromagnetism and Optics

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 Newtonian Synthesis: Dynamics of Particles and Systems, Waves

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.

The Maxwellian Synthesis: Dynamics of Charges and Fields, Optics

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.

Maker Optics

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.

Modern Physics

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.

Signals and Noise Laboratory

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.

Methods of Theoretical Physics

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.

Statistical Mechanics and Thermodynamics

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.

The Physics and Biology of Ultrasound

(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.

Quantum Mechanics of Two-Level Systems

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.

Dynamics

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.

Electromagnetic Theory I

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.

Quantum Mechanics I

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.

Molecular and Cellular Biophysics

(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.

General Relativity

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.

Special Topics

Independent Reading Course. A full course.

Fall and spring semester.

Senior Departmental Honors

Same description as PHYS 498. A single course.

Requisite: PHYS 498. Spring semester. The Department.

- Five College Courses
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- African Studies Certificate
- Asian Pacific American Certificate
- Buddhist Studies Certificate
- Coastal and Marine Sciences Certificate
- Culture Health Science Certificate
- Ethnomusicology Certificate
- International Relation Certificate
- Latin American Carribbean Latino Certificate
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- Native American Certificate
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- Russian East European Certificate
- Sustainability Studies Certificate Program