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Physics and Astronomy (PHAS)

Chair: Associate Professor Nelson Lloyd Christensen, Jr.

Emeritus Professor: Richard J. Noer

Professors: Cynthia A. Blaha, William J. Titus, Joel M. Weisberg

Associate Professor: Nelson Lloyd Christensen, Jr.

Assistant Professor: Melissa A. Eblen-Zayas, Arjendu K. Pattanayak, Kristin L. Wedding

Visiting Assistant Professor: Stephen Cristy Parker

Consonant with the liberal arts nature of Carleton, our department serves not only physics and astronomy majors but also other science majors requiring a background in physics or astronomy, and non-science majors desiring an introduction to these subjects. We have goals for the knowledge we would like students to acquire, the skills they should master, and the experiences they should have in learning and doing physics. For example, some of the general skills are the ability to communicate clearly in written work and oral presentation; the ability to locate information through library research and other means; and the ability to continue learning on a largely independent basis. More specific skills include logical problem-solving and mathematical analysis, experimental design and the use of measurement apparatus, and the use of computers for modeling physical phenomena and for data acquisition and analysis.

Requirements for a Major

Prospective physics majors are strongly encouraged to begin their study of physics and mathematics in the first year. Physics courses are somewhat sequential and are developed in close association with mathematics courses. The curriculum provides an excellent basis for graduate study in physics, astronomy, and in various fields of engineering, and for careers in high-school teaching, industry, and other areas.

Required courses for the major are Physics 115 and either 113 or 114, 228, 229, 230, 235, 336 and 338, 342, and 400, plus one applied physics course. (Choose from the following applied courses: Physics 234, 260, 261, 341, 343, 344 or 354; Astronomy 232 or 233: or others upon consultation with the department.) Required math courses are Mathematics 111, 121, 211, and 232. Additional courses that are often recommended include Physics 123, 223, 336, 350, 352, 353, 356, Astronomy 113, 356, Chemistry 123, Mathematics 241, 341, 351, and Computer Science 117.

Major Under Combined Plan in Engineering (See Engineering in index):

In addition to completing the requirements for the physics major listed above, the student should also take the following courses required for admission to the engineering schools: Mathematics 241, Chemistry 123, 230, and Computer Science 117. At the discretion of the department, the requirement of Physics 342 may be waived in some instances to allow the student more latitude in selection of courses.

Physics Courses (PHYS)

PHYS 100. The Origins of Modern Science This seminar will focus on the renaissance of science in the sixteenth and seventeenth centuries and its Greek and medieval predecessors. By studying the writings of key scientists and philosophers like Aristotle, Ptolemy, Copernicus, Galileo, Kepler, Descartes and Newton, we will try to evaluate not only what happened during the so-called "scientific revolution," but also what the participants themselves thought they were achieving. By reference to what seminar participants may know about modern science, we will try to decide whether the goals and methods of science have changed since this earlier period. 6 cr., S/CR/NC, MS, FallR. Noer

PHYS 112. Elementary Physics A unified view of the fundamental concepts of physics, without calculus, designed primarily for students who plan to major in the life sciences. Topics include classical mechanics and the conservation laws, wave motion, electric and magnetic fields, thermal physics, and atomic models. One laboratory per week. Assumes knowledge of trigonometry, but no calculus. 6 cr., MS, SpringS. Parker, W. Titus

PHYS 113. Introduction to Physics: Newtonian Mechanics An introduction to Newtonian mechanics using calculus. The kinematics and dynamics of some simple systems such as objects in motion close to the earth's surface or objects in simple harmonic motion are investigated using Newton's laws and related conservation laws. Weekly laboratory work. Prerequisite: Mathematics 121 (completion or concurrent registration.) This section takes a more computational approach and addresses topics in atomic and molecular physics. A special section of 113 is reserved in the fall for appropriately prepared first-year students. This section takes a more computational approach and addresses topics in atomic and molecular physics. 3 cr., MS, Fall,WinterM. Eblen-Zayas, A. Pattanayak, B. Titus

PHYS 114. Introduction to Physics: Gravity and the Cosmos An introduction of basic principles of physics in the realm of planetary systems, black holes and dark matter in the universe. Gravity, conservation of energy and principles of radiation will be used to explore large-scale phenomena in the cosmos. Weekly laboratory or observational work. Prerequisites: Mathematics 121 (completion or concurrent registration) and strong preparation in Newtonian mechanics. 3 cr., MS, WinterC. Blaha

PHYS 115. Introduction to Physics: Relativity and Particles An introduction to principles of physics in the domain of the very small and very fast. Topics include electric and magnetic forces and fields, the special theory of relativity, and selected applications to atomic, nuclear, and particle physics. Weekly laboratory work. Prerequisites: Mathematics 121 (completion or concurrent registration) and Physics 113. 3 cr., MS, Fall,WinterJ. Weisberg, W. Titus

PHYS 120. Revolutions in Physics The structure and development of key concepts in physics. In particular, we will examine the Newtonian synthesis, Einstein's theory of relativity, quantum mechanics and chaotic dynamics. We will see how the various developments alter our perspective on our relationship with the material universe. We will also consider the role of social context, creativity, aesthetics, and tradition in scientific discovery. No mathematical background beyond high-school algebra will be assumed. Occasional laboratory work. Not open to students majoring in mathematics or the natural sciences or to students who have taken 112, 113, 114 or 115. 6 cr., MS, SpringA. Pattanayak

PHYS 123. What Physicists Do A program of five lectures by invited speakers that is intended to give students some perspective on the kinds of work done by people with a physics background. Visitors from industry, government, business, and research and educational institutions will discuss their work and work-related experiences. Prerequisite: Physics 112 or 115. 1 cr., S/CR/NC, ND, SpringJ. Weisberg

PHYS 126. Physics of Laboratory Instrumentation A study of the principles of electricity, magnetism, and optics with emphasis on applications to physical measurements in chemistry and biology. Topics include electric and magnetic fields and potentials, DC and AC circuits, geometric and wave optics, and relevant properties of matter. Provides the physical background to effectively use a variety of laboratory instruments. Designed for non-majors who want additional background in physics. One laboratory per week. Prerequisites: Physics 112 or 115, Mathematics 111 and 121. 6 cr., MS, WinterS. Parker

PHYS 223. Presentation Skills in Physics Designed to help students improve their skills in oral and visual presentation of scientific topics. The course will begin with readings and discussion of effective oral presentation skills. Students will report on physics-related topics of their choice (e.g., their previous summer's research, or a topic studied in another course). Prerequisite: Physics 115. 2 cr., S/CR/NC, ND, FallJ. Weisberg

PHYS 228. Atomic and Nuclear Physics An elementary but analytical introduction to the physics of atoms and nuclei. Topics include the particle aspects of electromagnetic radiation, an introduction to quantum mechanics, the wave aspects of material particles, the structure of atoms, X-ray and optical spectra, instruments of nuclear and particle physics, nuclear structure and elementary particles. One laboratory per week. Prerequisite: Physics 115. 6 cr., MS, FallM. Eblen-Zayas

PHYS 228. Atomic and Nuclear Physics An elementary but analytical introduction to the physics of atoms and nuclei. Topics include the particle aspects of electromagnetic radiation, an introduction to quantum mechanics, the wave aspects of material particles, the structure of atoms, X-ray and optical spectra, instruments of nuclear and particle physics, nuclear structure and elementary particles. One laboratory per week. Prerequisite: Physics 115. Formerly Physics 128. 6 cr., MS, FallM. Eblen-Zayas

PHYS 229. Classical Mechanics An analytical treatment of classical mechanics from a Lagrangian and Hamiltonian standpoint. Equations of motion and their solutions are studied with special emphasis on the harmonic oscillator and central-force problems. Prerequisites: Physics 115 and Mathematics 211. 3 cr., MS, WinterW. Titus

PHYS 230. Computational Mechanics A numerical treatment of classical mechanics concentrating on examples which are difficult, if not impossible, to solve analytically. Topics may include examples from astrophysics and chaotic dynamics. Prerequisite: Physics 229. 3 cr., MS, WinterW. Titus

PHYS 234. Computer Simulations in Complex Physical Systems The development of techniques to study complex physical systems, both probabilistic and deterministic, using numerical simulations. Some of the systems to be investigated are random walks, percolation clusters, the Ising model, avalanches, traffic flow, and the spread of forest fires. Prerequisite: Physics 115 and one year experience with Mathematica. One laboratory and two class meetings per week. 6 cr., MS, Offered in alternate years. Not offered in 2006-2007.

PHYS 235. Electricity and Magnetism Electric and magnetic fields in free space, and their interactions with charges and currents. Topics include DC and AC circuits, Maxwells's equations, and electromagnetic waves. Weekly laboratory work. Prerequisites: Physics 115 and Mathematics 211. 6 cr., MS, SpringM. Eblen-Zayas

PHYS 247. Digital Electronics A study of the digital electronics involved in computers, ranging from basic logic circuits to microprocessors. Weekly lab. Each student will complete a term paper that will involve projections about future developments in computer electronics, and a lab project that will involve circuit design. Prerequisite: Computer Science 207. 6 cr., MS, Offered in alternate years. WinterN. Christensen

PHYS 260. Materials Science From a simple "Post-It" note to a complex computer microprocessor, modern products derive much of their utility from the structures and properties of their constituent materials. This course will provide a survey of the science of materials including structure (bonding, crystal structure, defects), classes of materials (polymers, ceramics, metals, composites), physical properties (mechanical, electromagnetic, thermal, optical) and techniques for materials characterization. In addition, the technological and societal impacts of materials development will be explored. Prerequisites: Physics 112 or 115 or Chemistry 123 or 128. 6 cr., MS, Offered in alternate years. Not offered in 2006-2007.

PHYS 261. Medical Physics The course covers the basic concepts of medical physics. Particular attention is paid to electromagnetism, mechanics and nuclear physics when applied to medical and biological phenomena. Topics include medical imaging techniques, nuclear medicine radiation protection, dosimetry, and physics in biology. Students will visit medical imaging facilities. Prerequisite: Physics 115 or 126. 6 cr., MS, Offered in alternate years. FallN. Christensen

PHYS 336. Quantum Mechanics I An examination of the structure of non-relativistic quantum mechanics and how this theory differs from those of classical physics. Topics include the mathematics of Hilbert space, the postulates of quantum mechanics, the motion of a particle in one dimension (including the free particle and the simple harmonic oscillator), the Heisenberg uncertainty principle, and spin. Prerequisites: Physics 229/230 and Mathematics 232. Familiarity with matrix algebra is assumed. 3 cr., MS, WinterA. Pattanayak

PHYS 337. Quantum Mechanics II A study of the principles and applications of non-relativisitic quantum mechanics. Possible topics may include the harmonic oscillator, the hydrogen atom, approximation techniques, and applications to atomic and nuclear physics. Prerequisite: Physics 336. 3 cr., MS, WinterA. Pattanayak

PHYS 338. Thermal Physics The fundamentals of the kinetic theory of gases and classical thermodynamics. Topics include the kinetic theory of gases; energy, entropy, and the laws of thermodynamics; heat engines and refrigerators; the Maxwell-Boltzmann distribution and the physics of efficient energy use. Prerequisite: Physics 115. 3 cr., MS, WinterJ. Weisberg

PHYS 341. Waves The analysis of wave phenomena, including normal mode expansions, the wave equation and boundary value problems, and interference, diffraction, and polarization. Applications are made to mechanical, sound, water and electromagnetic waves with particular emphasis on electromagnetism and optics. Prerequisites: Physics 229 and 235, and Mathematics 232. 6 cr., MS, Offered in alternate years. Not offered in 2006-2007.

PHYS 342. Contemporary Experimental Physics A study of experimental techniques and apparatus basic to the measurements which underlie and validate contemporary theories in physics. Topics include electrical measurements, data analysis and statistics, optical and laser techniques, particle detectors, and time coincidence techniques. Applications are made to experiments such as magnetic resonance, Mossbauer and nuclear spectroscopy and laser optics. Class time is devoted to studying the measurement techniques and considering phenomenological models of the effects observed in the laboratory. One laboratory per week. Prerequisites: Physics 128, 235, and 338. 6 cr., MS, SpringN. Christensen

PHYS 343. Electronics A study of the electrical circuits and electronics underlying modern physics instrumentation. Includes an introduction to microprocessor and microcomputer design. Approximately equal emphasis on analog and digital electronics. One laboratory per week. Prerequisite: Physics 235. 6 cr., MS, Offered in alternate years. Not offered in 2006-2007.

PHYS 344. Classical and Quantum Optics A junior/senior level course in classical and quantum optics. Includes the phenomena of interference, diffraction and coherence and quantum optical applications, such as unique statistical states of light or the operation of a laser. Modern applications of these areas are studied through such topics as fiber optics telecommunication, optical data storage, or manipulation of atoms by light. Prerequisites: Physics 235 and Mathematics 232. 6 cr., MS, Offered in alternate years. FallS. Parker

PHYS 350. Advanced Classical Mechanics Lagrangian and Hamiltonian methods including central force motion coupled harmonic oscillators and the study of continuous systems. Prerequisite: Physics 229/230. 3 cr., MS, FallW. Titus

PHYS 352. Advanced Electricity and Magnetism The classical theory of fields and waves. Electromagnetic theory including Maxwell's equations, radiation and relativity. Prerequisites: Physics 235 and Mathematics 341. 6 cr., MS, SpringJ. Weisberg

PHYS 353. Statistical Mechanics The principles of statistical mechanics, in the quantum context. Topics include the statistical concepts of temperature and entropy and their relation to those of classical thermodynamics; the canonical ensemble and the Boltzmann factor; and the Planck, Fermi-Dirac, and Bose-Einstein distributions and their applications to black-body radiation, phonons, and electrons in solids. Prerequisites: Physics 336 and 338. 3 cr., MS, FallW. Titus

PHYS 354. Solid State Physics An introduction to the physics of solids. Particular attention is paid to the properties exhibited by atoms and molecules because of their association and regular periodic arrangement in crystals. Topics include crystal structure and diffraction, the reciprocal lattice, phonons and lattice vibrations, thermal properties, free-electron theory and band structure. Prerequisites: Physics 336 and 338. 6 cr., MS, Offered in alternate years. Not offered in 2006-2007.

PHYS 356. Special Project Individual projects in experimental, theoretical, or computational physics. Available projects are often related to faculty research interests or to the development of course-support materials, such as new laboratory exercises. Prerequisite: Permission of the instructor. 2 or 3 cr., S/CR/NC, MS, Fall,Winter,SpringStaff

PHYS 400. Integrative Exercise An extensive study of a specific topic in physics, culminating in a 70-minute presentation during winter or spring term. A short background paper and a longer summary paper are also required. Students may arrange to complete the bulk of their work during winter or spring term (Physics 400, 6 credits), or divide their effort between terms (Physics 400, winter, 3 credits; Physics 400, spring, 3 credits). 6 cr., S/NC, ND, Winter,SpringStaff


Astronomy Courses:

ASTR 110. Introduction to Astronomy An introduction to current astronomy with an emphasis on how we know what we know. Topics include the solar system; the life cycles of stars; pulsars, quasars, and black holes; and the history and future fate of the universe. No mathematics background beyond high school algebra and trigonometry is assumed. 6 cr., MS, Fall,WinterC. Blaha, J. Weisberg

ASTR 113. Observational and Laboratory Astronomy Theory and practice of basic techniques in observational and laboratory astronomy. Certain problems involve the use of the 16-inch and 8-inch telescopes. Prerequisite: Astronomy 100, 110, 232, or 233, and permission of the instructor. 3 cr., S/CR/NC, MS, Fall,SpringC. Blaha

ASTR 232. Astrophysics I Cross-listed with PHYS 232. A study of stellar structure and evolution with an emphasis on the physical principles underlying the observed phenomena. Topics include the birth, evolution, and death of stars, pulsars, black holes, and white dwarfs. Prerequisites: Physics 128 and Physics 229/230 or permission of the instructor. 6 cr., MS, Offered in alternate years. Not offered in 2006-2007.

ASTR 233. Astrophysics II Cross-listed with PHYS 233. A study of galactic and extragalactic astronomy with an emphasis on the physical principles underlying the observed phenomena. Topics include the structure and dynamics of the Milky Way Galaxy and other galaxies, the interstellar medium, quasars and active galaxies, clusters and superclusters, and cosmology. Prerequisite: Physics 128 and 229/230 or permission of the instructor. 6 cr., MS, Offered in alternate years. SpringC. Blaha

ASTR 356. Special Project Individual projects in observational, theoretical, or computational astronomy. Available projects are often related to faculty research interests or to the development of course-support materials, such as new laboratory exercises. Prerequisite: Permission of the instructor. 2 or 3 cr., S/CR/NC, MS, Fall,Winter,SpringStaff