## Course Catalogue:Physics

Historically, the discipline of physics is identified as the branch of science that seeks to discover, unify, and apply the most basic laws of nature. Our curriculum introduces students to its principal subfields—electromagnetism, mechanics, thermal physics, optics, and quantum mechanics—and provides the most extensive training in mathematical and analytical methods of any of the sciences. Since this is the foundation upon which all other sciences and engineering are based, the study of physics provides a strong background for students who plan careers in areas such as physics, astrophysics, astronomy, geophysics, oceanography, meteorology, engineering, operations research, teaching, medicine, and law. Because physics is interested in first causes, it has a strong connection to philosophy as well.

Increasingly in the modern era, physicists have turned their attention to areas in which their analytical and experimental skills are particularly demanded, exploring such things as nanotechnology, controlled nuclear fusion, the evolution of stars and galaxies, the origins of the universe, the properties of matter at ultra-low temperatures, the creation and characterization of new materials for laser and electronics technologies, biophysics and biomedical engineering, and even the world of finance.

PHYS 150 and 160 have a calculus co-requisite and are intended for students majoring in the natural sciences, or other students with a strong interest in science. Courses with numbers lower than 150 are particularly suitable for students not majoring in a physical science. Prerequisites for any course may be waived at the discretion of the instructor. Grades in courses comprising the major or the minor must average C or better.

**BINARY ENGINEERING PLAN**

Joint-degree engineering programs are offered with Columbia University and The Thayer School of Engineering at Dartmouth College. Through these programs, in which students spend three years at Hobart and William Smith Colleges and two years at an engineering school, a student will receive a B.A. or B.S. from Hobart or William Smith and a B.S. or B.E. in engineering from the engineering school. Majoring in physics at HWS provides the best preparation for further work in most engineering fields. See "Joint Degree Programs" elsewhere in the *Catalogue *for details.

**REQUIREMENTS FOR THE MAJOR (B.A.)***disciplinary, 12 courses*

PHYS 150, PHYS 160, PHYS 270, PHYS 285, PHYS 383, MATH 130 *Calculus I, *MATH 131 *Calculus II, *and five additional courses in physics at the 200-, 300-, or 400-level, including at least one capstone course (any course numbered 460 or higher), unless the student completes an approved capstone experience. A course at the 200- or above from another science division department may be substituted for a physics course with the approval of the department chair.

**REQUIREMENTS FOR THE MAJOR (B.S.)***disciplinary, 16 courses*

All of the requirements for the B.A. physics major, plus four additional courses in the sciences. Only those courses which count toward the major in the departments that offer them satisfy this requirement.

**REQUIREMENTS FOR THE MINOR***disciplinary, 6 courses*

PHYS 150, PHYS 160, PHYS 270, and three additional physics courses.

**COURSE DESCRIPTIONS****PHYS 110 Star Trek Physics **Can you really learn physics watching Star Trek? This course says "yes." Students consider such Star Trek staples as warp drive, cloaking devices, holodecks, and time travel, and learn what the principles of physics tell us about these possibilities - and what these possibilities would mean for the principles of physics. Anyone who has ever enjoyed a science fiction book or movie will find that using Star Trek offers an excellent context for learning about a variety of topics in physics, including black holes, antimatter, lasers, and other exotic phenomena. (*Typically offered alternate years*)

**PHYS 112 Introduction to Astronomy **This course offers a survey of the celestial universe, including planets, stars, galaxies, and assorted other celestial objects which are not yet well understood. The Big Bang cosmological model is thoroughly explored, as are the various observational techniques employed to collect astronomical data. (*Offered occasionally*)

**PHYS 113 Suns and Planets **This course is designed to help the student understand the nature and process of science by studying the subject of astronomy. Specifically, this course provides an introduction to the general physical and observational principles necessary to understand the celestial bodies. We will specifically discuss what is known about our Solar System, including the Sun, the rocky and gaseous planets and their moons, and the minor planets and asteroids. The course will culminate in an overview of the discovery and characterization of planets around other stars where we will begin to put our Solar System in the context of other recently discovered exo-solar systems. (*Offered alternate years*)

**PHYS 114 Stars, Galaxies & the Universe **This course provides an introduction to the general physical and observational principles necessary to understand stars, galaxies and the Universe as a whole. We will discuss light, optics and telescopes, properties of stars, black holes, galaxies, and cosmology. The course will culminate in a discussion of the formation of the Universe starting with the Big Bang. (*Offered alternate years*)

**PHYS 115 Astrobiology **Astrobiology is the scientific study of the origin and evolution of life in the Universe. It brings together perspectives from astronomy, planetary science, geoscience, paleontology, biology and chemistry to examine the origin of life on Earth and the possibility of life elsewhere in the Universe. This course is designed to help students understand the nature and process of science through the lens of astrobiology. We will explore questions such as: What is life? How did I arise on Earth? Where else in the Universe might life be found? How do we know about the early history of life on Earth? And how do we search for life elsewhere? We will evaluate current theories on how life began and evolved on Earth and how the presence of life changed the Earth. We will review current understanding on the range of habitable planets in our solar system and around other stars. And we will discuss what life might look like on these other planets and what techniques we could use to detect it. This course is designed to fulfill a student's goal of experiencing scientific inquiry and understanding the nature of scientific knowledge. It does not count toward the major in Geoscience or Physics. (Arens, Hebb, Kendrick, *offered annually*)

**PHYS 120 Physics of Dance **The course is an exploration of the connection between the art of dance and the science of motion with both lecture/discussion sessions and movement laboratories. Topics include: velocity, acceleration, mass, force, energy, momentum, torque, equilibrium, rotation and angular momentum. "Dance it-Measure it" is the movement laboratory which combines personal experience of movement with scientific measurements and analysis. This is a science lab, not a dance technique course. (*Offered occasionally*)

**PHYS 135 Light: from Atoms and the Universe to Holograms and Telescopes** What are holograms? How do know the universe is expanding? How do we know the structure of DNA? What is the reason telescopes work? Why did Einstein conclude that space and time were relative? How do we know that distant stars are made of the same material we are made of? All these questions and more have answers that emerge from an understanding of light. In this course, you will learn the fundamental principles governing the behavior of light, and how we can use scientific reasoning to learn the answers to these and other questions. No previous knowledge of physics is required, but a familiarity with basic high school algebra is expected. Prerequisite: Students should be comfortable with high school level algebra and trigonometry. (Spector, *offered occasionally*)

**PHYS 140 Principles of Physics **This is a one-semester survey course in physics with laboratory, which makes use of algebra and trigonometry, but not calculus. It is designed particularly for architectural studies students, for whom it is a required course. It also provides a serious, problem-solving introduction to physics for students not wishing to learn calculus. The following topics are included: mechanics (particularly statics, stress, and strain), sound, and heat. This course satisfies the physics prerequisite for PHYS 160. (*Offered annually*)

**PHYS 150 Introduction to Physics I **This is a calculus-based first course in mechanics and waves with laboratory. Prerequisite: MATH 130 Calculus I (may be taken concurrently). (*Offered annually*)

**PHYS 160 Introduction to Physics II **This course offers a calculus-based first course in electromagnetism and optics with laboratory. Prerequisites: PHYS 150 and MATH 131 Calculus II (may be taken concurrently). (*Offered annually*)

**PHYS 210 Introduction to Astrophysics **This first course in Astrophysics will add the foundational rigors of physics to the observations of astronomy to generate a more thorough understanding of our universe. Topics for the course include Stellar dynamics and evolution (star formation, fusion and nucleosynthesis, hydrostatic equilibrium, post-main- sequence evolution, supernovae, white dwarfs, compact objects), Galactic formation and evolution, active galaxies, galactic clusters, dark matter, Big Bang and Universe evolution, and dark energy. (*Offered occasionally*)

**PHYS 225 Observational Astronomy **This course provides a "hands-on" introduction to observational astronomy. Students will learn how the sky moves and the celestial coordinate systems necessary to plan and implement astronomical observations. They will become proficient using the new 17" telescope at the Perkin Observatory to observe celestial objects including the Moon, the planets, starts, star clusters, nebulae, and galaxies. Students will obtain digital images of the astronomical objects and learn basic techniques of digital image processing. Students will use their own date form astronomical database to draw scientific conclusions about stars and planets. Prerequisite: PHYS 113 or PHYS 114 or PHYS 115 and CPSC 124 or permission of the instructor. (*Offered annually*)

**PHYS 240 Electronics **This course offers a brief introduction to AC circuit theory, followed by consideration of diode and transistor characteristics, simple amplifier and oscillator circuits, operational amplifiers, and IC digital electronics. With laboratory. Prerequisite: PHYS 160. (*Offered annually)*

**PHYS 252 Green Energy **The climate change crisis has spurred the need for and interest in sustainable energy technologies. In this course we will study the major green energy technologies: efficiency, wind, solar (photovoltaic and thermal), geothermal, current/wave energy, smart grids and decentralized production. The class will study each technology from the basic principles through current research. In parallel, students will work together on a green energy project. Project ideas include: developing a green energy production project on campus, or a campus/Geneva self-sufficiency study. (*Offered occasionally*)

**PHYS 260 Waves and Optics **Simple harmonic motion, coupled oscillators, and mechanical waves. Fourier decomposition of oscillatory motion. Electromagnetic waves and phenomena of scattering, reflection, interference, and diffraction. Modern optical techniques such as waveguides, interferometers, and stable cavities. Prerequisite: PHYS 160. (*Offered annually*)

**PHYS 270 Modern Physics **This course provides a comprehensive introduction to 20th-century physics. Topics are drawn from the following: special relativity; early quantum views of matter and light; the Schrdinger wave equation and its applications; atomic physics; masers and lasers; radioactivity and nuclear physics; the band theory of solids; and elementary particles. With laboratory. Prerequisites: PHYS 160 and MATH 131 Calculus II. (*Offered annually*)

**PHYS 285 Math Methods **This course covers a number of mathematical topics that are widely used by students of science and engineering. It is intended particularly to prepare physics majors for the mathematical demands of 300-level physics courses. Math and chemistry majors also find this course quite helpful. Techniques that are useful in physical science problems are stressed. Topics are generally drawn from: power series, complex variables, matrices and eigenvalues, multiple integrals, Fourier series, Laplace transforms, differential equations and boundary value problems, and vector calculus. Prerequisite: MATH 131 Calculus II. (*Offered annually*)

**PHYS 287 Computational Methods **This course explores topics in computational methodologies and programming within physics. Computers are a ubiquitous tool in physics data acquisition and analysis. Each semester we will explore a set of topics within this field. Topics may include the statistics of data analysis, techniques of linear and nonlinear fitting, frequency analysis, time-frequency analysis, signal and image processing. Technologies may include data acquisition systems, data analysis environments, and common scientific programming languages. Prerequisite: PHYS 285. (*Offered annually*)

**PHYS 340 Introduction to Astrophysics** This first course in Astrophysics will add the foundational rigors of physics to the observations of astronomy to generate a more thorough understanding of our universe. Topics for the course include Stellar dynamics and evolution (star formation, fusion and nucleosynthesis, hydrostatic equilibrium, post-main-sequence evolution, supernovae, white dwarfs, compact objects), Galactic formation and evolution, active galaxies, galactic clusters, dark matter, Big Bang and Universe evolution, and dark energy. (*Offered occasionally*)

**PHYS 351 Mechanics **Starting from the Newtonian viewpoint, this course develops mechanics in the Lagrangian and Hamiltonian formulations. Topics include Newton's laws, energy and momentum, potential functions, oscillations, central forces, dynamics of systems and conservation laws, rigid bodies, rotating coordinate systems, Lagrange's equations, and Hamiltonian mechanics. Advanced topics may include chaotic systems, collision theory, relativistic mechanics, phase space orbits, Liouville's theorem, and dynamics of elastic and dissipative materials. Prerequisites: PHYS 160 and MATH 131 Calculus II. (*Offered alternate years*)

**PHYS 352 Quantum Mechanics **This course develops quantum mechanics, primarily in the Schrdinger picture. Topics include the solutions of the Schrdinger equation for simple potentials, measurement theory and operator methods, angular momentum, quantum statistics, perturbation theory and other approximate methods. Applications to such systems as atoms, molecules, nuclei, and solids are considered. Prerequisite: PHYS 270. (*Offered alternate years*)

**PHYS 361 Electricity and Magnetism **This course develops the vector calculus treatment of electric and magnetic fields both in free space and in dielectric and magnetic materials. Topics include vector calculus, electrostatics, Laplace's equation, dielectrics, magnetostatics, scalar and vector potentials, electrodynamics, and Maxwell's equations. The course culminates in a treatment of electromagnetic waves. Advanced topics may include conservation laws in electrodynamics, electromagnetic waves in matter, absorption and dispersion, wave guides, relativistic electrodynamics, and Linard-Wiechert potentials. Prerequisites: PHYS 160 and MATH 131 Calculus II. (*Offered alternate years*)

**PHYS 375 Thermal Physics **This course reviews the laws of thermodynamics, their basis in statistical mechanics, and their application to systems of physical interest. Typical applications include magnetism, ideal gases, blackbody radiation, Bose-Einstein condensation, chemical and nuclear reactions, neutron stars, black holes, and phase transitions. Prerequisites: PHYS 160 and MATH 131 Calculus II. (*Offered alternate years*)

**PHYS 383 Advanced Laboratory **Advanced Laboratory is the capstone laboratory experience in which students perform a wide variety of experiments that cover the major concepts in Modern Physics and Quantum Mechanics, including wave-particle duality, NMR, particle decay, time dilation, particle scattering and absorption, and laser dynamics and spectroscopy. (*Offered annually*)

**PHYS 450 Independent Study**

**PHYS 456 1/2 Credit Independent Study**

**PHYS 460 Independent Capstone Project** Students complete a major independent project leading to a substantial written product. This project would either be original scientific research or mastery of a higher level topic in physics. In either case, the project will rely on integrating the student's knowledge from the other courses they have taken as part of the physics major.

**PHYS 465 Classical and Quantum Information and Computing **This course covers the intersection of physics with the study of information. There are two broad areas to this subject. One is the area of overlap with classical physics and the appearance of entropy in the study of computation. The other is the area of overlap with quantum physics, reflected in the explosive growth of the potentially revolutionary area of quantum computing. Topics will be drawn from Shannon's theory of information; reversible and irreversible classical computation; the no-cloning theorem; EPR states and entanglement; Shor's algorithm and other quantum algorithms; quantum error correction; quantum encryption; theoretical aspects of quantum computing; and physical models for quantum computing. Prerequisites: Two 300-level courses in Physics or Mathematics. *(Offered alternate years)*

**PHYS 470 Relativity, Spacetime, and Gravity **This course covers the ideas and some of the consequences of Einstein's special and general theories of relativity. Topics include postulates of special relativity, paradoxes in special relativity, geometry of Minkowski space, geometry of curved spacetime, geodesics, and exact solutions of the field equations, tests of general relativity, gravitational waves, black holes, and cosmology. Prerequisites: PHYS 270 and PHYS 285 and one 300-level course in Physics, *(Offered alternate years).*

**PHYS 480 Symmetry **This course provides an advanced treatment of symmetry considerations in theoretical physics. The guiding principle is that symmetries have emerged as the central consideration in theoretical physics in the modern theory. Applications will general include classical field theory, Noether's Theorem, supersymmetric quantum mechanics, gauge invariance, the Korteweg-de Vries equation, and the renormalization group. This course fulfills the capstone requirement in Physics. Prerequisites: PHYS 270 and two 300 level physics courses or permission of the instructor. (*Offered alternate years*)

**PHYS 495 Honors**