*The material on this page is from the 1995-96 catalog and may be out of date. Please check the current year's catalog for current information.*

*Professors Ruff, Pribram, Semon (on leave, 1995-1996), and Wollman, *Chair*; Associate Professor Smedley; Assistant Professors Lin and Notte; Mr. Sanders*

The study of physics, generally regarded as the most fundamental of the sciences, is an important part 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 the student's particular needs, provides direct experience of the central role experimental research plays in the advancement of science.

A major program can be structured to meet the individual needs of students planning graduate study in physics or engineering, as well as those considering a variety of careers in business, teaching, government, law, or medicine. The requirement for a major is nine courses in physics or astronomy, including the following seven (usually taken in the order given): Physics 108, 222, 211, 231, 301, 308, and 458 (senior thesis). The additional two courses must include one of the following: Physics s30, s45, or any physics or astronomy course numbered 232 or higher. Physics 107 may count toward the major requirement if it is taken in sequence with Physics 108. Students planning graduate study in physics or engineering are encouraged to take at least six additional courses numbered 300 or higher. In exceptional cases, a student who otherwise meets the nine-course requirement may petition the Department to take a comprehensive examination in lieu of the thesis project.

A student interested in using physics as a basis for an engineering career should inquire about the Bates "three-two plans" with Dartmouth, Rensselaer, Columbia, Washington, or Case. Ask for a descriptive brochure. By careful planning at registration time, similar combination curricula may sometimes be worked out with other engineering institutions.

**General Education. **The following sets are available: Astronomy 101-102, 101-104, 102-104; Physics 101-102, 103-104, 107-108. The quantitative requirement may be satisfied through one of the following: any course in astronomy or physics, or any unit numbered s30 or higher. The following units may serve as options for the third course: Physics s23, s30, or s33. A student may request the Department to approve a two-course set not currently designated, but must do so before registering for the set.

**Astronomy Courses**

**101. An Introduction to the Large Scale.** Although Immanuel Kant proposed the existence of galaxies more than two hundred years ago, most of what we know about the galaxies has been learned in recent decades. Driving this sudden explosion of knowledge are the new technologies of radio, infrared, X-ray, and gamma-ray astronomy. This course explores the methods of contemporary astronomical research as they have been applied to the modern discovery of the galaxies. Laboratory exercises introduce techniques of astronomy. Facilities include the Stephens Observatory 0.3-meter telescope, the planetarium, and portable telescopes. Enrollment is limited to 16 per section. [Mr. Wollman].

**102. The Domain of the Sun.** A survey of the solar system. Topics include theories of origin, results of the space program, new and unexpected discoveries about the sun, and developments in the search for extraterrestrial life. Enrollment is limited to 16 per section. Mr. Notte. F

**104. The Evolution of Cosmology. **As long as there have been natural scientists, there have been efforts to comprehend the size, shape, and internal motions of the universe as a whole. The application of Einstein's general theory of relativity to these questions has yielded new and unexpected possibilities. This course traces the essential developments in our perception of the universe, with special attention to contemporary models. Enrollment is limited to 16 per section. Mr. Notte. W

**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. This course is the same as Physics 381. Prerequisites: Physics 211, 222, 301. [Mr. Wollman].

**Physics Courses**

**101. Revolutions in Physics: Space and Time.** A study of Newton's theory of motion and Einstein's theory of relativity. The conceptual revolutions these theories caused in our notions of space and time in the seventeenth and twentieth centuries are examined. Laboratory work is integrated with the class work. Designed primarily for non-science students, the course does not presuppose previous physics courses. There is more emphasis on conceptualization than on computation, but geometry and elementary algebra are used. Enrollment is limited to 16 per section. Staff. F

**102. Revolutions in Physics: Light and Matter.** A study of the conceptual revolutions begun by Young in 1802 and Einstein in 1905 concerning light; and by Thomson, Bohr, and deBroglie from 1897 to 1923 concerning atoms. The culmination of these revolutions in the quantum theory and its Copenhagen interpretation is examined for insight into the Heisenberg uncertainty principle and the wave-particle duality of radiation and matter. Laboratory work and the mathematical level are similar to that of Physics 101. Enrollment is limited to 16 per section. Staff. W

**103. Musical Acoustics.** An introduction to sound and the acoustics of musical instruments through the study of mechanical vibrations. Concepts such as waves, resonance, standing waves, and Fourier synthesis and analysis are developed and applied to discussion of hearing, scales and harmony, musical instruments, the human voice, and auditorium acoustics. No background in physics or mathematics beyond algebra is assumed. Demonstrations and laboratory exercises are integrated with class work. This course is essentially the same as Physics s24. Recommended background: algebra and trigonometry. Not open to students who have received credit for Physics s24. Enrollment is limited to 16 per section. [Mr. Smedley].

**104. Physics of Electronic Sound. **An analysis of the basic elements of high fidelity sound recording and reproduction, electronic music, and room acoustics. Demonstrations and laboratory exercises are integrated with class work, as in Physics 103. Recommended background: Physics 103, Musical Acoustics. Enrollment is limited to 16 per section. [Mr. Smedley].

**107. Classical Physics.** A calculus-based introduction to Newtonian mechanics, electricity and magnetism, and geometrical optics. Topics include kinematics and dynamics of motion, applications of Newton's laws, energy and momentum conservation, rotational motion, electric and magnetic fields and forces, electric circuits, the laws of reflection and refraction, and the theory of basic optical instruments. Laboratory investigations of these topics are computerized for data acquisition and analysis. Corequisite: Mathematics 105. Enrollment is limited to 16 per section in the fall semester and 10 per section in the winter semester. Mr. Ruff, Mr. Smedley, Mr. Wollman. F W

**108. Modern Physics.** This course applies the material covered in Physics 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 such experiments as the charge-to-mass ratio for electrons, the photoelectric effect, and electron diffraction. Prerequisite: Physics 107 or written permission of the instructor to preregister. Corequisite: Mathematics 106. Enrollment is limited to 10 per section in the fall semester and 16 per section in the winter semester. Mr. Wollman, Mr. Ruff, Mr. Smedley. F W

**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. Prerequisites: Physics 107 and Mathematics 106. Open to first-year students. Mr. Ruff. W

**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: Physics 108. Mr. Notte. F

**231. Laboratory Physics I. ** Students perform selected project labs important in the development of contemporary physics and are introduced to use of the computer, electronic instruments, machine tools, vacuum systems, and the photographic darkroom. Prerequisite: Physics 108 (may be taken concurrently with written permission of the instructor to preregister). Ms. Lin. F W

**232. Laboratory Physics II. ** For students with a special interest in experimental research, this course provides an opportunity for open-ended experiments and developmental projects. Prerequisite: Physics 231. Ms. Lin. F W

**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, Laplace transforms, 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 quantum mechanics. Prerequisite: Physics 108. Corequisite: Mathematics 206. Mr. Smedley. W

**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. Angular momentum and perturbation theory are considered in sufficient detail to permit introductory discussion of the spin-orbit interaction and the Zeeman effect. Prerequisite: Physics 301. Mr. Pribram. F

**341e. Solid State Physics.** A study of crystal structures and 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: Physics 222 and 308. [Mr. Pribram].

**360. Independent Study.** This course provides an opportunity, on a tutorial basis, for a student to investigate a selected topic of individual interest. Topics are selected jointly by the student and tutor. Staff. F W

**361o. Thermodynamics.** 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. Ability to operate with partial differential equations is expected. Prerequisite: Physics 211. Corequisite: Mathematics 206. [Mr. Notte].

**365. Special Topics.** A course or seminar on a departmentally selected topic in an area of physics outside the scope of regular course offerings. May be taken more than once for credit on different topics. Staff.

**373o. 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: Physics 222. Ms. Lin. F

**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. This course is the same as Astronomy 381. Prerequisites: Physics 211, 222, 301. [Mr. Wollman].

**409. Quantum Theory.** A formal development of quantum theory using Dirac notation, including application to the two-dimensional harmonic oscillator and the hydrogen atom. The general theory of angular momentum and time-independent perturbation theory are developed and used to derive the fine and hyperfine structures of hydrogen, the Stark, Zeeman, and Paschen-Back effects, and the polarizability and electric dipole moments of simple atoms. Time-dependent perturbation theory is developed and applied to simple radiation problems. Prerequisite: Physics 308. Mr. Ruff. W

**412e. 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. Prerequisites: Physics 211 and 301. [Mr. Semon].

**422o. 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. Prerequisites: Physics 222 and 301. Mr. Smedley. F

**457. Honors Study.** A program of independent study for students doing honors projects in the departmental honors program. Candidates for honors participate in the departmental seminar. Staff. W

**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. Required of all physics majors. Staff. F W

**Short-Term Units**

**s23. Einstein: The Man and His Ideas.** An introduction to the life of Albert Einstein and to his Special Theory of Relativity. The unit begins with a study of Einstein's life, through biographies and his own writings. Next, his Special Theory of Relativity is developed, and its seemingly bizarre predictions about time, length, and mass are discussed. The experimental verifications of these predictions are then studied. Finally, some of the philosophical implications of the theory are discussed, as well as some of its applications to nuclear weapons and modern theories of the universe. Permission of the instructor is required. [Mr. Semon].

**s25. Alternative Introduction to Physics.** The study of physics is a creative and satisfying intellectual adventure shared by a relatively small number of people, most of whom are men. The instructors believe that by taking advantage of the Short Term schedule flexibility, "we can make this experience attractive to a more diverse group." Physics s25 is an alternative to Physics 107; it emphasizes student-directed laboratory exploration, classroom discussion, and collaboration. As a complementary activity, visiting middle-school students participate in laboratory investigations designed by the course participants. Ongoing group discussion of unit activities and procedures is aimed at creating a more inclusive and welcoming atmosphere. Students who are interested in physics but discouraged by perceptions of the field are especially encouraged to enroll. Recommended background: Mathematics 105 or high-school calculus. Open to first-year students, to whom preference is given. Not open to students who have received credit for Physics 107. Enrollment is limited to 16. Ms. Lin, Mr. Wollman.

**s30. Electronics.** 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: Physics 108. Enrollment is limited to 12. Mr. Notte.

**s33. Engineering Physics.** An investigation of topics in applied physics which are fundamental to the fields of mechanical, civil, and electrical engineering. Topics include statics, fluid mechanics, thermodynamics, and electrical networks. The computer is used extensively as a problem-solving tool, and instruction in the use of a computer language is provided. Prerequisites: Physics 107 and Mathematics 106. Open to first-year students. Not open to students who have received credit for Physics 208. Enrollment is limited to 20. Mr. Ruff.

**s36. Work-Study Internship in the Natural Sciences.** Participation by qualified students in the work of some institution or agency concerned with the application of scientific knowledge. By specific arrangement and departmental approval only. Each intern is supervised by a staff member. Staff.

**s45. Seminar in Theoretical Physics.** An intensive investigation into a contemporary field of physics. Special topics vary from year to year. Areas of investigation have included general relativity, relativistic quantum mechanics, the quantum theory of scattering, and quantum optics. Prerequisite: Physics 308. Mr. Semon.

**s46. Internship in the Natural Sciences.** An off-campus participation by qualified students as team members in an experimental program in a research laboratory project. By specific arrangement and departmental approval only. Staff.

**s50. Individual Research.** Registration in this unit is granted by the Department only after the student has submitted a written proposal for a full-time research project to be completed during the Short Term and has secured the sponsorship of a member of the Department to direct the study and evaluate results. Staff.

Copyright © 1995 President and Trustees of Bates College. All Rights Reserved.

Last modified: August 14, 1995