Physics and Astronomy

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 work collaboratively with their peers; 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 the Physics 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 many post-Carleton career paths, including teaching, medicine, working in industry, and graduate study in physics, astronomy, and in various fields of engineering.

Most first-year students considering a major in physics will take either two 5-week courses (Physics 131 AND Physics 151) or one 10-week course (Physics 143 or Physics 144). Although taught from slightly different perspectives, the two 5-week courses or the 10-week course will cover fundamental topics in Newtonian mechanics and special relativity that prepare students for further work in physics and related fields. We also offer a section of Physics 143 with problem solving that is taught in the spring term. This section provides additional problem-solving instruction and is appropriate for students who could benefit from additional support in the study of college-level physics.

Required courses, 72 credits total

Introductory courses required are either:

Other required Physics courses:

Required mathematics courses:

Additional courses that are often recommended include Physics 123, 346, 356, Astronomy 113, 356, Chemistry 123, Mathematics 241, 261, 341, 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:

In addition to completing the requirements for the physics major listed above, the student should also take the following courses required for admission to our partner institution, Washington University: Mathematics 241, Chemistry 123, and Computer Science 111.

Physics Courses (PHYS)

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. The abstracts for the talks can be found at https://www.carleton.edu/physics-astronomy/phys-123-speaker-series/. Prerequisite: Physics 131, 143, 144, 145, 151, 152, or 165. 1 credit; S/CR/NC; NE; Spring; Arjendu K Pattanayak
PHYS 131 Introduction to Physics: Newtonian Mechanics and Lab A traditional introduction to classical mechanics using the Newtonian worldview. The kinematics and dynamics of some simple systems are investigated using Newton's laws, vector analysis, and the conservation laws of momentum and energy. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work. Prerequisite: Concurrent registration in or successful completion of Mathematics 101 or 111, not open to students who have completed Physics 143, 144 or 145 at Carleton. 3 credits; LS, QRE; Fall; Arjendu K Pattanayak, Chris J West
PHYS 143 Physical Systems: Mechanics and Relativity and Lab This course begins with an introduction to classical mechanics using the Newtonian worldview. Descriptions of motion and change in motion of some simple systems at human speeds are investigated using Newton's laws, vector analysis, and the conservation laws of momentum and energy. The course moves beyond the Newtonian framework to consider a relativistic framework where time and space are intertwined and explores the motion of objects whose speeds approach the speed of light. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work. Prerequisite: Previous completion of Mathematics 101 or 111. Not open to students who have completed Physics 131, 144, 145 or 151 at Carleton. 6 credits; LS, QRE; Winter, Spring; Chris J West, Andrew Nine
PHYS 144 Astrophysical Systems: Mechanics and Relativity and Lab This course begins by reviewing Newtonian mechanics, with applications of vector analysis and the concepts of momentum and energy to large-scale gravitational phenomena in the universe. The course moves beyond the Newtonian framework to consider a relativistic framework where time and space are intertwined and explores the motion of objects whose speeds approach the speed of light. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work. Prerequisite: Previous completion of Mathematics 120 or 121. Not open to students who have completed Physics 131, 143, 145 or 151 at Carleton. 6 credits; LS, QRE; Winter; Barry N Costanzi
PHYS 145 Mechanics and Waves and Lab This course begins with the study of the motion of objects on the human scale using Newton's laws. The course provides the foundation for the study of conservation of energy and momentum, waves, and fluids. Biologic, medical, chemical, nuclear, and geologic applications may be considered. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work. Prerequisite: Mathematics 101 or 111. Not open to students who have completed Physics 131, 143, or 144 at Carleton. 6 credits; LS, QRE; Spring; Chris J West
PHYS 151 Introduction to Physics: Relativity and Particles and Lab An introduction to principles of physics in the realm of the very small and very fast. The course provides an introduction to special relativity where time and space are intertwined and explores the motion of objects whose speeds approach the speed of light. Comfort with algebra and the integration and differentiation of elementary functions is assumed. Weekly laboratory work. Prerequisite: Mathematics 101 or 111 (completion or concurrent registration) and Physics 131 (completion or concurrent registration). Not open to students who have completed Physics 143 or 144 at Carleton. 3 credits; LS, QRE; Fall; Seth Kimbrell
PHYS 152 Introduction to Physics: Environmental Physics and Lab 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. Prerequisite: Mathematics 101, 111 (completion or concurrent registration) and Physics 131 (completion or concurrent registration), 143, 144 or 145. 3 credits; LS, QRE; Fall; Arjendu K Pattanayak, Chris J West
PHYS 165 Introduction to Electricity, Magnetism, and Optics and Lab A study of the principles of electricity, magnetism, and optics with an emphasis on real-world applications to areas such as electronics, medicine, or materials science. Topics include electric and magnetic fields, electric potentials, DC and AC circuits and geometric and wave optics. 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, 143, 144, or 145. Mathematics 101 or 111. 6 credits; LS, QRE; Winter; Seth Kimbrell
PHYS 226 Atomic and Nuclear Physics Theory 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, and applications of these concepts to atomic, nuclear, and particle physics. This course covers the theory portion of PHYS228 without the lab component that will be a separate course, allowing students to proceed through theory courses in the physics major. Prerequisite: Physics 143, 144 or 151. 4 credits; NE, QRE; Not offered 2023-24
PHYS 227 Atomic and Nuclear Physics Lab This lab course covers applications of quantum mechanics to X-ray and optical spectra and instruments of nuclear and particle physics. The course meets for one laboratory session per week and covers the lab portion of Physics 228 that is required for upper-level physics lab classes. Prerequisite: Physics 143, 144 or 151; Physics 226. 2 credits; NE; Not offered 2023-24
PHYS 228 Atomic and Nuclear Physics and Lab An introduction to quantum mechanics and select applications that explore physics in the realm of the very small world or atoms and nuclei. Topics include wave-like and particle-like behavior of both light and matter, behavior of particles in confined spaces, material properties of solids, radioactive decay, and experimental techniques and instrumentation for exploring these optical, atomic, and nuclear processes. One laboratory per week. Prerequisite: Physics 143, 144 or 151 and Mathematics 120. 6 credits; LS, QRE; Fall; Barry N Costanzi, Jay D Tasson
PHYS 231 Analytical and Computational Mechanics An analytical and computational treatment of classical mechanics and dynamics. We start from a reconsideration of complicated Newtonian problems and also develop the Lagrangian and Hamiltonian formalism of classical mechanics. A variety of systems, including some whose equations of motion cannot be solved analytically, will be explored. Possible examples include harmonic oscillators, central-force problems, chaotic dynamics, astrophysical systems, and medieval siege engines. Prerequisite: Physics 131, 143 or 144 and Mathematics 210 or 211 (completion or concurrent registration) or instructor permission. 6 credits; NE, QRE; Winter; Arjendu K Pattanayak
PHYS 232 Astrophysics I 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. Prerequisite: Physics 226, 228 or 231. 6 credits; NE, QRE; Spring; Ryan C Terrien
PHYS 233 Astrophysics II 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 or 231. 6 credits; QRE, NE; Not offered 2023-24
PHYS 234 Computer Simulations in Complex Physical Systems The development of techniques to study complex physical systems from a probabilistic and numerical standpoint, focused on cellular automata models. 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 computer programming skills are assumed. Prerequisite: Physics 131, 143, or 144, or instructor permission. 6 credits; LS, QRE; Spring; Jay D Tasson
PHYS 235 Electricity and Magnetism and Lab Electric and magnetic fields in free space, and their interactions with charges and currents. Topics include electric fields and magnetic fields of various charge and current distributions, induction, DC and AC circuits and Maxwell's equations. Weekly laboratory work explores course content in more practical detail. Prerequisite: Physics 165, 226, 228 or Physics 231; Mathematics 210 or Mathematics 211; or instructor permission. 6 credits; LS, QRE; Spring; Seth Kimbrell, Marty Baylor
PHYS 251 Theory and Applications of Remote Sensing Remote sensing – interpreting information about physical systems at a distance using the electromagnetic spectrum – enables scientists to monitor climate change, detect material resources, track urban development, or map the surface of other planets, among a host of other applications. This course will explore key satellite remote sensing methods, such as visible and thermal imagery, visible through mid-infrared spectroscopy, radar, gamma ray and neutron spectroscopy, and laser altimetry, introducing both the physical theory and practical data analysis techniques. Prerequisite: 100-level PHYS (151, 152, 143, 144, 145, 165), Astronomy 110, ENTS 120, or Geology 110. Math 120 or 121 also required. 6 credits; NE, QRE; Not offered 2023-24
PHYS 297 Assessment and Communication of External Physics Activity An independent study course intended for students who have completed an external activity related to the physics major (for example, an internship or an externship) to communicate (both in written and oral forms) and assess their physics learning from that activity. Prerequisite: Permission of department chair and homework in advance of the external physics activity. 1 credit; NE; Not offered 2023-24
PHYS 311 Nonlinear Optoelectronic Dynamics The course will start from basic electromagnetism and model the dynamics of laser light interfering via modulated optoelectronics, including feedback with time-delays. Techniques from non-linear time-series data analysis will be used to characterize the various different kinds of dynamics. Basic concepts of information theory, network dynamics, and machine learning based on reservoir computing will be introduced. There will be significant hands-on work, with an exploration of applications to signal processing, optical communication, and random number generation. Prerequisite: Physics 228 and 235. 6 credits; NE; Not offered 2023-24
PHYS 312 Astronomical Detection and Measurement A study of astronomical detection and measurement across the electromagnetic spectrum, encompassing both the underlying physical principles and their application. Building on a foundation of radiometry, optics, and measurement statistics, this course will explore the design and function of modern electromagnetic measurement systems. Possible topics include high-dispersion spectroscopy, spatial interferometry, and the analysis of sensitivity and noise in electromagnetic detection for coherent and incoherent detectors. Prerequisite: Physics 228. 6 credits; NE, QRE; Not offered 2023-24
PHYS 333 Survey of Particle and Nuclear Physics A detailed survey of selected topics in particle and nuclear physics. Particle physics topics might include the Standard Model interactions and mediators, Feynman diagrams, symmetries and tests of conservation laws, Dirac equation and possibly QED Feynman rules. Nuclear physics topics might include the Liquid Drop, Fermi Gas, and Shell models of the nucleus, discussion of radiation, energy deposition in media, and discussion of quantum chromodynamics. Fluency in multi-variable calculus is expected. Prerequisite: Physics 235, previous or concurrent registration in Physics 335. 6 credits; NE; Winter; Chris J West
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 226 or 228, and Physics 231 and Mathematics 232. Familiarity with matrix algebra is assumed. 6 credits; NE, QRE; Winter; Jay D Tasson
PHYS 341 Waves The analysis of wave phenomena, including normal mode expansions, the wave equation and boundary value problems, and interference, diffraction, dispersion, and polarization. Applications are made to mechanical, sound, water and electromagnetic waves with particular emphasis on both the unifying principles across all wave phenomena, as well as the nuances of particular types of waves. Prerequisite: Physics 231 and 235, and Mathematics 232. 6 credits; NE, QRE; Winter
PHYS 342 Contemporary Experimental Physics and Lab 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 227 or 228) and 235 and (Physics 335 or Physic 346) or instructor permission. 6 credits; LS, QRE; Spring; Melissa Eblen-Zayas, Ryan C Terrien
PHYS 343 Electronics and Lab 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 credits; LS, QRE; Fall; Melissa Eblen-Zayas
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. Prerequisite: Physics 235 and Mathematics 232. 6 credits; NE; Not offered 2023-24
PHYS 345 Advanced Optics This is a laboratory course that will serve as a follow-up to 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: Corequisite Physics 344 or permission of the instructor. 2 credits; QRE, LS; Not offered 2023-24
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 226 or 228. 6 credits; NE, QRE; Fall; Arjendu K Pattanayak
PHYS 347 General Relativity Einstein'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 235 and Physic 231. 6 credits; NE; Not offered 2023-24
PHYS 352 Advanced Electricity and Magnetism The course introduces techniques for applying electromagnetic theory to charge and current distributions beyond what is covered in prior Electricity and Magnetism courses. Additional topics include applications to Maxwell's equations, radiation, and relativity. Prerequisite: Physics 235, Mathematics 341 strongly recommended. 6 credits; NE, QRE; Spring; Arjendu K Pattanayak
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. Prerequisite: Physics 335 or 346. 6 credits; NE, QRE; Spring; Barry N Costanzi
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 231. 6 credits; NE, QRE; Fall; Jay D 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. 2-3 credits; S/CR/NC; NE; Fall, Winter; Jay D Tasson, Arjendu K Pattanayak, Melissa Eblen-Zayas, Ryan C Terrien, Marty Baylor, Barry N Costanzi
PHYS 400 Integrative Exercise An extensive study of a specific topic in physics, culminating in a 60-minute presentation during winter or spring term and a 7500 word paper. 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). 3-6 credits; S/NC; Fall, Winter, Spring; Jay D Tasson, Barry N Costanzi, Seth Kimbrell, Ryan C Terrien, Melissa Eblen-Zayas, Arjendu K Pattanayak

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 credits; QRE, LS; Fall, Winter; Ryan C Terrien, Andrew Nine
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, 127, 232, 233, Physics 226, 228, 232, 233 or instructor permission. 3 credits; S/CR/NC; LS, QRE; Fall, Spring; Seth Kimbrell, Andrew Nine
ASTR 232 Astrophysics I 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. Prerequisite: Physics 226, 228, 231 or instructor permission. 6 credits; NE, QRE; Spring; Ryan C Terrien
ASTR 233 Astrophysics II 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 or 231 or instructor permission. 6 credits; NE, QRE; Not offered 2023-24
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: Instructor Permission. 2-3 credits; NE; Not offered 2023-24