## Physics and Astronomy (PHAS)

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 151 and 131 or 132 or 141 or 142, 228, 229, 230, 235, 335 (or 336 and 337), 342, and 400, plus one applied physics course. (Choose from the following: Physics 234, 260, 261, 341, 343, 344, 347 or 354; Astronomy 232 or 233, Biology 360, ENTS 262 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, 340, 352, 355, 356, Astronomy 113, 356, Chemistry 123, Mathematics 241, 341, 351, and Computer Science 111. Students considering graduate school in physics are strongly encouraged to take Physics 346, 352 and 355.

**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 111.

### Physics Courses (PHYS)

**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 131, 132, 141, 142, 151, 152, 153, or 165. *6 cr., MS; NE, QRE, Not offered in 2012-2013.*

**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 131, 132, 141, 142, 151, 152, 153, 161, 162 or 165. *1 cr., S/CR/NC, ND; NE, QRE, Spring*—**K. Martin-Wells**

**PHYS 131. Introduction to Physics: Newtonian Mechanics**
An introduction to classical mechanics using the Newtonian worldview. The kinematics and dynamics of some simple systems including objects in free fall, simple harmonic motion, planetary motion, and the motion of charged particles in electromagnetic fields are investigated using Newton's laws, vector analysis, and the conservation laws of linear momentum, angular momentum, and energy. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work. Not open to students who have completed Physics 132, 141, or 142 at Carleton. Prerequisite: Mathematics 111. *3 cr., MS; LS, QRE, Fall,Winter,Spring*—**J. Tasson, W. Titus, M. Wiebold**

**PHYS 132. Introduction to Physics: Gravity and the Earth**
An introduction to the basic principles of Newtonian mechanics and conservation laws using the earth and the gravitational force law as a conceptual framework. The many influences of gravity on the structure of the earth from its shape to the tides, and techniques for measuring gravity will be discussed. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory. Not open to students who have completed Physics 131, 141 or 142 at Carleton. Prerequisite: Mathematics 111. *3 cr., MS; LS, QRE, Spring*—**W. Titus**

**PHYS 141. 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 momentum will be used to explore large-scale phenomena in the cosmos. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory or observational work. Not open to students who have completed Physics 131, 132, or 142 at Carleton. Prerequisites: Mathematics 121 or 131 (completion or concurrent registration) and strong preparation in Newtonian Mechanics. *3 cr., MS; LS, QRE, Winter*—**K. Martin-Wells, J. Weisberg**

**PHYS 142. Introductory Mechanics: Matter and Interactions**
An introduction to Newtonian mechanics using calculus. The kinematics and dynamics of objects in motion are investigated using Newton's laws and related conservation laws. Examples of systems studied include table-top objects, simple astronomical systems, or objects in harmonic motion. This section emphasizes a bottom-up atomic perspective and introduces a computational approach to allow the consideration of atoms and molecules inside solids as well. Weekly laboratory or computational work. Not open to students who have completed Physics 131, 132, or 141 at Carleton. Prerequisite: Mathematics 121 (completion or concurrent registration) and strong preparation in physics. *3 cr., MS; LS, QRE, Fall*—**K. Martin-Wells**

**PHYS 151. Introduction to Physics: Relativity and Particles**
An introduction to principles of physics in the domain of the very small and very fast. Topics include the special theory of relativity, and selected applications to atomic, nuclear, and particle physics. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work. *Prerequisite:* Mathematics 121 or 131 (completion or concurrent registration) and Physics 131(completion or concurrent registration) or 132 or 141 or 142. *3 cr., MS; LS, QRE, Fall,Winter,Spring*—**K. Martin-Wells, J. Tasson**

**PHYS 152. Introduction to Physics: Environmental Physics**
An introduction to principles of physics and their application to the environment. Topics include energy and its flows, engines, energy efficiency, energy usage and conservation in vehicles and buildings, the atmosphere, and climate change. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work or field trips. Prerequisites: Mathematics 111 (completion or concurrent registration) and Physics 131 or 132 or 141 or 142 (or their equivalents). *3 cr., MS; LS, QRE, Spring*—**J. Weisberg**

**PHYS 153. Fluid and Waves**
A study of the properties of fluids (both static and dynamic) and the principles of waves and wave motion (including both sound and light). Topics include simple harmonic motion, buoyancy and Archimedesâ€™ principle, Bernoulliâ€™s equation, viscosity, Poiseuilleâ€™s equation, standing waves, musical instruments, and the Doppler effect. One laboratory per week. Prerequisite: Physics 131 or 132 or 141 or 142 and Mathematics 111 . *3 cr., MS; LS, QRE, Spring*—**K. Martin-Wells**

**PHYS 165. Introduction to Electricity, Magnetism, and Optics**
A study of the principles of electricity, magnetism, and optics with an emphasis on real-world applications including electronics, laser physics, astronomy, and medicine. Topics include electric and magnetic fields, electric potentials, DC and AC circuits, geometric and wave optics, and relevant properties of matter. Designed for science majors who want additional background in physics. Comfort with algebra and the integration and differentiation of elementary functions is assumed. One laboratory per week. *Prerequisite:* Physics 131 or 132 or 141 or 142, Mathematics 121 or 131. *6 cr., MS; LS, QRE, Winter*—**M. Wiebold**

**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 151, 152, 153, 161, 162 or 165. *2 cr., S/CR/NC, ND, Not offered in 2012-2013.*

**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 151. *6 cr., MS; LS, QRE, Fall*—**M. Baylor**

**PHYS 229. Analytical 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 131, 132, 141, or 142 and Mathematics 211; or permission of the instructor. *3 cr., MS; NE, Winter*—**J. Tasson**

**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; NE, Winter*—**J. Tasson**

**PHYS 234. Computer Simulations in Complex Physical Systems**
The development of techniques to study complex physical systems from a probabilistic and numerical standpoint using *Mathematica*. Subject material is applicable to all the sciences and mathematics. Some topics considered are random walks, percolation clusters, avalanches, traffic flow, the spread of forest fires and diseases, and a brief introduction to Bayesian statistics. No *Mathematica* skills are assumed. *Prerequisite:* Physics 131,132,141 or 142 or permission of instructor. *6 cr., MS; LS, QRE, Offered in alternate years. Fall*—**W. Titus**

**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 151 or 161 or 165 and Mathematics 211; or permission of the instructor. *6 cr., MS; LS, QRE, Spring*—**M. Wiebold**

**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 208. *6 cr., MS; LS, QRE, Not offered in 2012-2013.*

**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 151, 152, 153, 161 162 or 165 or Chemistry 123 or 128. *6 cr., MS; NE, Offered in alternate years. Not offered in 2012-2013.*

**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. Note that this course is not appropriate for pre-medical, pre-dental or pre-veterinary requirements. Prerequisite: Physics 151, 152, 153, 161, 162 or 165. *6 cr., MS; NE, Offered in alternate years. Not offered in 2012-2013.*

**PHYS 335. Quantum Mechanics**
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. Multidimensional applications will include the harmonic oscillator, the hydrogen atom. Approximation techniques and applications will be presented. *Prerequisite:* Physics 228, 229/30 and Mathematics 232. Familiarity with matrix algebra is assumed. *6 cr., MS; NE, Winter*—**B. Titus**

**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. *Prerequisite:* Physics 228, 229/230 and Mathematics 232. Familiarity with matrix algebra is assumed. *3 cr., MS; NE, Winter*—**W. Titus**

**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; NE, Winter*—**W. Titus**

**PHYS 339. Thermal and Statistical Physics I**
The fundamentals of classical thermodynamics and statistical mechanics. Topics may include the kinetic theory of gases; energy, entropy, and the laws of thermodynamics; heat engines and refrigerators; the Maxwell-Boltzmann distribution; the physics of efficient energy use as well as the statistical concepts of temperature and entropy. Prerequisites: Physics 228. *3 cr., MS; NE* *3 cr., MS; NE, Not offered in 2012-2013.*

**PHYS 340. Thermal and Statistical Physics II**
Applications of the principles of thermal and statistical physics. Topics may include the canonical ensemble and the Boltzmann factor; the Planck, Fermi-Dirac, and Bose-Einstein distributions and their applications to black-body radiation, phonons, and electrons in solids. Prerequisites: Physics 339. *3 cr., MS; NE, Fall*—**W. Titus**

**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; NE, Not offered in 2012-2013.*

**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. *Prerequisite:* Physics 228 and Physics 235. *6 cr., MS; LS, QRE, Spring*—**M. Eblen-Zayas**

**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; LS, QRE, Not offered in 2012-2013.*

**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; NE, Winter*—**M. Baylor**

**PHYS 345. Advanced Optics**
This is a laboratory course that will serve as a follow-up to material covered in Physics 344, Classical and Quantum Optics. students will conduct a number of experiments pertaining to optical phenomena. The experiments will display effects pertaining to classical, quantum , and non-linear optics. The lab will take place once a week for four hours each session. *Prerequisite:* Physics 344 or permission of the instructor. *2 cr., MS; LS, QRE, Offered in alternate years. Winter*—**M. Baylor**

**PHYS 346. Thermodynamics and Statistical Mechanics**
The fundamentals of classical thermodynamics and statistical mechanics. Topics include the laws of thermodynamics; heat engines and refrigerators; the Maxwell-Boltzmann distribution; the various canonical distributions; the statistical concepts of temperature and entropy; Fermi-Dirac, and Bose-Einstein distributions with applications to black-body radiation, phonons, and electrons in solids; the Ising model; and an introduction to critical phenomena. *Prerequisite:* Physics 228. *6 cr., MS; NE, Fall*—**W. Titus**

**PHYS 347. General Relativity**
Einsteinâ€™s theory of general relativity is developed from basic physical principles. Also presented is the mathematics of curved space time. Astrophysical applications of general relativity, including spherically symmetric objects, black holes, cosmology and the creation and detection of gravitational waves are given. *Prerequisite:* Physics 230 and 235. *6 cr., MS; NE, Not offered in 2012-2013.*

**PHYS 348. Introduction to Quantum Field Theory**
Building from the marriage of special relativity and quantum mechanics, the course will examine the structure of relativistic quantum field theory. Possible topics may include the Dirac field, Feynman diagrams and perturbation theory in quantum electrodynamics, renormalization, and select applications in particle physics and condensed-matter physics. The course may also consider current challenges in the field such as that presented by gravity. *Prerequisite:* Physics 336/337 or Physics 335. *6 cr., MS; NE, Spring*—**Jay Tasson**

**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 strongly recommended. *6 cr., MS; NE, Spring*—**M. Baylor**

**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 335, 336, 339 or 346. *6 cr., MS; NE, Offered in alternate years. Not offered in 2012-2013.*

**PHYS 355. Topics in Advanced Classical Mechanics**
Lagrangian and Hamiltonian methods including central force motion, coupled harmonic oscillators, and the study of continuous systems. Additional subjects may include fluid dynamics, classical field theory or other specialized topics. *Prerequisite:* Physics 229 and 230. *6 cr., MS; NE, Offered in alternate years. Fall*—**J. Tasson**

**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; NE, Fall,Winter,Spring*—**Staff**

**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,Spring*—**Staff**

### 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; LS, QRE, Fall,Winter*—**C. 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 110, 232, or 233, or permission of the instructor. *3 cr., S/CR/NC, MS; LS, QRE, Fall,Spring*—**J. Weisberg**

**ASTR 127. Topics in Modern Astrophysics**
Special topics in modern astrophysics will be explored in order to understand the physical processes at work in a variety of cosmic settings. Possible topics include the solar weather and its impact on Earth, extra-solar planets, black holes, dark matter, gravitational lensing, large-scale structures and dark energy in an accelerating universe. *Prerequisite:* Astronomy 100, 110 or Physics 131, 132, 141 or 142. *6 cr., MS, WR; NE, WR2, QRE, Spring*—**C. 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 228 and Physics 229/230 or permission of the instructor. *6 cr., MS; NE, QRE, Offered in alternate years. Not offered in 2012-2013.*

**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 228 and 229/230 or permission of the instructor. *6 cr., MS; NE, QRE, Offered in alternate years. Spring*—**C. 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; NE, Fall,Winter,Spring*—**Staff**