# Catalog

## Physics and Astronomy

Professors Lin, and Smedley (chair); Associate Professors Lundblad and Gould; Assistant Professors Diamond-Stanic and Oishi; Lecturer Saha (Earth and Climate Sciences and Physics)

Physics, the study of space, time, matter, and energy, is a fundamental component of a liberal arts 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 provides a direct understanding 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.The following courses normally are offered every other year: PHYS 103, 106, 112, 341, 373, 412, and NS/PH 117. Students should consult the online schedule to determine when these courses are offered.

Required Courses:

All of the following:

PHYS 211. Newtonian Mechanics.

PHYS 222. Electricity, Magnetism, and Waves.

PHYS 231. Laboratory Physics/Lab.

PHYS 301. Mathematical Methods of Physics.

PHYS 308. Introductory Quantum Mechanics.

PHYS 361. Thermal Physics.

PHYS s31. Spacetime, Waves, and Photons.

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:

One of PHYS 107, 108, or 109 (only if taken prior to PHYS s31 or a 200-level physics course). Any course in the physics and astronomy department numbered 200 or higher.

#### Minor Requirements

The requirement for a minor is six courses in physics, including:All of the following:

PHYS 108. Introductory Physics of Living Systems II/Lab or PHYS s31. Spacetime, Waves, and Photons.

PHYS 222. Electricity, Magnetism, and Waves.

PHYS 211. Newtonian Mechanics.

The additional three courses must be selected from the following:

PHYS 107 (only if taken prior to PHYS 108) or PHYS 109 (only if taken prior to PHYS s31).

Any course in the physics and astronomy department numbered 200 or higher.

#### Pass/Fail Grading Option

Pass/fail grading may not be elected for courses applied toward the major or minor.#### 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 106. Introduction to Astronomy/Lab.

How can we use light to learn about the universe? How can we measure the properties of planets, stars, and galaxies? How can we explore our cosmic origins and the history of the universe? This course provides an introduction to modern astronomy with an emphasis on how we know what we know. Enrollment limited to 36. (Community-Engaged Learning.) Normally offered every year. [L] [Q] [QF] [S] [SR] A. Diamond-Stanic.Concentrations

This course is referenced by the following General Education Concentrations

##### ASTR 201. Introduction to Stellar and Planetary Astrophysics.

An introduction to stellar and planetary astrophysics, focusing on the basic physics required to understand and interpret astronomical observations of stars and planets. Building on a foundation of the introductory physics sequence, this course explores the consequences of Newtonian gravity and few-body dynamics, hydrostatic balance, nuclear reactions, and radiative transfer for the structure and evolution of stellar and planetary systems. Prerequisite(s): PHYS 107 or 109 and 108 or s31. [Q] [QF] [S] [SR] A. Diamond-Stanic, J. Oishi.Concentrations

This course is referenced by the following General Education Concentrations

##### ASTR 202. Galaxies and Cosmology.

An introduction to the astrophysics of galaxies and cosmology with an emphasis on the physical principles required to understand and interpret astronomical observations. Building on a foundation of the introductory physics sequence, this course explores properties of the Milky Way Galaxy, galaxy formation and evolution, the interstellar and intergalactic medium, dark matter and dark energy, the expansion history of the universe, and modern cosmology. Prerequisite(s): PHYS 107 or 109 and 108 or s31. . Enrollment limited to 25. [Q] [QF] [S] [SR] A. Diamond-Stanic.Concentrations

This course is referenced by the following General Education Concentrations

##### AT/PH 336. General Relativity.

General Relativity is a well-tested physical theory first formulated by Albert Einstein, which intricately links gravity to geometry. Course topics include Special Relativity; tensors; geodesics; curvature; and Einstein's field equations and solutions, including applications to black holes, gravitational waves, and cosmology. Additional topics may include experimental tests of General Relativity, the Einstein-Hilbert Action, quantum gravity, and alternative theories of gravity. Mathematical concepts are introduced as needed, but prior experience with linear algebra and differential equations is assumed. Recommended background: PHYS 422. Prerequisite(s): PHYS 108 or s31, 222, and 301. Enrollment limited to 25. [Q] [S] Staff.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 24. [L] [Q] [QF] [S] [SR] J. Smedley.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 unsustainable energy resources, how they are utilized, and their environmental impacts, including climate change. No background in physics or mathematics beyond algebra is assumed. [Q] [QF] [S] [SR] J. Smedley.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 107. Introductory Physics of Living Systems I/Lab.

An introduction to physics designed for students majoring in life sciences and/or interested in pre-health studies. Topics include geometrical optics, Newtonian mechanics, acoustics, fluids and thermal physics. Class meetings integrate group-based laboratory investigations, simulations and problem solving. Not open to students who have received credit for PHYS 109. Enrollment limited to 29. Normally offered every year. [L] [Q] [QF] [S] [SR] Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 108. Introductory Physics of Living Systems II/Lab.

A continuation of PHYS 107, designed for students majoring in life science and/or interested in pre-health studies. Topics include wave optics, electricity and magnetism, quantum and nuclear physics. Class meetings integrate group-based laboratory investigations, simulations and problem solving. Prerequisite: PHYS 107 or 109. Not open to students who have received credit for FYS 274. Enrollment limited to 29. Normally offered every year. [L] [Q] [QF] [S] [SR] H. Lin.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 109. Energy, Matter, and Motion.

A calculus-based introduction to physics for students interested in the physical sciences. Starting from the concept of energy, the course develops mechanics and thermodynamics with a focus on conservation laws for mass, momentum, and energy. Students examine the atomic nature of matter and its implications. They consider current areas of research as well as applications in physics-adjacent disciplines (e.g., biology, oceanography, materials science, etc.) in order to learn the methods and techniques of the course. Prerequisite(s): MATH 105 or 106. Not open to students who have received credit for PHYS 107. Enrollment limited to 20. Normally offered every semester. J. Oishi.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, simulations, and video analysis are integrated into each class meeting. Enrollment limited to 24. [L] [Q] [QF] [S] [SR] J. Smedley.Concentrations

This course is referenced by the following General Education Concentrations

##### NS/PH 117. Brain Imaging: How Imaging Reveals the Brain and How the Brain Creates Behavior.

This introductory course surveys how breakthroughs in microscopy and imaging have enabled key discoveries about the brain. Students begin by investigating challenges the brain poses as an imaging sample and discuss the origins of these challenges in fundamental physical principles. After studying the structure and function of the nervous system as well as the physiology of neurons, students investigate both classical and cutting-edge imaging techniques. These techniques are introduced in the context of specific neuroscience case studies relevant to human health and behavior. Familiarity with high-school-level algebra and trigonometry is expected. Enrollment limited to 49. [Q] [S] [SR] J. Castro, T. Gould.Concentrations

This course is referenced by the following General Education Concentrations

##### EA/PH 119. The Anthropocene.

This research-based course examines the current geological epoch, the Anthropocene, where humans are the agents of environmental change. How does climate change at present differ from those in the past? How do we know humans really are the drivers of climate change? How can we expect climate change to manifest in the near future? Why is biodiversity important? The course addresses these questions from scientific and mathematical perspectives. The course also critically examines IPCC projections and proposals like the Green New Deal. Students construct their own narrative of the course topics through independent or collaborative research. Normally offered every year. [L] [Q] [QF] [S] [SR] R. Saha.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 or 109. Open to first-year students. Enrollment limited to 25. Normally offered every year. [Q] [QF] [S] [SR] H. Lin.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 216. Computational Physics.

An introduction to computational methods for simulating physical systems, this course focuses on the numerical analysis and algorithmic implementation necessary for efficient solution of integrals, derivatives, linear systems, differential equations, and optimization. While the course presents a rigorous introduction to the numerical analysis underlying these techniques, the emphasis remains on practical solutions to important physical problems. Students solve problems across the wide range of applications of computational physics including astrophysics, biological population dynamics, gravitational wave detection, urban traffic flow, and materials science. No prior experience in programming is required, though students without a technical computing background are encouraged to take PHYS s10 before enrolling. Prerequisite(s): MATH 106 and PHYS 108. Prerequisite(s) or corequisite(s): MATH 205. Open to first-year students. Enrollment limited to 19. Normally offered every year. [Q] [QF] [S] [SR] J. Oishi.Concentrations

This course is referenced by the following General Education Concentrations

##### EA/PH 220. Dynamical Climate.

An introduction to the dynamical behavior of climate on geologic and human timescales. 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. Python is used as the main computational tool; no prior experience is required. Prerequisite(s): MATH 106 and any 100-level earth and climate sciences course. Not open to students who have received credit for GE/PH 220. Enrollment limited to 29. Normally offered every year. [Q] [QF] [S] [SR] R. Saha.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 222. Electricity and Magnetism.

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): MATH 106 and PHYS 108 or 109. Prerequisite(s), which may be taken concurrently: PHYS 108. Recommended background, which may be taken concurrently: MATH 206. Open to first-year students. Enrollment limited to 29. Normally offered every year. [Q] [QF] [S] [SR] H. Lin.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 230. Electronics.

A laboratory-oriented study of the basic principles and characteristics of electronic components and their applications in circuits and instruments found in a research laboratory. Both analog and digital systems are studied, as are microcontrollers and their applications. Prerequisite(s): PHYS 222. Not open to students who have received credit for PHYS s30. Enrollment limited to 16. Normally offered every year. [L] [Q] [QF] [SR] N. Lundblad.Concentrations

This course is referenced by the following General Education Concentrations

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

Students investigate selected experiments relevant to the development of contemporary physics and the practice of experimental physics research. They are introduced to the use of electronic instruments and computers for data acquisition and analysis, techniques of error analysis, and the practice of speaking and writing about experimental physics. Prerequisite(s): PHYS 211, 222, 230, or s31. Enrollment limited to 12. [W2] Normally offered every semester. [L] [Q] [QF] [S] [SR] T. Gould, N. Lundblad.Concentrations

This course is referenced by the following General Education Concentrations

##### MA/PH 255E. Nonlinear Models and Chaos.

A model is a simplified description of a system in mathematical and/or conceptual terms. Models help us understand how systems work and behave. The goals of this course are threefold: building models of natural systems, exploring their underlying mathematical structures and similarities, and simulating them with computers. Concepts acquired from simple systems in physics are applied to more complex systems in areas of biology, environment, climate, and social dynamics. Prerequisite(s): MATH 105 or 106 and PHYS 107. Open to first-year students. Enrollment limited to 29. Normally offered every year. [Q] [QF] [S] [SR] R. Saha.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) or corequisite(s): MATH 205. Recommended background, which may be taken concurrently: MATH 206. Enrollment limited to 25. Normally offered every year. [Q] [S] Staff.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 301 and s31. Enrollment limited to 25. Normally offered every year. [Q] [S] J. Oishi.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 309. Quantum Computing.

In the emerging field of quantum computing, the laws of nature are used to store and process information in new ways. Leveraging the extraordinary properties of quantum mechanics enables an exponential speed-up for certain classes of computational problems. In this course students are introduced to the ideas of the qubit, quantum gates, and quantum circuits; learn about experimental progress; explore quantum algorithms; and implement their own code on quantum cloud computing resources. Prerequisite(s): MATH 205. Prerequisite(s) or corequisite(s): PHYS 308. Enrollment limited to 15. Normally offered every year. [Q] [QF] [S] [SR] Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### AT/PH 336. General Relativity.

General Relativity is a well-tested physical theory first formulated by Albert Einstein, which intricately links gravity to geometry. Course topics include Special Relativity; tensors; geodesics; curvature; and Einstein's field equations and solutions, including applications to black holes, gravitational waves, and cosmology. Additional topics may include experimental tests of General Relativity, the Einstein-Hilbert Action, quantum gravity, and alternative theories of gravity. Mathematical concepts are introduced as needed, but prior experience with linear algebra and differential equations is assumed. Recommended background: PHYS 422. Prerequisite(s): PHYS 108 or s31, 222, and 301. Enrollment limited to 25. [Q] [S] Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS 341. Condensed Matter.

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. Recommended background: PHYS 308 or 361. Enrollment limited to 25. [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 s31 and PHYS 211 or 222. Enrollment limited to 25. [Q] [QF] [S] [SR] R. Saha.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 s31 and PHYS 222. Enrollment limited to 25. [Q] [S] T. Gould.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. Enrollment limited to 25. Normally offered every year. [Q] [S] J. Oishi.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. Enrollment limited to 25. [Q] [S] J. Oishi.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. Enrollment limited to 25. 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. Enrollment limited to 25. 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. Enrollment limited to 25. Instructor permission is required. [W3] Normally offered every year. Staff.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS s10. Basic Computational Science Lab Skills.

A hands-on introduction to computational thinking for scientists and engineers. This course focuses on practical skills using UNIX command line tools, typesetting mathematics in LaTeX, handling data, version control, basic software development practices, and an introduction programming in Python. Students learn how to use computers as research tools, designing and documenting experiments using software. Open to first-year students. Enrollment limited to 25. [QF] [SR] J. Oishi.Concentrations

This course is referenced by the following General Education Concentrations

##### PHYS s31. Spacetime, Waves, and Photons.

An exploration of several core ideas in modern physics: special relativity (Einstein's formulation of space and time underlying the modern understanding of the universe), the wave and particle (photon) nature of light, and the consequences of energy quantization. Laboratory investigations consider related phenomena. The course may examine additional topics in quantum mechanics and nuclear or particle physics. Prerequisite(s): MATH 106 and PHYS 107 or 109. Enrollment limited to 30. Normally offered every year. [L] [Q] [S] N. Lundblad, H. Lin.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