**Mission****History of Bard****Learning at Bard****Admission****Academic Calendar****Division of the Arts****Division of Languages and Literature****Division of Science, Mathematics, and Computing****Division of Social Studies****Interdivisional Programs and Concentrations****The Bard College Conservatory of Music****Bard Abroad****Additional Study Opportunities and Affiliated Institutes****Civic Engagement****Campus Life and Facilities****Graduate Programs****Educational Outreach****Levy Economics Institute of Bard College****The Bard Center****Finances****Scholarships, Awards, and Prizes****Faculty****Honorary Degrees and Bard College Awards****Boards and Administration of Bard College****Bard Campus Map and Travel Directions****Bard College Contact Information**

## Bard College Catalogue 2020-21

## Physics

### Faculty

Hal Haggard (director), Paul Cadden-Zimansky, John Cullinan*, Gidon Eshel*, Antonios Kontos, Christopher LaFratta*, Simeen Sattar*, Shuo Zhang

* *affiliated faculty*

### Overview

The Physics Program provides a firm foundation for work in a variety of areas, including graduate work in physics and allied fields. A student usually takes the core courses listed below, although in some cases the student and faculty may decide that not all the courses are appropriate because of advanced preparation or the particular focus of the student’s work. The student also chooses a number of electives according to personal interests. Students are expected to follow the standard divisional procedure for Moderation and to fulfill the college-wide distribution and First-Year Seminar requirements.

### Requirements

Prior to Moderation, a student has usually completed Physics 141 and 142, *Introduction to Physics I* and *II*; Mathematics 141 and 142, *Calculus I *and *II*; and Physics 241, *Modern Physics*. Majors are required to complete the courses listed above plus Physics 221 and 222, *Mathematical Methods of Physics I *and* II*; Physics 303, *Mechanics*; Physics 312, *Electricity and Magnetism*; Physics 314, *Thermal Physics*; Physics 321, *Quantum Mechanics*; and the Senior Project.

### Recent Senior Projects in Physics

- “The Invisible Sun: Building a Radio Interferometer Telescope”
- “Methane Sensing in the Field: An Attempt to Measure Methane over Large Areas via Arduino and Aerial Drones”
- “Optimizing Glide-Flight Paths”
- “A Study of Neural Networks for the Quantum Many-Body Problem”

### Courses

In addition to the core required courses, electives include courses or tutorials in laboratory (*Optics, Introduction to Electronics*) or theoretical (*General Relativity, Condensed Matter Physics*) subjects, and other advanced studies.*The following descriptions represent a sampling of courses from the past four years.***Acoustics***Physics 116*

An introduction to the phenomena of acoustics, particularly aspects that are important in the production and perception of music. The physics of sound is covered in depth, and characteristics of acoustic and electronic instruments are discussed. Mathematical and laboratory techniques are introduced as needed.**Global Energy***Physics 120*

CROSS-LISTED: ARCHITECTURE, EUS

A laboratory-based course designed to introduce nonscience majors to different types of energy (mechanical, thermal, electromagnetic, chemical, nuclear); the methods by which modern societies produce, transmit, and convert between these types; how different demand sectors (electricity, heating, transportation) shape our energy production infrastructure; the promises of future energy technology and the insurmountable physical constraints on them; and the environmental and economic costs associated with different types of energy production.**Climate Change***Physics 124*

CROSS-LISTED: EUS

This lab course explores the physical principles underlying climate and anthropogenic climate change. It surveys the most compelling lines of evidence for climate change and studies current observations in the broader context of past climates. Policy mitigation efforts and obstacles to their implementation are also discussed. While not technical per se, the course requires that students have the ability to solve linear algebraic equations and perform basic manipulation of data.**Time Examined: Its Physical Nature and Measurement***Physics 125*

CROSS-LISTED: EUS

St. Augustine famously proclaimed “What, then, is time? If no one asks of me, I know; if I wish to explain to him who asks, I know not.” Fifteen hundred years later, Einstein revolutionized physics by recognizing that time is malleable: he showed that simultaneity depends on how you are moving, and that clocks in motion or acted on by gravity measure time differently. This course examines the evolving understanding of the nature of time. *Prerequisite:* passing score on Part I of the Mathematics Diagnostic.**Introduction to Physics I ***Physics 141*

A calculus-based survey of physics. The first semester covers topics in mechanics, heat and thermodynamics, and wave motion. The course stresses ideas—the unifying principles and characteristic models of physics. Labs develop the critical ability to elicit understanding of the physical world. *Corequisite*: Mathematics 141.**Introduction to Physics II***Physics 142*

This is the second part of a calculus-based survey course, continuing with electricity and magnetism, light, and basic atomic and modern physics.**Astronomy***Physics 145*

Have you ever looked up at the night sky and wondered what you were seeing? Astronomy, one of the oldest of the natural sciences, studies planets, stars, galaxies, and the universe as a whole, from its earliest time to the present day. Topics discussed in this course include the solar system, history of astronomy, telescopes, the sun, galaxies, and cosmology. *Prerequisite:* passing score on Part I of the Mathematics Diagnostic.**Introduction to Electronics***Physics 210*

An introduction to the construction and understanding of the analog and digital electronics that factor into almost every piece of modern technology. Beginning with analog components such as voltage dividers, filters, rectifiers, and transistors, the class uses these building blocks to create and understand amplifiers, oscillators, and integrated circuits, before concluding the course with an exploration of logic circuits and computational architecture. Enrollment by permission of the instructor.**Mathematical Methods of Physics I***Physics 221*

This course presents methods of mathematics that are useful in the physical sciences. While some proofs and demonstrations are given, the emphasis is on the applications. Topics include: power series, probability and statistics, multivariable differentiation and integration, and curvilinear coordinate systems. *Prerequisites:* Mathematics 141 and 142, or the equivalent.**Mathematical Methods of Physics II***Physics 222*

This is the second part of a two-part introduction to mathematical topics and techniques that are commonly encountered in the physical sciences, including complex numbers and analytic functions, Fourier series and orthogonal functions, standard types of partial differential equations, and special functions. *Prerequisites:* Mathematics 141 and 142, or the equivalent.**Optics***Physics 230*

From observing the cosmos to single cells, understanding optics is what has allowed us to visualize the unseen world. This laboratory course provides an overview of the theoretical techniques and experimental tools used to analyze light and its properties. Through the manipulation of light using lenses, polarizers, and single-photon detectors, students learn the physics that underlies microscopes, spectrometers, lasers, modern telecommunication, and human vision. *Prerequisite:* Physics 142 or permission of the instructor.**Modern Physics***Physics 241*

An extension of introductory physics that concentrates on developments stemming from the theory of relativity, quantum mechanics, and statistical mechanics. While a major focus is on understanding classical and quantum waves, discussions also include particle physics, nuclear physics, optical and molecular physics, condensed matter physics, astronomy, and cosmology. *Prerequisites:* Physics 141 and 142; Mathematics 141 and 142.**Astrophysics***Physics 250*

An introduction to modern astrophysics, from the solar system to the basic ideas of cosmology. Starting from methods of measuring astronomical distances and the laws of planetary motion, the class studies the cosmos using classical mechanics, special relativity, and basic quantum mechanics. Topics may include the life cycle of stars, star classification, black holes, galaxies, dark matter, the search for alien life, the Big Bang theory, and dark energy. *Prerequisite:* Physics 241.**Mechanics ***Physics 303*

This course in particle kinematics and dynamics in one, two, and three dimensions covers conservation laws, coordinate transformations, and problem-solving techniques in differential equations, vector calculus, and linear algebra. Lagrangian and Hamiltonian formulations are also studied. *Prerequisites:* Physics 141 and 142; Mathematics 141 and 142.**Electricity and Magnetism ***Physics 312*

Topics covered include electrostatics, conductors, and dielectrics; Laplace’s equation and characteristic fields; magnetostatics, magnetodynamics, and the magnetic properties of matter; flow of charge and circuit theory; and Maxwell’s equations and the energy-momentum transfer of electromagnetic radiation. *Prerequisites:* Physics 141 and 142 and Mathematics 213.**Thermal Physics ***Physics 314*

This course studies the thermal behavior of physical systems, employing thermodynamics, kinetic theory, and statistical mechanics. Thermodynamical topics include equations of state, energy and entropy, and the first and second laws of thermodynamics. Both classical and quantum statistical mechanics are covered, including distribution functions, partition functions, and the quantum statistics of Fermi-Dirac and Bose-Einstein systems. Applications include atoms, molecules, gases, liquids, solids, and phase transitions. *Prerequisites:* Physics 141-142; Mathematics 141-142.**Quantum Mechanics ***Physics 321*

The course explores the Schroedinger equation and Hilbert space formalism of quantum mechanics and then examines simple quantum systems including objects in potential wells, the quantum harmonic oscillator, and hydrogen atom electronic states. Additional material includes qubits, quantized angular momentum, and wave packets.* Prerequisites: *Physics 241 and either Physics 221, Mathematics 213, or Mathematics 242.**General Relativity***Physics 327*

An introduction to Einstein’s theory of gravity. Beginning with a discussion of special relativity, this course teaches the mathematics of differential geometry in order to describe the formulation of gravity as the curvature of space and time. Experimental verifications of the theory, such as the variability of the rate of the flow of time with height and the bending of starlight, are also discussed. Applications covered may include calibration of the Global Positioning System (GPS), black holes, cosmology, and gravitational waves. *Prerequsite:* Physics 241, Physics 303, or Mathematics 241, or permission of the instructor.