An introduction to the concepts of modern engineering, emphasizing modeling, analysis, synthesis, design, and control. Applications to mechanical and electrical systems. Prerequisites: Mathematics 45 and Physics 24.

This course will teach you about the conceptual foundations of modern physics. We will cover a wide range of examples and concepts that span many sub-disciplines while emphasizing the unity of physics and its fundamental character. We will discuss general concepts from Relativity to Quantum Mechanics to Cosmology and black holes, from superconductivity and the beauty of phase transitions to the Standard Model of particle physics and quantum entanglement. We will use high school math to explore the details of these concepts. Visual interactive simulations will replace equations wherever possible, and homeworks will help you explore explicit cases with basic computations. Near the end of the semester, you will choose a topic from current physics news that you will present to the class.

Einstein’s special theory of relativity is developed from the premises that the laws of physics are the same in all inertial frames and that the speed of light is a constant. The relationship between mass and energy is explored and relativistic collisions analyzed. The families of elementary particles are described.

A first-year elective that aims to foster an appreciation of the insights that material science provides into understanding natural phenomena and current technology. It draws heavily on condensed matter physics, but incorporates substantial amounts of chemistry, materials science, and some electrical engineering.

An introduction to electromagnetism and optics. Maxwell’s equations are discussed in differential and integral form. Maxwell’s equations are then used to develop an introduction to the field of optics. Beyond the presentation of Maxwell’s equations, selected topics include Gauss’s and Stokes’s theorems, the wave equation including the Poynting vector, electromagnetic energy, basic circuits, diffraction, Snell’s law, interference, and the physical origin of the index of refraction. Applications include fusion, circuit elements, motors, diffraction gratings and thin films. Each week there are two 50-minute lectures as well as two 50-minute recitation sections. In the recitation sections material is reviewed, homework is discussed, and small groups work at the blackboard on new problems.

Prerequisites: Physics 23 and Physics 24

An introduction to electromagnetism and optics. Maxwell’s equations are discussed in differential and integral form. Maxwell’s equations are then used to develop an introduction to the field of optics. Beyond the presentation of Maxwell’s equations, selected topics include Gauss’s and Stokes’s theorems, the wave equation including the Poynting vector, electromagnetic energy, basic circuits, diffraction, Snell’s law, interference, and the physical origin of the index of refraction. Applications include fusion, circuit elements, motors, diffraction gratings and thin films. Each week there are two 50-minute lectures as well as two 50-minute recitation sections. In the recitation sections material is reviewed, homework is discussed, and small groups work at the blackboard on new problems.

Prerequisites: Physics 23 and Physics 24

The application of mathematical methods to the study of particles and of systems of particles; Newton, Lagrange, and Hamilton equations of motion; conservation theorems; central force motion, collisions, damped oscillators, rigid-body dynamics, systems with constraints, variational methods. Prerequisites: Physics 23 & 24 and Mathematics 65 or permission of the instructor.

Beginning with the equal probability of accessible microstates of an isolated system, the course develops the quantum and classical statistical mechanics and thermodynamics of simple systems of many particles: classical and quantum gases, isolated spins in a magnetic field, photons, and phonons. The laws of thermodynamics are developed from statistical considerations and applied to uniform phases, phase and chemical equilibria, heat engines, refrigerators, and other practical devices. Finally, kinetic theory is applied to a computation of transport properties of gases. Lectures are held in either the 50-minute thrice weekly format or the 70-minute twice weekly format. These are supplemented with a 50-minute recitation section that focuses on student questions and supplementary problems done in groups. In some years students also work in groups on a simulation project, which is presented orally to the class at the end of the semester. Besides providing a foundation in statistical physics, this course aims to develop students' abilities to approximate, to estimate, and to apply broad physical principles to real-world situations.

Prerequisite: Physics 52. Corequisite: Physics 111 or permission of the instructor.

An intermediate laboratory in electronics involving the construction and analysis of a variety of analog and digital circuits using resistors, capacitors, diodes, transformers, operational amplifiers, photodiodes, light-emitting diodes, digital logic gates, flip-flops, and clocks. Applications include rectifiers, amplifiers, differentiators and integrators, passive and active filters, oscillators, counting circuits, digital-to-analog and analog-to-digital conversion. Unlike other laboratory courses, each student works at a separate laboratory station with all equipment necessary to build and test the various circuits.

A seminar course focusing on recent developments in the chemistry, physics, and engineering of photovoltaics, fuel cells, and batteries.

Theory of classical electromagnetic fields, with an emphasis on advanced analytical techniques and concepts. The course builds on the introductory material of Physics 51, and emphasizes the solution of Maxwell’s equations in various physical applications by analytical means. The first part of the course deals with electrostatics and the solution of Laplace’s and Poisson’s equations in various coordinate systems and with various boundary conditions. The course proceeds to examine the effect of matter on static fields, and then to pursue static magnetic fields and materials analogously. The final sequence of the course deals with electrodynamics and the fundamentals of electromagnetic radiation.

Scattering, including the Born approximation and partial wave expansion. Path integrals. Time-dependent perturbation theory. Quantum theory of the electromagnetic field. Prerequisite: Physics 116. 2 credit hours. The course covers Chapters 8, 13, and 14 (the chapters not covered in Physics 116) of *A Modern Approach to Quantum Mechanics*. The course is run as a discussion course, in which students read sections of the text before class and via email indicate areas for which there are questions or a need for discussion. The final exam is typically a 2-hour oral exam.

Experiments are selected from the fields of nuclear, solid-state, and optical physics, utilizing multichannel and time coincidence nuclear instrumentation, an x-ray machine, an optical spectrophotometer, lasers and interferometers, and a pulsed NMR instrument. Prerequisite: Physics 134.

A seminar devoted to effective writing strategies and conventions that apply across academic disciplines. The course emphasizes clarity, concision, and coherence in sentences, paragraphs, and arguments.

A general survey of modern astrophysics. The course starts with the fundamental physical concepts underlying much of astrophysics, including gravitation and orbital mechanics, and radiative processes (including blackbody radiation, line emission and rudiments of radiative transfer). We then move on to discuss the stellar structure, evolution and death, the physics of compact stars, the interstellar medium and star-formation, and the structure and evolution of the galaxies, galaxy clusters and the universe. The course meets for three lecture periods each week. The students are evaluated based on their homework and test performance. In addition, each student makes a 15-minute presentation on the topic of his choice; these are spaced throughout the semester and are meant to compliment the material being currently discussed in lecture. This gives the students an opportunity to research at least one topic in considerably more depth than we are able to do in class. Offered jointly with Pomona and Joint Sciences. Prerequisite: Physics 51 or equivalent.

Classical mechanics is introduced beginning with inertial frames and the Galilean transformation, followed by momentum and momentum conservation in collisions, Newton’s laws of motion, spring forces, gravitational forces, and friction. Differential and integral calculus are used extensively throughout. Work, kinetic energy and potential energy are defined, and energy conservation is discussed in particle motion and collisions. Rotational motion is treated, including angular momentum, torque, cross-products, and statics. Other topics include rotating frames, pseudoforces, and central-force motion. Simple harmonic and some nonlinear oscillations are discussed, followed by waves on strings, sound, and other types of waves, and wave phenomena such as standing waves, beats, two-slit interference, resonance, and the Doppler effect. Lectures are twice per week, and there are also two recitation sections per week, in groups of about 20 students, all of whom solve new problems at the board nearly every session.

This course provides a relatively sophisticated introduction to classical mechanics. Students are given challenging problems which have them apply Newton’s laws and conservation laws to better understand how our world works.  Students study both static and dynamic systems, and learn to develop mathematical models of systems. Invitation to enroll in the course is based on performance on a placement exam administered typically on the first Saturday of the fall semester.

Beginning with modern atom interferometry experiments, this course moves directly to the Schrödinger equation. After a thorough consideration of solutions in one dimension, the principles of quantum mechanics are examined, including the role of operators, eigenfunctions and eigenvalues, superposition, commutators, and uncertainty relations. After discussion of angular momentum and some simple three-dimensional systems, applications of quantum mechanics to atomic and molecular physics, solid state physics, nuclear physics, and particle physics are stressed. Each week there are three 50-minute lectures as well as a recitation section in which small groups work on new problems that extend the material under discussion in significant ways. In addition, there is a term paper on an area of interest in quantum mechanics and/or its applications.

Classical experiments of modern physics, including thermal radiation, Rutherford scattering, barrier penetration of microwaves, gamma radiation interactions using pulse height analysis, the Hall effect, the Cavendish experiment, and a chaotic pendulum. Prerequisites: Physics 52 or concurrently. 1 credit hour.

The course takes a modern approach by introducing Dirac notation at the beginning. This is done through discussion of the Stern-Gerlach device and spin 1/2 particles, following the treatment of Townsend, Feynman and Sakurai. The course then proceeds through various nonrelativistic topics, including: general formalism, one-dimensional and three-dimensional problems, angular momentum states, Bell's theorem and its experimental verification, perturbation theory, and identical particles. Applications to atomic and nuclear systems are also discussed.

A laboratory-lecture course on the techniques and theory of classical and modern optics. Topics of study include diffraction, interferometry, Fourier transform spectroscopy, grating spectroscopy, lasers, and coherence of waves. In addition, the course develops the theory of sample variance, nonlinear least-squares fitting, the \( \chi^2 \) criterion for goodness of fit, and normalized residuals. The course is more loosely structured than earlier laboratory courses, and seeks to develop skills in experimental design and execution with flexible, multi-part experiments. The available experiments are

1. Fraunhofer and Fresnel diffraction
2. grating spectroscopy of mercury, hydrogen/deuterium, and solar absorption lines
3. scanning Fabry-Perot interferometry of a He-Ne laser, including the Lamb dip and the Zeeman effect
4. white light fringes, the He-Ne wavelength, and the refractive index of air are measured with a Michelson interferometer
5. Fourier transform spectroscopy of the sodium doublet and a pressure-broadened mercury lamp
6. quantum optics
7. thin lenses and geometric optics
8. Fresnel coefficients for the reflection of light

Team projects in applied physics, with corporate or national laboratory affiliation. The team interacts with both a faculty advisor and a liaison from the sponsoring organization to achieve project goals. Prerequisite: Upper-division standing.

Oral presentations and discussions of selected topics, including recent developments. Participants include physics majors, faculty members, and visiting speakers. Required for all junior and senior physics majors.