Associate Professor Walden, chair∙; Jarvis Professor Silverman; Associate Professors Branning (acting chair, fall) and Geiss; Assistant Professor Barwick; Laboratory Lecturer in Physics Palandage; Visiting Assistant Professor Cox; Visiting Lecturer Shapiro
Physics is the study of energy, matter, and the interactions that govern their behavior. It is a wide-ranging and fundamental field of inquiry that links together all of the physical sciences. Research in physics addresses questions as seemingly diverse as how atoms are put together, how galaxies form and evolve, and why some balls bounce better than others. Although the everyday world with which we are familiar differs enormously in scale from the atomic and galactic domains, all of these examples share common unifying principles, such as the conservation of mass-energy, that the physicist seeks to uncover and understand. These basic principles and their most significant applications form the focus of an undergraduate program in physics.
Physics is also an interdisciplinary science, providing the theoretical underpinnings for the concepts and technologies fundamental to major fields such as chemistry, biology, medicine, electronics, geology, and to the applied fields of optics, nanotechnology, computer science, and engineering. Lasers, MRI, and high-speed computing are but a few of the technological advances made possible by the applications of the principles of physics. An education in physics provides students with a solid understanding of basic modern science and trains them to solve complex problems. This training prepares undergraduate majors in physics for a wide variety of careers, many of which take them well outside the boundaries of what is traditionally considered “physics.”
Course levels—PHYS 131L, 231L, and 232L are courses designed as preparation for students who are planning on majoring in physics, engineering, or other physical sciences. They make use of calculus and require prior completion of, or concurrent registration in, appropriate mathematics courses. Students who are considering one of these majors are strongly advised to take PHYS 131L and MATH 131 in the fall term of the first year.
PHYS 101L and 102L provide a one-year introduction to the fundamentals of physics with no mathematics prerequisites. These courses are intended for students who are not planning further work in physics, and they do not fulfill requirements for the physics major. This is the introductory sequence most often taken by biology majors and by students preparing for medical school.
The other courses at the 100 level are open to any interested student, and have no mathematics prerequisites. The courses offered vary from year to year.
The courses at the 300 and 400 levels constitute advanced work in physics. They are aimed at both physics majors and students in the other sciences. Students should take PHYS 300 as early as possible, preferably in the spring semester of their sophomore year. Please note that the 300-level courses are mostly offered in alternate years.
The physics major—Students must take PHYS 131L, 231L, and 232L, and five courses at the 300 level or above, three of which must be PHYS 300, PHYS 307, and PHYS 320. PHYS 399 and PHYS 490 do not count towards fulfillment of this requirement. In addition, the student must take PHYS 405, the senior exercise. Outside the department, the student must take MATH 231 and 234 and CHEM 111L. Students must obtain grades of C- or better in all of these courses. It is strongly recommended that students preparing for graduate study in physics take three or more additional courses in physics at the 300 level or above, and at least one year of mathematics at the 300 level or above. The Writing Intensive Part II requirement is fulfilled by PHYS 320.
The interdisciplinary computing major in physics—See the “Interdisciplinary Computing Major” section of the Bulletin. Students contemplating the interdisciplinary computing major in physics should contact the chair of the Physics Department, who will direct them to appropriate faculty members for guidance and assistance in setting up a plan of study.
Study Away—Physics majors with an interest in studying abroad should plan well in advance of the semester they will be away. This particularly important since most upper-level physics courses at Trinity are offered biennially. Students wishing to use courses taken abroad in partial fulfillment of the requirements for the physics major must obtain the prior approval of the department chair.
Honors—Students seeking honors in physics must complete at least one additional physics course beyond the minimum required for the physics major. This course may be a semester of independent research (PHYS 399 or 490). Honors candidates must attain an average of at least a B+ in all physics courses. Honors are awarded to qualified students by a vote of the faculty.
Advanced Placement—Students who have earned an Advanced Placement exam grade in physics of 4 or 5 may receive course credit. See the “Advanced Placement” section of the Bulletin for details. Exceptionally well-prepared students who are exempt from PHYS 131 and from both MATH 131 and MATH132/142 may petition the chair of the department to take PHYS 232L prior to PHYS 231L.
Spring Term
[103. Stars and Galaxies]— This course provides an introduction to current views of the contents, structure, and evolution of the astronomical universe outside our solar system. Topics to be considered include cosmology, stellar evolution, the discovery of neutron stars, the formation of galaxies, the “discovery” of our own galaxy, and the search for black holes. Occasional viewing sessions and other observational exercises will be assigned. (Enrollment limited)
Fall Term
101. Principles of Physics I— An introduction to the fundamental ideas of physics. Beginning with kinematics—the quantitative description of motion—the course covers the Newtonian mechanics of point masses, Newton’s theory of universal gravitation, the work-energy principle, and the conservation of energy and momentum. Three lectures and one laboratory per week. A student taking Physics 101 cannot earn credit for Physics 131. (1.25 course credits) (Enrollment limited)-Cox, Shapiro
131. Mechanics and Heat— This course, the first part of a three-term calculus-based introduction to physics, is designed to provide the student with a working knowledge of the language and the analytical tools of Newtonian mechanics and of thermodynamics. Newton’s laws are used to study the motion of individual particles and of systems of particles. The ideas of work, energy, momentum, and impulse are introduced. Newton’s universal law of gravitation and a brief introduction to rigid-body motion round out the exposition of classical mechanics. The remainder of the term is devoted to a presentation of the First and Second Laws of Thermodynamics and their applications to the prototypical thermodynamics system, the ideal gas. Three class meetings and one laboratory per week. A student taking Physics 131 cannot earn credit for Physics 101. Prerequisite: Concurrent Registration in or previous completion of Mathematics 131 with a grade of C- or better. (1.25 course credits) (Enrollment limited)-Palandage, Shapiro, Silverman
232. Optics and Modern Physics— Concluding the three-term calculus-based introductory physics sequence, this course begins with the study of interference and diffraction, which provide compelling evidence for the wave nature of light. We then turn to geometrical optics to understand the properties of lenses, mirrors, and optical instruments. The remainder of the course is devoted to the treatment of phenomena at the atomic and subatomic levels using the ideas of quantum physics. From the introduction of the photon, the Bohr atom, and de Broglie’s matter waves, we proceed to the unified description provided by Schrodinger’s wave mechanics. This is used to understand basic properties of atoms, beginning with hydrogen, and to describe the interaction between electromagnetic radiation and matter. As time permits, the course will include a brief introduction to the theory of special relativity and to nuclear physics. Three class meetings and one laboratory per week. Prerequisite: C- or better in Physics 231L and either Mathematics 132 or 142, with concurrent registration in Mathematics 231 strongly recommended. (1.25 course credits) (Enrollment limited)-Branning, Palandage
[301. Classical Mechanics]— A detailed analytical treatment of Newtonian mechanics. Lagrange’s and Hamilton’s equations are developed and applied to the analysis of motion governed by several exemplary force laws. The general problem of motion under the influence of a central force is formulated and applied to problems of planetary motion and to Rutherford scattering of particles. Other topics to be treated include the dynamics of rigid bodies, oscillations of systems of masses connected by springs and elements of the mechanics of continuous media such as fluids. Prerequisite: C- or better in Physics 231 and either Mathematics 231 or Mathematics 234.
304. Statistical and Thermal Physics— This course provides an intermediate-level presentation of basic principles of statistical physics with applications to scientific inference, stochastic phenomena, and thermodynamics. Classical thermodynamics describes the equilibrium properties and phase transformations of macroscopic physical systems in terms of relations independent of any atomic model of matter. Statistical physics, by contrast, provides a fundamental theoretical foundation for the thermodynamic relations in terms of the specific statistical laws obeyed by the elementary particles of matter and general considerations of probability theory. Together, thermodynamics and statistical physics provide the tools for studying the behavior of aggregates of particles far too numerous to be analyzed by solving directly the equations of motion of either classical or quantum mechanics. Among the concepts, systems, and processes to be discussed are heat, work, temperature, pressure, energy, entropy, chemical potential, chemical equilibria, gases, liquids, solids, solutions, neutron stars, and fluctuation phenomena (not necessarily in that order and subject to time constratints). Prerequisite: C- or better in Physics 232L. (Enrollment limited)-Silverman
[307. Modern Physics]— This course provides a reasonably comprehensive picture of our current understanding of phenomena at the atomic and subatomic levels, using basic ideas of quantum physics. Topics to be covered include the structure of atoms, molecules, solids, and nuclei; the interaction of electromagnetic radiation with matter; and, time permitting, an introduction to special relativity and particle physics. Prerequisite: C- or better in Physics 232L.
[313. Quantum Mechanics]— A thorough study of the general formalism of quantum mechanics together with some illustrative applications, including the postulates of quantum mechanics; states, observables, and operators; measurements in quantum mechanics; the Dirac notation; simple systems: the square well, the harmonic oscillator, the hydrogen atom; approximation techniques and perturbation theory; and elements of the quantum theory of angular momentum. Prerequisite: C- or better in Physics 232L.
[314. Applications of Quantum Mechanics]— This course surveys the application of quantum mechanics to a number of quantum systems or quantum processes basic to atomic, molecular, nuclear, and condensed matter physics. Examples may include the energy level structure of atoms and molecules, taking account also of the contribution of electron and nuclear spin to the fine and hyperfine structure, the effects of electric and magnetic fields on atoms (Stark effect and Zeeman effect), nuclear alpha decay as an illustration of quantum tunneling, molecular vibration as an example of the quantum harmonic oscillator, the quantum theory of light absorption and emission, and the quantum basis for conductivity in solids and superconductivity in metals at very low temperatures. Procedures for solving the quantum equation of motion (Schroedinger equation) exactly and by different methods of approximation (such as time-independent and time-dependent perturbation theory, the WKB aproximation, and use of the variational principle) may also be discussed. Prerequisite: C- or better in Physics 232L.
315. Contemporary Optics— A survey of current techniques and applications for classical and nonclassical light. Topics may include Fourier optics, nonlinear optics, statistical optics, holography, polarization, interferometry, quantum cryptography, optoelectronics, and ultrafast optics. Prerequisite: C- or better in Physics 231L and Physics 232L (Enrollment limited)-Branning
399. Independent Study— Submission of the special form, available in the Registrar’s Office, and the approval of the instructor and chairperson are required for enrollment. (1-2 course credits) -Staff
405. Senior Exercise— This exercise is intended to familiarize the student with a problem of current interest in physics, and to develop his or her ability to gather and interpret the information relevant to the problem. During the fall semester each senior student will meet with an assigned faculty adviser to plan an essay or research project to be completed during the year. Topics may involve any aspects of physics, including its various applications. While students may write on original research they have undertaken, they are not required to do so. This exercise is required for the physics major. Senior Physics Majors Only. (0.5 course credit) -Staff
490. Research Assistantship— Submission of the special registration form, available in the Registrar’s Office, and the approval of the instructor and chairperson are required for enrollment. (0.5-1 course credit) -Staff
Spring Term
102. Principles of Physics II— A continuation of Physics 101L, this course covers topics such as electricity and magnetism, elementary thermodynamics, the theory of special relativity, classical wave behavior, and the description of microscopic physical systems via quantum theory. Three lecture periods and one laboratory period per week. Prerequisite: Physics 101L or 131L. (1.25 course credits) (Enrollment limited)-Barwick, Geiss
[111. Frontiers of Physics]— A course for non-science majors which examines selections of the exciting developments in contemporary physics. Topics to be explored may include (but are not limited to) (1) aspects of Einstein’s theory of special and general relativity such as the nature of space, time, and gravity, the search for gravitational waves, the structure of exotic astrophysical objects like neutron stars and black holes, and the origin, evolution, and expected fate of the universe; (2) advances in physicists’ understanding of the quantum structure of matter such as the Standard Model accounting for the families of elementary particles (e.g. quarks, electrons, neutrinos and others); (3) nuclear physics and the generation of energy by fission and fusion, (4) speculative “theories of everything” such as string theory, (5) extraordinary macroscopic quantum processes such as superconductivity and superfluidity; (6) novel materials with remarkable properties (such as graphene and meta-materials), and other topics. The development will be carried out with a minimum of mathematics and at a pre-calculus level. (Enrollment limited)
231. Electricity, Magnetism, and Waves— This second part of the three-term calculus-based introductory sequence is devoted primarily to the study of electromagnetism. The emphasis is on the description of electric and magnetic phenomena in terms of fields. Topics to be covered include electrostatics and magnetostatics, electromagnetic induction, Maxwell’s equations, electromagnetic waves, and the characterization of energy and momentum in the electromagnetic field. The remainder of the course is taken up with basic properties of waves in general: wave kinematics, standing waves and resonance, and the Doppler effect. Three lecture periods and one laboratory period per week. Prerequisite: C- or better in Physics 131L and concurrent registration in or previous completion of either Mathematics 132 or Mathematics 142 with a grade of C- or better. (1.25 course credits) (Enrollment limited) -Barwick, Palandage, Silverman
300. Mathematical Methods of Physics— This course focuses on mathematical methods essential to the expression and application of the laws of physics. It is designed to provide a mathematics background for other upper-level physics courses and for physics research, and thus ideally should be taken in the junior year. Topics to be discussed may vary somewhat from year to year depending on the emphasis of the instructor, but will ordinarily include elements of vector analysis, differential geometry, linear algebra, functions of a complex variable, Fourier analysis, and some of the special functions of mathematical physics. Additional topics, such as probability theory, the calculus of variations, or an introduction to group theory, may be taken up if time permits. Prerequisite: C- or better in Physics 231L and Mathematics 231. (Enrollment limited) -Walden
302. Electrodynamics— A study of the unified description of electromagnetic phenomena provided by Maxwell’s equations in differential form. The scalar and vector potentials, multipole expansions, boundary value problems, propagation of electromagnetic waves, radiation from accelerated charges. Prerequisite: C- or better in Physics 231 L and Mathematics 231 (concurrent registration in Mathematics 234 is strongly recommended). -Silverman
[304. Statistical Physics]— This course provides an intermediate-level presentation of basic principles of statistical physics with applications to scientific inference, stochastic phenomena, and thermodynamics. Classical thermodynamics describes the equilibrium properties and phase transformations of macroscopic physical systems in terms of relations independent of any atomic model of matter. Statistical physics, by contrast, provides a fundamental theoretical foundation for the thermodynamic relations in terms of the specific statistical laws obeyed by the elementary particles of matter and general considerations of probability theory. Together, thermodynamics and statistical physics provide the tools for studying the behavior of aggregates of particles far too numerous to be analyzed by solving directly the equations of motion of either classical or quantum mechanics. Among the concepts, systems, and processes to be discussed are heat, work, temperature, pressure, energy, entropy, chemical potential, chemical equilibria, gases, liquids, solids, solutions, neutron stars, and fluctuation phenomena (not necessarily in that order and subject to time constratints). Prerequisite: C- or better in Physics 232L. (Enrollment limited)
[307. Modern Physics]— This course provides a reasonably comprehensive picture of our current understanding of phenomena at the atomic and subatomic levels, using basic ideas of quantum physics. Topics to be covered include the structure of atoms, molecules, solids, and nuclei; the interaction of electromagnetic radiation with matter; and, time permitting, an introduction to special relativity and particle physics. Prerequisite: C- or better in Physics 232L. (Enrollment limited)
[320. Modern Physical Measurements]— A series of measurements in a focused area of modern experimental physics, this course is designed to offer an in-depth exposure to and understanding of instruments and techniques employed in current experimental investigations. It also provides experiences pertinent to participation in experimental research typified by Physics 490. The series of experiments to be performed will be determined in advance by the student(s) and the instructor(s). Prerequisite: C- or better in Physics 232L. (Enrollment limited)
325. Condensed Matter Physics— An introduction to the fundamental physics which governs the properties of solids at a microscopic level. Topics will include crystal structures and symmetries, phonons, diffraction, reciprocal space, optical properties, superconductivity, magnetism, band theory, and the electronic properties of conductors and semiconductors. Time permitting, applications in the fields of materials science and nanotechnology will be considered. Prerequisite: C- or better in Physics 231L and Physics 232L (Enrollment limited) -Walden
399. Independent Study— Submission of the special form, available in the Registrar’s Office, and the approval of the instructor and chairperson are required for enrollment. (1-2 course credits) -Staff
405. Senior Exercise— This exercise is intended to familiarize the student with a problem of current interest in physics, and to develop his or her ability to gather and interpret the information relevant to the problem. During the fall semester each senior student will meet with an assigned faculty adviser to plan an essay or research project to be completed during the year. Topics may involve any aspects of physics, including its various applications. While students may write on original research they have undertaken, they are not required to do so. This exercise is required for the physics major. Senior Physics Majors Only. (0.5 course credit) -Staff
490. Research Assistantship— Submission of the special registration form, available in the Registrar’s Office, and the approval of the instructor and chairperson are required for enrollment. (0.5-1 course credit) -Staff