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(Offered as PHYS 102 and MATH 102) On January 27th, 1921, Albert Einstein gave a lecture titled “Geometry and Experience" at the Prussian Academy of Science. In this lecture he reflects on the interdependence of geometry and physics. To commemorate the centenary of such an inspiring event, this course will explore the natural connections between geometry (axioms, the notions of space and time, dimension and curvature) and relativity (the relativity principle, simultaneity, thought experiments). No background in physics or mathematics (besides basic high school algebra and trigonometry) will be assumed.

The course is designed for students who do not intend to major in mathematics or physics.

The course is designed for students who do not intend to major in mathematics or physics.

Professors Contreras and Jagannathan.

We will develop the concept of energy from a Physics perspective. We will introduce the various forms that energy can take and discuss the mechanisms by which it can be generated, transmitted, and transformed. The law of conservation of energy will be introduced both as a useful tool, and as an example of a fundamental physical law. The environmental and financial costs and benefits of various methods of energy generation and consumption will be discussed. Demonstrations and hands-on laboratory experiences will be an integral part of the course. The course is intended for non-science majors and not for students who have either completed or intend to complete the equivalent of PHYS 117 or CHEM 110.

The course is designed as an in-person course with active lab work.

Requisite: A working knowledge of high-school algebra, geometry and trigonometry. Limited to 20 students. Omitted 2020-21. Professor Hunter.

The aim of the course is to foster an understanding of and intuition for the modern-day electronic devices and circuits that are central to many aspects of our research, work, and play. A practical hands-on approach serves this aim well. After investigating the electrical characteristics of electronic components, including discrete semiconductor devices and integrated circuits (ICs), we go on to build and analyze both analog and digital circuits in order to gain insight into electronic control devices, data acquisition systems, and computers. Brief introductory lecture/discussion periods will be followed by experiments to help students understand new concepts. While the course is elementary, experienced students will be able to explore more complex circuitry and will be encouraged to apply some of their newly developed electronics knowledge and creativity to ongoing research projects in other fields. Two eighty-minute meetings per week of Lecture/Discussion/Laboratory.

Limited to 20 students. Omitted 2020-21. Professor Carter.

We live in a moment of great advances in astronomy and fundamental physics that are changing our understanding of the material world, from the microscopic realm of elementary particles to the large-scale structure of the universe. The course will emphasize the profound, but well-settled, ideas of the quantum theory and the theory of relativity that underpin our theories of the physical universe, as well as the many open questions that are being actively investigated today. Stepping back in time, we will review the concepts of pre-twentieth century physics that set the stage for the early twentieth century revolutions in physics. We will then connect these concepts to the present-day picture of the universe and its origins. No prior college-level mathematics or physics is assumed; however, high school algebra and geometry will be used, and additional simple mathematical concepts will be introduced as needed.

Fall semester. Professor Hall.

This course will begin with a description of the motion of particles and introduce Newton’s dynamical laws and a number of important force laws. We will apply these laws to a wide range of problems to gain a better understanding of the laws and to demonstrate the generality of the framework. The important concepts of work, mechanical energy, and linear and angular momentum will be introduced and the unifying idea of conservation laws will be discussed. Additional topics may include, the study of mechanical waves, fluid mechanics and rotational dynamics. Three hours of lecture and one three-hour laboratory per week.

To provide course interaction we will do required synchronous small group meetings, required synchronous individual meetings with the instructors, and some optional synchronous meetings. However, the main class lectures and laboratory exercises will be done remotely.

Requisite: MATH 111. Limited to 48 students. Fall semester: The Department. Spring semester: Professor Carter and Dr. Moyer.

Most of the physical phenomena we encounter in everyday life are due to the electromagnetic force. This course will begin with Coulomb’s law for the force between two charges at rest and introduce the electric field in this context. We will then discuss moving charges and the magnetic interaction between electric currents. The mathematical formulation of the basic laws in terms of the electric and magnetic fields will allow us to work towards the unified formulation originally given by Maxwell. His achievement has, as a gratifying outcome, the description of light as an electromagnetic wave. Laboratory exercises will emphasize electrical circuits and electronic measuring instruments. Three hours of lecture and discussion and one three-hour laboratory per week.

Because of the expected enrollment, the lectures and labs will be online only and remote. Additional small group discusssions may have synchrnous sections either in-person or online.

Requisite: PHYS 116 or 123. Limited to 48 students. Fall semester: Professors Friedman and Jagannathan. Spring semester: Department.

The idea that the same simple physical laws apply equally well in the terrestrial and celestial realms, called the Newtonian Synthesis, is a major intellectual development of the seventeenth century. It continues to be of vital importance in contemporary physics. In this course, we will explore the implications of this synthesis by combining Newton’s dynamical laws with his Law of Universal Gravitation. We will solve a wide range of problems of motion by introducing a small number of additional forces. The concepts of work, kinetic energy, and potential energy will then be introduced. Conservation laws of momentum, energy, and angular momentum will be discussed, both as results following from the dynamical laws under restricted conditions and as general principles that go well beyond the original context of their deduction. Four hours of lecture and discussion and one three-hour laboratory per week.

Lectures and discussions will be in-person for those able to attend and asynchronous for those not able to attend. Labs will be in-person for those able to attend and will be synchronous for those unable to attend. Should the pandemic render in-person classes impossible, lectures will become synchronous and labs will be done using remote kits.

Requisite: MATH 111. Admission with consent of the instructor. Limited to 24 students. Fall semester. Professor Hunter

In the mid-nineteenth century, completing nearly a century of work by others, Maxwell developed an elegant set of equations describing the dynamical behavior of electromagnetic fields. A remarkable consequence of Maxwell’s equations is that the wave theory of light is subsumed under electrodynamics. Moreover, we know from subsequent developments that the electromagnetic interaction largely determines the structure and properties of ordinary matter. This course will begin with Coulomb’s Law but will quickly introduce the concept of the electric field. Students will explore moving charges and their connection with the magnetic field, study currents and electrical circuits, and discuss Faraday’s introduction of the dynamics of the magnetic field and Maxwell’s generalization. Laboratory exercises will concentrate on circuits and electronic measuring instruments. Four hours of lecture and discussion and one three-hour laboratory per week.

Course meetings will be synchronous to the extent possible. Depending on the distribution of student locations, the meetings may be entirely online or a hybrid of online and in-person. The meeting times are subject to change, based on student time zones and availability. Students will receive a kit that allows completion of the labs.

Requisite: MATH 121 and PHYS 116 or 123. Limited to 24 students. Spring semester. The Department.

Phenomena that repeat over regular intervals of time and space play a fundamental role in physics and its applications. This course explores oscillations and waves in contexts from a simple mass on a spring to mechanical waves in solids, liquids, and gasses as well as electromagnetic waves. It emphasizes broadly applicable phenomena including superposition, boundary effects, interference, diffraction, coherence, normal modes, and the decomposition of arbitrary wave amplitudes into normal modes, as with Fourier analysis. The laboratory experiments on oscillations, mechanical waves and optics provide hands-on experience of the concepts discussed in the rest of the course. Two hours of lecture and discussion and one three-hour laboratory per week.

All course meetings will be in-person to the extent possible. Provisions will be available for remote learning, including recorded class meetings, online activities, synchronous discussions and office hours, and kits that allow completion of the labs.

Requisite: PHYS 116/123 and MATH 121 or consent of the instructor. Limited to 24 students. Fall semester. Professor Hanneke.

The theories of relativity (special and general) and the quantum theory constituted the revolutionary transformation of physics in the early twentieth century. Certain crucial experiments precipitated crises in our classical understanding to which these theories offered responses; in other instances, the theories implied strange and/or counterintuitive phenomena that were then investigated by crucial experiments. After an examination of the basics of Special Relativity, the quantum theory, and the important early experiments, we will consider their implications for model systems such as a particle in a box, the harmonic oscillator, and a simple version of the hydrogen atom. We will also explore the properties of nuclei and elementary particles, and study other topics such as lasers, photonics, and recent experiments of interest in contemporary physics. Three class hours per week.

This course is designed to involve in-person lectures and discussions, with problem sets and projects; but provisions will be available for remote and asynchronous learning, including recorded class meetings, online activities, and synchronous office hours at times TBA.

Requisites: MATH 121 and PHYS 117 or 124 or equivalent or consent of the instructor. Fall semester. Professor Hall.

How do we gather information to refine our models of the physical world? This course is all about data: acquiring data, separating signals from noise, analyzing and interpreting data, and communicating results. Much – indeed nearly all – data spend some time as an electrical signal, so we will study analog electronics. In addition, students will become familiar with contemporary experimental techniques, instrumentation, and/or computational methods. Throughout, students will develop skills in scientific communication, especially in the written form. Six hours of laboratory work per week.

All course meetings will be in-person to the extent possible. Provisions will be available for remote learning, including recorded class meetings, online activities, synchronous discussions and office hours, and kits that allow completion of the labs.

Requisite: PHYS 225 or consent of the instructor. Open to juniors and seniors. Spring semester. The Department.

The basic laws of physics governing the behavior of microscopic particles are in certain respects simple. They give rise both to complex behavior of macroscopic aggregates of these particles, and more remarkably, to a new kind of simplicity. Thermodynamics focuses on the simplicity at the macroscopic level directly, and formulates its laws in terms of a few observable parameters like temperature and pressure. Statistical Mechanics, on the other hand, seeks to build a bridge between mechanics and thermodynamics, providing in the process, a basis for the latter, and pointing out the limits to its range of applicability. Statistical Mechanics also allows one to investigate, in principle, physical systems outside the range of validity of Thermodynamics. After an introduction to thermodynamic laws, we will consider a microscopic view of entropy, formulate the kinetic theory, and study several pertinent probability distributions including the classical Boltzmann distribution. Relying on a quantum picture of microscopic laws, we will study photon and phonon gases, chemical potential, classical and degenerate quantum ideal gases, and chemical and phase equilibria. Three class hours per week.

This course is designed to involve in-person lectures and discussions, with problem sets; but provisions will be available for remote and asynchronous learning, including recorded class meetings, online activities, and synchronous office hours at times TBA.

Requisite: PHYS 225 or consent of the instructor. Spring semester. The Department.

The human body offers a rich set of applications of introductory physics principles. In this course we will use and refine the physicist’s approach of constructing intentionally (over)simplified models of the human body to gain qualitative and quantitative insights into its function. We will focus primarily on mechanical phenomena, such as locomotion and transport within the body, and on the mechanical properties of the materials that make up the body. We will develop physics concepts, including fluid mechanics, solid mechanics, diffusion, and heat transfer, as needed.

Requisite: PHYS 116 and MATH 111, or consent of the instructor. Omitted 2020-21. The Department.

A two-level quantum system is one whose states are represented by unit rays in a two-dimensional vector space. Such a system is the simplest non-trivial quantum mechanical entity. Nevertheless, a two-level system or a collection of such systems exhibits all of the challenging and subtle features for which the quantum theory is notorious. Examples of two-level systems we will consider are the polarization states of a photon, the spin of an electron or similar particle, and any atomic system for which only two of its many energy levels are important in a given problem. After an overview of the current state of quantum mechanics, we will spend about three weeks on a synopsis of the concepts of pre-quantum (classical) physics. We will review complex numbers and matrix algebra mainly to establish a common notation. We then begin to explore quantum kinematics and dynamics of a two-level system in the language of matrices, as well as in the abstract language of vector spaces. We extend the theory to a collection of two-level systems and discuss *entanglement*, the devil at the heart of quantum conundrums. Discussions of the Uncertainty Principle, the Einstein-Podolsky-Rosen challenge, Schrodinger’s Cat, Bell’s theorem, the no-cloning theorem and quantum teleportation follow. The work in the course consists of regular problem sets, two midterm tests, and a final short project presentation and report. No college physics is presupposed. Two meetings per week.

Requisites: MATH 211 and MATH 271/272. Omitted 2020-21.

This course begins with the foundation of classical mechanics as formulated in Newton’s Laws of Motion. We then use Hamilton’s Principle of Least Action to arrive at an alternative formulation of mechanics in which the equations of motion are derived from energies rather than forces. This Lagrangian formulation has many virtues, among them a deeper insight into the connection between symmetries and conservation laws. From the Lagrangian formulation we will move to the Hamiltonian formulation and the discussion of dynamics in phase space, exploring various avenues for the transition from the classical to the quantum theory. We will study motion in a central force field, the derivation of Kepler’s laws of planetary motion from Newton’s law of gravity, two-body collisions, and physics in non-inertial reference frames. Other topics may include the dynamics of driven, damped oscillators, and non-linear dynamics of chaotic systems. Three class hours per week.

Requisite: PHYS 116/123 PHYS 125, MATH 211 or consent of the instructor. Omitted 2019-20. The Department.

A development of Maxwell’s electromagnetic field equations and some of their consequences using vector calculus. Topics covered include: electrostatics, steady currents and static magnetic fields, time-dependent electric and magnetic fields, and the complete Maxwell theory, energy in the electromagnetic field, Poynting’s theorem, electromagnetic waves, and radiation from time-dependent charge and current distributions. Three class hours per week.

This course is designed to involve in-person lectures and discussions, with problem sets and other activities; but provisions will be available for remote and asynchronous learning, including recorded class meetings, online activities, and synchronous office hours at times TBA.

Requisite: PHYS 117/124, PHYS 125, MATH 211 or consent of the instructor. Fall semester. Professor Hall.

Wave-particle duality and the Heisenberg uncertainty principle. Basic postulates of Quantum Mechanics, wave functions, solutions of the Schroedinger equation for one-dimensional systems and for the hydrogen atom. Three class hours per week.

This course is designed to involve in-person lectures and discussions, with problem sets; but provisions will be available for remote and asynchronous learning, including recorded class meetings, online activities, and synchronous office hours at times TBA.

Requisite: MATH 211 and PHYS 225 or consent of the instructor. Spring semester. The Department.

Quantum Mechanics is well known for its counterintuitive and seemingly paradoxical predictions. Despite its failure to give us a clear, intuitive picture of the world, the theory is remarkably successful at predicting the outcomes of experiments, although those predictions are probabilistic rather than deterministic. Because of its unparalleled success, the thorny issues about the theory’s foundations were often ignored during its first fifty years. Recent advances in both theory and experiment have again brought these issues to the fore. This course will review some of the most interesting and intriguing facets of quantum mechanics and its potential applications to information and computing. Topics to be covered will include the Schrödinger cat paradox and the quantum measurement problem; Bell’s inequalities, entanglement, and related phenomena that establish the “weirdness” of quantum mechanics; secure communication using quantum cryptography; and how quantum computers (if built) can solve certain problems much more efficiently than classical ones. We will also explore recent experiments in which quantum phenomena appear on the macroscopic scale, as well as technological progress towards building a large-scale, general-purpose quantum computer.

The early part of the semester will consist of synchronous and asynchronous lectures with multiple "clicker" questions. The later part of the course will be taught seminar style with in-depth reading and discussion of research articles.

Requisite: Physics 225. Fall semester. Professor Friedman.

(Offered as PHYS 400, BIOL 400, BCBP 400, and CHEM 400) How do the physical laws that dominate our lives change at the small length and energy scales of individual molecules? What design principles break down at the sub-cellular level and what new chemistry and physics becomes important? We will answer these questions by looking at bio-molecules, cellular substructures, and control mechanisms that work effectively in the microscopic world. How can we understand both the static and dynamic shape of proteins using the laws of thermodynamics and kinetics? How has the basic understanding of the smallest molecular motor in the world, ATP synthase, changed our understanding of friction and torque? We will explore new technologies, such as atomic force and single molecule microscopy that have allowed research into these areas. This course will address topics in each of the three major divisions of Biophysics: bio-molecular structure, biophysical techniques, and biological mechanisms.

For Spring 2021: This course will be a hybrid model using both asynchronous and synchronous group work. The course will meet in-person as health and safety considerations permit.

Requisite: CHEM 161/165, PHYS 116/123, PHYS 117/124, BIOL 191 or evidence of equivalent coverage in pre-collegiate courses. Spring semester. Professors Jaswal and Loinaz.

The course is an elementary introduction to Einstein's theory of gravity and modern cosmology. After a brief review of the special theory of relativity, we will investigate vector and tensor fields in terms of their properties under changes of coordinates. We will study geometric ideas such as geodesics, parallel transport, and covariant differentiation, and present the Principle of Equivalence as the central physical principle behind Einstein's theory of gravity. After introducing the stress tensor, we will state the field equations and obtain the simplest solutions to them, and derive the physical implications of the theory for the motion of planets and light in the vicinity of massive stars. We will then discuss modern cosmology, including an introduction to the particle physics needed to describe the thermal history of the universe just after the Big Bang.

Requisite: PHYS 225 and MATH 211; or consent of the instructor. Fall Semester: William Loinaz

*For Spring 2021: This course will be taught in a hybrid format using both asynchronous and synchronous lectures and group work. The course will meet in-person as health and safety considerations permit. *

Independent reading course.

Fall and spring semester.

Same description as PHYS 498.

Requisite: PHYS 498. Spring semester. The Department.