Professors Ruff, Pribram, Semon, Wollman, Chair, and Smedley (on leave, fall semester and Short Term); Associate Professor Lin; Assistant Professor Gensemer; Mr. Clough

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 a student 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 students 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.

Major Requirements. A major program can be be structured to meet the individual needs of students planning graduate study in physics or engineering, as well as those students considering 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 457 or 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. Either Physics 107 or s25 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.

Pass/Fail Grading Option. Pass/fail grading may not be elected for courses applied toward the major.

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, or Case Western Reserve (a descriptive brochure is available). 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.

General Education. The following sets are available: any two 100-level courses in astronomy and physics. A student who has earned AP credit equivalent to Physics 107 may complete a set by taking one 100-level course in physics or astronomy. The following units may serve as options for the third course: Astronomy s21 or s22; Physics s25, s28, s30, or s33. A student may request that the department approve a two- course set not currently designated, but must do so before registering for the set. The quantitative requirement may be satisfied through any course in astronomy and physics, except Physics 228, or with any unit numbered s25 or higher.

Courses in Astronomy

Courses in Physics
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 discussions 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. Recommended background: algebra and trigonometry. Enrollment limited to 64. J. 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. Enrollment limited to 64. J. Smedley.

105. Physics in Everyday Life. Designed for non-science majors, this course introduces physics by studying objects in our everyday environment and the principles upon which they are based. Topics include colored paints, cameras, microwave ovens, radios, televisions, telephones, xerox machines, laser printers, electrostatic air filters, electric power generation and distribution, lasers, medical imaging, nuclear radiation, and nuclear bombs. Recommended background: High School Algebra, Geometry. Enrollment is limited to 40. M. Semon. This course may not fulfill the natural science set requirement but may act as a third course in fulfillment of the requirement. New course beginning Winter 2002 semester.

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. Prerequisite(s) or Corequisite(s): Mathematics 105. Enrollment is limited to 64 per section in the fall semester and 40 in the winter semester. E. Wollman.

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 experiments such as the charge-to-mass ratio for electrons, the photoelectric effect, and electron diffraction. Prerequisite(s): Physics 107. Prerequisite(s) or Corequisite(s): Mathematics 106. Enrollment is limited to 40 in the fall semester and 64 per section in the winter semester. J. Pribram.

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): Physics 107. Open to first-year students. H. Lin.

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): Physics 108. Open to first-year students. M. Semon.

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. This course is the same as Environmental Studies 228 and Religion 228. Enrollment limited to 40. T. Tracy, J. Smedley.

231. Laboratory Physics I. 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): Physics 108. G. Ruff.

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(s): Physics 231 and s30. G. Ruff.

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. Corequisite(s): Mathematics 206. M. Semon.

308. Introductory Quantum Mechanics. An investigation of the basic principles of quantum mechanics in the Schrdinger representation and the application of these principles to tunneling, the harmonic oscillator, and the hydrogen atom. Basic theoretical concepts such as Hermitian operators, Ehrenfests theorem, commutation relations, and uncertainty principles are developed as the course proceeds. Prerequisite(s): Physics 108 and 301. G. Ruff.

315. Acoustics. A mathematical introduction to acoustics, including the vibration of strings, bars, plates, and membranes. The acoustic wave equation is developed and applied to reflection, transmission, radiation, and absorption of sound waves, as well as to the acoustics of pipes and resonators. Acoustical principles also are applied to musical instruments, the human voice, and environmental noise. Prerequisite(s): Physics 211 or 222, and 301. J. Smedley.

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): Physics 108 and 301. Prerequisite or Corequisite(s): Physics 222. Recommended background: Physics 308. J. Pribram.

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 is required. Students may register for no more than one independent study per semester. Staff.

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. The ability to understand partial derivatives is expected. Prerequisite(s): Physics 108. Prerequisite(s) or Corequisite(s): Mathematics 206, and Physics 211 or 222. J. Pribram.

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): Physics 222. G. Ruff.

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): Physics 211, 222, and 301. This course is the same as Astronomy 381. E. Wollman.

385. Electromagnetic Radiation and Cosmology. This course develops fundamentals of astrophysics through a study of modern physical cosmology, with special attention to the role of electromagnetic radiation as both agent in and informant about the universe. Specific topics include the dynamics and thermodynamics of cosmic expansion, early universe nucleosynthesis, the cosmic microwave background radiation, structure formation, and dark matter. Both standard and nonstandard modes are considered. Prerequisite(s): Physics 211 and 222. This course is the same as Astronomy 385. E. Wollman. New course beginning Winter 2002 semester.

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(s): Physics 308. G. Ruff.

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): Physics 211 and 301. H. Lin.

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): Physics 222 and 301. E. Wollman.

457, 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 Physics 457 in the fall semester and for Physics 458 in the winter semester. Majors writing an honors thesis register for both Physics 457 and 458. Staff.

Short Term Units
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 male. The instructors believe that by taking advantage of the Short Term schedules flexibility, this experience can be made 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 may 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 negative perceptions of the field are especially encouraged to enroll. Recommended background: Mathematics 105 or high school calculus. Not open to students who have received credit for Physics 107. Open to first-year students, to whom preference is given. Enrollment limited to 16. H. Lin, J. Pribram, E. Wollman.

s28. Digital Signals. Digitized signals are playing an increasing role in scientific measurements, telecommunications, and consumer electronics. While it is often claimed that "the future is digital," there are trade-offs and limitations associated with any signal processing technique. This unit exposes students to the realities of analog and digital data acquisition, basic forms of signal processing, and their application to scientific measurements and to consumer electronics, including audio. Hands-on experience is gained by constructing simple electronic circuits, and by creating signal acquisition and manipulation computer software. No previous electronics or computer programming experience is necessary. Recommended background: Mathematics 105. This unit is the same as Chemistry s28. Open to first-year students. Enrollment limited to 15. M. Ct.

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(s): Physics 108. Enrollment limited to 12. G. Ruff, H. Lin.

s32. Physics and the Calculus of Variations. This unit begins by developing the calculus of variations and applying it to problems it was invented to solve (e.g., finding paths of least distance and surfaces of minimum area). It then uses the calculus of variations to derive classical mechanics from Hamilton's Principle (that systems evolve in the way that minimizes the difference between their potential and kinetic energies), and geometrical optics from Fermat's Principle (that light follows the path of least time). The unit ends by studying the role of variational principles in current theories of particles and fields. Prerequisite(s): Mathematics 206. Recommended background: Physics 301. M. Semon. New unit beginning Short Term 2002.

s33. Engineering Physics. An investigation of topics in applied physics that 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. Prerequisite(s): Physics 107 and Mathematics 106. Open to first-year students. Enrollment limited to 20. Staff.

s35. Chaos. An introduction to chaotic dynamics. The driven harmonic oscillator is employed to introduce the important mathematical tools of phase diagrams, Poincaré sections, and bifurcation diagrams. These tools are then used to develop insight into the central notions of chaos, such as period doubling, basins of attraction, Lyapunov exponents, and fractal dimensions. Prerequisite(s): Physics 211 or Mathematics 219. Enrollment limited to 15. 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, quantum optics, and variational methods and principles. M. Semon.

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 is required. Students may register for no more than one independent study during a Short Term. Staff.