# Catalog

## Physics and Astronomy

Professors Lin (chair), Semon, Smedley, and Wollman; Associate Professor Lundblad; Assistant Professor Gould; Visiting Assistant Professors Porter and Saha; Lecturer Clough

Physics, the study of space, time, matter, and energy, is a fundamental component of a liberal education. Introductory courses in physics and astronomy are designed to give students a broad background in the fundamentals of the discipline, an introduction to the logic and philosophy of science, and insight into the understanding and applications of contemporary physics and astrophysics. Advanced courses provide greater depth and sophistication as the student's background in physics and mathematics develops. Laboratory investigation, designed to accommodate each student's particular needs, provides direct experience of the central role that experimental research plays in the advancement of science. More information on physics and astronomy can be found on the website (bates.edu/physics-astronomy).

#### Major Requirements

The major in physics can be structured to meet the individual needs of students planning graduate study in physics or engineering, as well as those considering careers in business, teaching, government, law, or medicine. To learn physics effectively, it is important that courses be taken in the recommended order and, if at all possible, with the recommended background. Nevertheless, prerequisites and corequisites can be waived in appropriate circumstances, especially in cases of incoming students with strong backgrounds. Students considering graduate study in physics or engineering should take PHYS 409 and 422 as well as other courses numbered 300 or higher. In exceptional cases, a student who otherwise meets the ten-course requirement may petition the department to take a comprehensive examination in lieu of the senior thesis project. The requirement for a major is ten courses in physics.Required Courses, usually taken in this order:

One of the following:

PHYS 108. Modern Physics/Lab.

FYS 274. Physics in the Twentieth Century/Lab.

All of the following:

PHYS 211. Newtonian Mechanics.

PHYS 222. Electricity, Magnetism, and Waves.

PHYS 231. Laboratory Physics I/Lab.

PHYS 301. Mathematical Methods of Physics.

PHYS 308. Introductory Quantum Mechanics.

One of the following:

PHYS 409. Quantum Theory.

PHYS 412. Advanced Classical Mechanics.

PHYS 422. Electromagnetic Theory.

PHYS 457 or PHYS 458. Senior Thesis. Only one semester of senior thesis may count toward the minimum ten-course requirement.

Additional Courses: Two additional courses must be selected from the following:

PHYS 107. Classical Physics/Lab (only if taken prior to PHYS 108, concurrently with FYS 274, or if assigned as Advanced Placement credit).

PHYS 214. Renewable Energy.

PHYS 216. Computational Physics.

PHYS 218. Engineering Physics.

PHYS 220. Climate Change and Modelling.

PHYS s27. The Asteroid Impact Threat: What Can We Do?

PHYS s30. Electronics/Lab.

Any physics course numbered 300 or higher.

#### Minor Requirements

The requirement for a minor is six courses in physics, including the following three, usually taken in this order:One of the following:

PHYS 108. Modern Physics/Lab.

FYS 274. Physics in the Twentieth Century/Lab.

Both of the following:

PHYS 222. Electricity, Magnetism, and Waves.

PHYS 211. Newtonian Mechanics.

The additional three courses must be selected from the following:

PHYS 107. Classical Physics/Lab (only if taken prior to 108, or concurrently with FYS 274)

PHYS s27. The Asteroid Impact Threat: What Can We Do?

PHYS s30. Electronics/Lab.

Any course numbered 200 or higher, except for INDS 228.

Environmental studies majors who elect the Energy concentration may not select the physics minor.

#### Pass/Fail Grading Option

Pass/fail grading may not be elected for courses applied toward the minor or major.#### General Education

Students majoring in physics may satisfy the [W2] requirement by completing any four of the following courses in the sophomore and/or junior year: PHYS 211, 214, 222, 231, 301, 341, 381, s27.#### Engineering

A student interested in using physics as a basis for an engineering career should inquire about the Bates dual-degree plans with Dartmouth, Rensselaer, Columbia, Washington University in St. Louis, or Case Western Reserve (consult the website, bates.edu/physics-astronomy/academics/engineering). By careful planning at registration time, similar combination curricula may sometimes be designed with other engineering institutions. Students participating in a dual-degree program declare a major in engineering.##### ASTR 104. Cosmology in the Twentieth Century.

The twentieth century saw the emergence of a coherent scientific understanding of the physical universe as a whole. According to this understanding, the universe has evolved from a hot, dense, and rapidly expanding soup of elementary particles into the system of galaxies we see today. But the picture is not complete, and topping the list of unresolved puzzles is the identity of the so-called dark matter. We cannot see the dark matter (hence its name), but we do measure its gravitational influences on matter we can see. The disconcerting conclusion is that there is much more dark matter than visible matter. This course examines the development of modern cosmology, with attention to both that which seems to be well-understood and that which is not yet understood. Enrollment limited to 64. Normally offered every year. [Q] [S] E. Wollman.Concentrations

This course is referenced by the following General Education Concentrations

##### AT/GE 110. Lunar and Planetary Science/Lab.

An introduction to the solar system using the methods of physics and geology. The historical development of our understanding of planetary motion leads to the contemporary view of celestial mechanics essential to exploration by spacecraft. The composition, formation, and age of the solar system are examined, together with the physical processes involved in the development of planetary interiors and surfaces. Basic algebra and geometry are used throughout. Laboratory work emphasizes the principles of remote sensing and exploration technology. Nighttime telescope work is expected. Enrollment limited to 56. Normally offered every year. [L] [Q] [S] Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### AT/GE s11. Finding Ourselves in the Cosmos.

With the help of small telescopes and cameras, students observe the night sky and form a picture of our location in space relative to members of our own solar system and to the stars and galaxies. Students observe star trails, motions of the sun and moon, positions of planets, star clusters, nebulae, and galaxies. Images are processed digitally. A strong background in basic geometry and algebra is recommended. The course includes as many observation nights as the weather allows. Recommended background: Geometry and algebra.New course beginning Short Term 2016. Enrollment limited to 16. One-time offering. [L] [Q] [S] R. Saha.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 103. Musical Acoustics/Lab.

An introduction to the science of sound and the acoustics of musical instruments through the study of mechanical vibrations and waves. Concepts such as resonance, standing waves, and Fourier synthesis and analysis are developed and applied to theoretical and laboratory investigations of musical sound. Additional topics include hearing, psychoacoustics, and musical scales and harmony. No background in physics or mathematics beyond algebra is assumed. Laboratory work, problem solving, and simulations are integrated into class activities. Enrollment limited to 72. [L] [Q] [S] J. Smedley.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 105. Physics in Everyday Life.

Designed for nonscience majors with no prior background in physics, this course introduces physics by studying how everyday objects work. Laws of motion, electric and magnetic forces, light and optics, and other physics topics are examined through the study of cameras, space travel, musical instruments, wind turbines, ball sports, color paints, bumper cars, roller coasters, photocopying machines, lasers, and medical imaging. Recommended background: high school algebra and geometry. Enrollment limited to 64. [Q] [S] J. Porter.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 106. Energy and Environment.

This course examines energy as a fundamental concept in physics and an essential element of human society. Basic principles of energy conservation and transformation are developed in order to understand sustainable and nonsustainable energy resources, how they are utilized, and their environmental impacts. No background in physics or mathematics beyond algebra is assumed. Not open to students who have received credit for CHEM 105 or s38. Enrollment limited to 72. [Q] [S] J. Smedley.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 107. Classical Physics/Lab.

A calculus-based introduction to Newtonian mechanics, electricity, and magnetism. Topics include kinematics and dynamics of motion, applications of Newton's laws, energy and momentum conservation, rotational motion, electric and magnetic fields and forces, and electric circuits. Laboratory investigations of these topics are computerized for data acquisition and analysis. Prerequisite(s) or corequisite(s): MATH 105, 106, 205 or higher. Enrollment limited to 72 per section. Normally offered every year. [L] [Q] [S] M. Semon.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 108. Modern Physics/Lab.

This course applies the material covered in PHYS 107 to a study of physical optics and modern physics, including the wave-particle duality of light and matter, quantum effects, special relativity, nuclear physics, and elementary particles. Laboratory work includes experiments such as the charge-to-mass ratio for electrons, the photoelectric effect, and electron diffraction. Prerequisite: PHYS 107. Not open to students who have received credit for FYS 274. Enrollment limited to 72 per section. Normally offered every year. [L] [Q] [S] Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### GE/PH 111. Polar Environment, Climate, and Ecosystems.

This course explores the global importance of the polar environment and ecosystem, and how they are affected by climate change. Topics include the physical environment of the polar regions, feedbacks on the global climate, the past history of glaciations, the polar ecosystem, and the change occuring now. Ice volume and sea level rise are estimated. Basic algebra and geometry are used throughout. Recommended background: basic algebra and geometry. Enrollment limited to 60. Normally offered every semester. [Q] [S] R. Saha.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 112. Physics of Sports/Lab.

Concepts in Newtonian mechanics are developed through the study of motions associated with a wide range of sports activities. Experiments, problem solving, and computer work are integrated into each class meeting. Enrollment limited to 24. [L] [Q] [S] J. Smedley.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 115. Physics for Policymakers.

This course presents a minimally mathematical survey of advanced physics aimed at providing future policymakers, executives, and elected officials with background necessary to be comfortable with the increasing scientific and technological nature of economic and political issues. Topics covered include energy and power, atoms, heat, radioactivity and nuclear power, gravity and space, electricity and magnetism, waves and light, climate change, quantum physics, and relativity. Enrollment limited to 50. [Q] [S] N. Lundblad.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 211. Newtonian Mechanics.

A rigorous study of Newtonian mechanics. Beginning with Newton's laws, the concepts of energy, momentum, and angular momentum are developed and applied to gravitational, harmonic, and rigid-body motions. Prerequisite(s): MATH 106 and PHYS 107. Open to first-year students. Normally offered every year. [Q] [S] H. Lin.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 214. Renewable Energy.

Renewable energy sources, including solar, gravitational, and geothermal energy, are considered essential to the pursuit of a sustainable future for technological society. This course focuses on the physics of renewable energy, with some attention to problems inhibiting its development. Prerequisite(s): MATH 106, and PHYS 108 or FYS 274. [Q] [S] J. Smedley.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 216. Computational Physics.

This course introduces computational methods for simulating physical systems and solving problems in physics and other areas. Programming languages like MATLAB and Mathematica are used to run simulations and visualizations. No prior experience in programming required. Collaborative assignments and laboratory activities are integrated into the course. Prerequisite(s): MATH 106, and PHYS 108. Open to first-year students. Enrollment limited to 20. [Q] [S] R. Saha.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 218. Engineering Physics.

Topics include rotational dynamics, static equilibrium, the stability of structures, properties of solids, fluid mechanics, thermodynamics, and geometrical optics. Examples are drawn from various areas of engineering, astrophysics, biology, biomechanics, and medicine. Labs are integrated into the class meetings. Prerequisite(s): PHYS 107. Enrollment limited to 40. [Q] [S] M. Semon.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 220. Climate Change and Modeling.

A quantitative introduction to the science of climate change and climate modeling that explores the impact of both human activities and natural variability on climate. Simple conceptual models are developed, with the goal of understanding the role of feedbacks, stability, and abrupt changes. Topics include the basic physics of climate, El Niño/La Niña, climate models, the greenhouse effect and global warming, and glacial cycles. Prerequisite(s): MATH 106 or higher and PHYS 108 or FYS 274. [Q] [S] R. Saha.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 222. Electricity, Magnetism, and Waves.

A detailed study of the basic concepts and fundamental experiments of electromagnetism. The development proceeds historically, culminating with Maxwell's equations. Topics include the electric and magnetic fields produced by charge and current distributions, forces and torques on such distributions in external fields, properties of dielectrics and magnetic materials, electromagnetic induction, and electromagnetic waves. Prerequisite(s): PHYS 107; Prerequisite(s), which may be taken concurrently: MATH 206 and PHYS 108 or FYS 274. Open to first-year students. Normally offered every year. [Q] [S] H. Lin.Concentrations

This course is referenced by the following General Education Concentrations

##### INDS 228. Caring for Creation: Physics, Religion, and the Environment.

This course considers scientific and religious accounts of the origin of the universe, examines the relations between these accounts, and explores the way they shape our deepest attitudes toward the natural world. Topics of discussion include the biblical Creation stories, contemporary scientific cosmology, the interplay between these scientific and religious ideas, and the roles they both can play in forming a response to environmental problems. Cross-listed in environmental studies, physics, and religious studies. Enrollment limited to 40. [S] J. Smedley, T. Tracy.Interdisciplinary Programs

This course counts toward the following Interdisciplinary Program(s)

##### PHYS 231. Laboratory Physics I/Lab.

Students perform selected experiments important in the development of contemporary physics. They also are introduced to the use of computers, electronic instruments, machine tools, and vacuum systems. Prerequisite(s): PHYS 108 or FYS 274, and PHYS 211, 222, or s30. Enrollment limited to 12. [W2] Normally offered every year. [L] [Q] [S] T. Gould.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 301. Mathematical Methods of Physics.

A study of selected mathematical techniques necessary for advanced work in physics and other sciences. The interpretation of functions as vectors in Hilbert space provides a unifying theme for developing Fourier analysis, special functions, methods for solving ordinary and partial differential equations, and techniques of vector calculus. These methods are applied to selected problems in acoustics, heat flow, electromagnetic fields, and classical and quantum mechanics. Prerequisite(s): PHYS 211; Prerequisite(s), which may be taken concurrently: MATH 205 and 206. Normally offered every year. [Q] [S] T. Gould.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 308. Introductory Quantum Mechanics.

An investigation of the basic principles of quantum mechanics in the Schrödinger representation and the application of these principles to tunneling, the harmonic oscillator, and the hydrogen atom. Basic theoretical concepts such as Hermitian operators, Ehrenfest's theorem, commutation relations, and uncertainty principles are developed as the course proceeds. Prerequisite(s): PHYS 108 or FYS 274, and 301. Normally offered every year. [Q] [S] H. Lin.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 341. Solid State Physics.

A study of crystal structures and the electronic properties of solids, together with an investigation of some active areas of research. Topics include crystal binding, X-ray diffraction, lattice vibrations, metals, insulators, semiconductors, electronic devices, superconductivity, and magnetism. Prerequisite(s): PHYS 222 and 301. Prerequisite(s), which may be taken concurrently: PHYS 308. [Q] [S] N. Lundblad.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 360. Independent Study.

Students, in consultation with a faculty advisor, individually design and plan a course of study or research not offered in the curriculum. Course work includes a reflective component, evaluation, and completion of an agreed-upon product. Sponsorship by a faculty member in the program/department, a course prospectus, and permission of the chair are required. Students may register for no more than one independent study per semester. Normally offered every semester. Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 361. Thermal Physics.

The theory of equilibrium states is developed in a general way and applied to specific thermodynamic systems. The concepts of classical and quantum statistical mechanics are formulated. Prerequisite(s): PHYS 108 or FYS 274. Prerequisite(s), which may be taken concurrently: MATH 206, and PHYS 211 or 222. [Q] [S] T. Gould.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 373. Classical and Modern Optics.

A general course on light treated as an electromagnetic wave, including the theory and operation of common optical instruments. A significant part of the course is devoted to topics in modern optics, such as the use of lasers and the nonlinear effects produced by intense light sources. Prerequisite(s): PHYS 108 or FYS 274, and PHYS 222. [Q] [S] T. Gould.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 381. Astrophysics.

This course investigates the physics of astronomical phenomena and the instruments and techniques with which these phenomena are studied. Topics, which vary from year to year, include stellar structure and evolution, the interstellar medium, galaxies and galaxy clusters, dark matter, cosmic background radiation, and physical cosmology. Prerequisite(s): PHYS 211, 222, and 301. Not open to students who have received credit for ASTR 381. [Q] [S] E. Wollman.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 409. Quantum Theory.

A formal treatment of quantum theory using Dirac notation, including an introduction to approximation methods and their applications. The general theory of angular momentum and time-independent perturbation theory are developed and used to derive the fine and hyperfine structures of hydrogen. Additional topics may include quantum statistics, quantum dynamics, and time-dependent perturbation theory. Prerequisite(s): PHYS 308. Normally offered every year. [Q] [S] H. Lin.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 412. Advanced Classical Mechanics.

A development of the Lagrangian and Hamiltonian formulations of classical mechanics, together with the ideas of symmetry and invariance and their relation to fundamental conservation laws. Additional topics include kinematics and dynamics in noninertial reference frames, a detailed analysis of rigid-body motion, and the theory of small oscillations and normal modes. Prerequisite(s): PHYS 211 and 301. [Q] [S] E. Wollman.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 422. Electromagnetic Theory.

Starting from Maxwell's equations, this course develops electrostatics from solutions to Poisson's equation, magnetostatics using the vector potential, electrodynamics with scalar and vector potentials, and properties of electromagnetic waves. Simple radiation problems are discussed, as well as the relativistic formulation of electrodynamics. Prerequisite(s): PHYS 222 and 301. Normally offered every year. [Q] [S] T. Gould.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 457. Senior Thesis.

An independent study program for students working on a research problem in a field of interest, culminating in the writing of a senior thesis. Students register for PHYS 457 in the fall semester. Majors writing an honors thesis register for both PHYS 457 and 458. Instructor permission is required. [W3] Normally offered every year. Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 458. Senior Thesis.

An independent study program for students working on a research problem in a field of interest, culminating in the writing of a senior thesis. Students register for PHYS 458 in the winter semester. Majors writing an honors thesis register for both PHYS 457 and 458. Instructor permission is required. [W3] Normally offered every year. Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS s27. The Asteroid Impact Threat: What Can We Do?.

Sixty-five million years ago, an asteroid or comet the size of Mt. Everest slammed into the Earth, triggering events that led to the extinction of the majority of all species then living. Smaller objects orbiting the Sun are numerous and are capable of obliterating large cities. We may not be able to do anything about an object the size of Mt. Everest heading our way, but we might be able to deflect a smaller yet catastrophically deadly object. Students investigate how to alter the orbit of a threatening asteroid of dangerous but potentially manageable size. Prerequisite(s): MATH 106 or higher, and PHYS 107, 108, or FYS 274. [Q] [S] E. Wollman.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS s30. Electronics/Lab.

A laboratory-oriented study of the basic principles and characteristics of semiconductor devices and their applications in circuits and instruments found in a research laboratory. Both analog and digital systems are included. Prerequisite(s): PHYS 108 or FYS 274. Enrollment limited to 12. Normally offered every year. [L] [Q] [S] N. Lundblad.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS s50. Independent Study.

Students, in consultation with a faculty advisor, individually design and plan a course of study or research not offered in the curriculum. Course work includes a reflective component, evaluation, and completion of an agreed-upon product. Sponsorship by a faculty member in the program/department, a course prospectus, and permission of the chair are required. Students may register for no more than one independent study during a Short Term. Normally offered every year. Staff.Concentrations

This course is referenced by the following General Education Concentrations