(for 2012–2013 academic year)
Professors Aveni, Balonek, Galvez
Associate Professors Parks (
Chair), Segall
Assistant Professors Bary, Crotty, J. Levine, Metzler
Visiting Assistant Professor Herne
Postdoctoral Fellow Svitelskiy
A student should major in the Department of Physics and Astronomy if he or she is interested in fundamental questions about the nature of matter and the nature of the universe, or in practical questions of engineering, applied physics, or space science.
To be successful, a student should also enjoy mathematics and quantitative reasoning. More than half of the graduating seniors in this department go to graduate school in various disciplines, and many earn PhDs in physics, astronomy, and engineering. Approximately 25 percent enter technical careers directly after graduation. The rest pursue careers in teaching, business (often technology-based), management, and even medicine.
The department offers several courses of general interest, not intended for majors. These courses are ASTR 101, Solar System Astronomy;
ASTR 102, Stars, Galaxies, and the Universe; ASTR 230, Astronomy in Culture; PHYS 105, Mechanical Physics; and
PHYS 111, 112, Fundamental Physics.
The major program begins with
PHYS 131, 232, and
233, a three-term, calculus-based introductory physics course with laboratory. Entering first-year students should take
PHYS 131 in the fall term. After these three courses students enroll in
PHYS 334,
Introduction to Quantum Mechanics and Special Relativity, and
PHYS 336, Electronics, which are normally taken concurrently in the spring of the sophomore year. The four fractional-credit courses,
PHYS 201–204, Mathematical Methods for Physics, are also required and are normally taken concurrently with
PHYS 233 and
PHYS 334. In the junior and senior years, four additional upper-level courses (300 or 400 level, excluding
PHYS 334, PHYS 336, and
ASTR 312) are completed, one of which is
PHYS 410, Advanced Topics and Experiments, a required research project, completed in the fall semester of the senior year.
In addition to these physics courses,
MATH 111, 112, and
113 must be taken as soon as possible. These are the minimum requirements for a major in physics. Students who wish to prepare for graduate studies in physics or astronomy should complete
PHYS 431, 432, 433, and
434. To enrich the program, a student should choose additional physics and astronomy electives at the 300 and 400 levels. Advanced courses in other science departments, especially mathematics, are also encouraged. Students should also become familiar with one high-level computer language.
A student interested in astronomy or astrophysics should enroll in this program. It requires
MATH 111, 112, and
113; PHYS 131, 232, 233, and
334; the fractional-credit courses
PHYS 201-204, Mathematical Methods for Physics; as well as
ASTR 210, Intermediate Astronomy and Astrophysics; ASTR 312, Astronomical Techniques; one of the following:
ASTR 414, Astrophysics; ASTR 416, Galactic and Extragalactic Astronomy; or
ASTR 313, Planetary Science; two additional astronomy or physics courses at the 300 or 400 level (excluding
PHYS 334, PHYS 336, and
ASTR 312); and
PHYS 410,
Advanced Topics and Experiments. A student interested in planetary astronomy should also consider the astrogeophysics program, listed earlier in this chapter.
To be eligible to graduate with a major in any of the programs of this department, a student is expected to achieve a grade of C– or better in each of the courses required for the major. There are no exceptions to this policy. Additionally, a student’s cumulative GPA for all courses counted toward the major must be at least 2.00.
The minor in physics requires
PHYS 131, 232, 233, and two additional physics courses (note that
PHYS 201-204 count as one course credit), at least one of which must be at the 300 or 400 level. The minor in astronomy requires two of the following:
ASTR 101, 102, 230; two additional astronomy courses that count towards the astronomy-physics major; and two physics courses that count towards the physics major. For both the minors, a grade of C– or better in all courses that count toward the minor is required.
To qualify for graduation with honors, physic and astronomy-physics students must complete and defend an honors thesis in the spring of the senior year. Normally, the honors thesis is an extension of the work completed in the capstone course
PHYS 410 in which the results are written more formally and placed more carefully in the context of existing research. At the discretion of the adviser, an alternate form of the thesis is a manuscript submitted for publication in a journal. The option of an honors thesis is by invitation only; qualified students who perform exceptionally well in
PHYS 410 are invited by the department chair, in consultation with department members, to try for honors. The thesis and defense are evaluated by department members and an external examiner to determine whether either honors or high honors will be awarded. In addition to the honors thesis, students must enroll in two additional upper-level physics or astronomy courses (300 or 400 level) beyond those needed to satisfy the basic major requirements. One of these courses may be an independent study course in which the
PHYS 410 research project is extended and advanced. A GPA of at least 3.30 must be achieved in all upper-level courses required for honors.
See “Honors and Awards: Physics and Astronomy” in Chapter VI.
The department offers two ways to prepare for engineering: major in physics at Colgate and after graduation go to graduate school in engineering, or use one of the combined plans available in the department. To allow a student to combine education in the liberal arts with engineering training, Colgate has cooperative agreements with Columbia University, Rensselaer Polytechnic Institute, and Washington University. A student may spend three years at Colgate and two at the engineering school (the 3-2 plan) to earn bachelor’s degrees from both institutions. The student may be eligible to continue study for a master of science (MS) degree, which can sometimes be completed in as little as one additional year after earning the bachelor’s degree in engineering. Eligibility for the MS program is determined by the engineering school.
It is imperative for students interested in the 3-2 plan to begin the physics and math curriculum in the fall term of the first year. To be eligible for the 3-2 plan, a student must complete all physics major courses through
PHYS 336 and
PHYS 431 (or
451), plus one other upper-level physics course to be chosen in consultation with the pre-engineering adviser.
Prerequisites for admission to engineering schools vary among schools and fields of study; therefore, it is necessary to indicate an interest in pre-engineering to the physics faculty as soon as possible.
Students intending to pursue graduate studies in physics, astronomy, or engineering should discuss their plans with their major advisers as early as possible, and should also consult the notes under the heading Major Program in Physics.
The Department of Educational Studies offers a teacher education program for majors in physics who are interested in pursuing a career in elementary or secondary school teaching. Please refer to “Educational Studies.”
Credit for
PHYS 111 will be granted to students who score 4 or 5 on the AP Physics B exam or the AP Physics C-Mechanics exam. Credit for
PHYS 112 will be granted to students who score 4 or 5 on the AP Physics C-E&M exam. Placement into
PHYS 232 without completion of
PHYS 131 can sometimes be allowed following discussion with the department chair and the
PHYS 232 instructor. Department majors who do not complete
PHYS 131 will be required to complete an additional upper-level course to meet the major requirements. Placement out of
PHYS 232 or
233 based on high school courses (including AP) is not normally possible.
Transfer of credit for physics and astronomy courses from other colleges or universities requires approval by the department chair. In particular, summer courses taken with the expectation of transfer credit must be pre-approved by the department chair well in advance of enrollment.
The department administers the physical science and astrogeophysics majors and serves as a home department for students in these programs. The department also contributes a course to an interdisciplinary program in prehistoric studies:
ASTR/SOAN 230.
PHYS courses count toward the Natural Sciences and Mathematics area of inquiry/distribution requirement, unless otherwise noted.
All credit-bearing laboratories carry 0.25 course credits unless noted otherwise. Please see the “Academic Credit” section in Chapter VI for additional information and restrictions.
105/105L Mechanical Physics I E. Galvez
This course covers fundamental principles of Newtonian mechanics and their applications in science, engineering, and in particular, architecture. Selected topics including waves, fluids, optics, electricity and magnetism, and thermal physics are aimed toward applications in the geosciences. This course is not suitable for students majoring in departments or programs requiring two or more semesters of physics. The required credit-bearing laboratory
PHYS 105L must be taken concurrently with
PHYS 105. Offered in the fall only.
111/111L Fundamental Physics I R. Metzler, Staff
This introductory course emphasizes concepts and principles of mechanics, heat, waves, and sound. The focus is on building concepts, grasping principles, and learning how consequences of principles and concepts can be quantitatively calculated and measured. The required credit-bearing laboratory
PHYS 111L must be taken concurrently with
PHYS 111. Offered in the fall only.
112/112L Fundamental Physics II K. Segall, Staff
This course develops concepts and principles of electricity, magnetism, light, and modern physics. The required credit-bearing laboratory
PHYS 112L must be taken concurrently with
PHYS 112. Prerequisite:
PHYS 111. Offered in the spring only.
131/131L Atoms and Waves M.E. Parks, Staff
An introduction to modern physics via the concepts and discoveries of the 20th century. Topics include the structure and dynamics of atoms, special relativity, wave-particle duality of matter, and fundamentals of quantum mechanics. This course is required for students planning to major in physics, physics-astronomy, or physical sciences and for students interested in pre-engineering.
PHYS 131 treats contemporary physics using algebra, trigonometry, and a minimum of calculus. Two lectures, two problem-solving recitations, and one laboratory meeting per week. The required credit-bearing laboratory
PHYS 131L must be taken concurrently with
PHYS 131. (Formerly
PHYS 120/120L, General Physics I.) Prerequisites: secondary school physics and math, and for continuing students, co-registration with
MATH 111. Offered in the fall only.
201–204 Mathematical Methods for Physics P. Crotty, C. Herne, O. Svitelskiy, Staff
This sequence of four 0.25-credit courses provides the mathematical foundation required for sophomore- through senior-level physics courses.
PHYS 201 is an introduction to computational physics and linear algebra.
PHYS 202 introduces complex numbers and complex exponentials as solutions to differential equations.
PHYS 203 teaches Fourier sums and integrals.
PHYS 204 teaches the gradient, divergence, and curl in several coordinate systems, and also introduces series solutions to differential equations.
PHYS 201–204 are intended to be studied in sequential order. Prerequisites:
PHYS 232 (formerly
PHYS 121) and completion of or co-registration in
MATH 113, or permission of instructor.
232/232L Introduction to Mechanics J. Bary, Staff
A study of classical mechanics using astronomical themes. The principles of kinematics, dynamics, conservation laws, and gravitation are developed and used to understand the properties of astronomical objects such as planetary systems, binary stars, and galaxies. Treatment is more thorough than in PHYS 111. Differential calculus and vector manipulation are used throughout. The course is required for students planning to major in physics, astronomy-physics, or physical sciences and for students interested in pre-engineering, and is also recommended for chemistry majors. Two lectures, two recitation meetings, and one laboratory session per week. The required credit-bearing laboratory PHYS 232L must be taken concurrently with
PHYS 232. (Formerly
PHYS 121/121L, General Physics II.) Prerequisites:
PHYS 131 (formerly
PHYS 120) or
CHEM 111, and
MATH 111, or permission of instructor. Students who plan to continue into
PHYS 233 should co-enroll in
MATH 112. Offered in the spring only.
233/233L Introduction to Electricity and Magnetism J. Levine
The classical theory of electricity and magnetism is assembled from observations of nature and physical inference, using differential and integral calculus. Emphasis is on the fundamental roles played by the electric and magnetic fields, their geometrical properties, and their dynamics. Principles of elementary circuits are also included. This course is required for students planning to major in the physical sciences and pre-engineering. Four lectures and one laboratory meeting per week. The required credit-bearing laboratory
PHYS 233L must be taken concurrently with
PHYS 233. (Formerly
PHYS 122/122L, General Physics III.) Prerequisites:
PHYS 232 (formerly
PHYS 121) and
MATH 112. Students planning to take physics courses beyond
PHYS 233 (formerly
PHYS 122) should co-register in
MATH 113 and
PHYS 201-204. Offered in the fall only.
304/304L Physical Optics C. Herne
A study of physical optics from the basics to advanced topics, such as optical instrumentation, Fourier optics, laser physics, and holography. The course prepares students for knowledgeable use of optical instruments in fields such as astronomy and teaches modern laser techniques for use in basic and applied research. Four lecture meetings and one laboratory meeting each week. The required credit-bearing laboratory
PHYS 304L must be taken concurrently with
PHYS 304. (Formerly
PHYS 404.) Prerequisites:
PHYS 201-204 and
PHYS 233 (formerly
PHYS 122). Offered in the spring only, in alternate years.
310, 410 Advanced Topics and Experiments Staff PHYS 310 is an optional junior-year research experience open to qualified students.
PHYS 410 is a required senior-year capstone research experience. Under the guidance of a faculty mentor, each student works on an experimental or theoretical project that ideally produces original results. A final thesis and a formal oral presentation are essential components of both courses. Enrollment in
PHYS 310 is by permission only. Both courses are offered in the fall only.
334 Introduction to Quantum Mechanics and Special Relativity P. Crotty, Staff
This course provides the mathematical and conceptual foundation to understand two important developments in modern physics: special relativity and quantum theory, concentrating on wave mechanics. (Formerly
PHYS 216.) Prerequisite:
PHYS 233 (formerly
PHYS 122). Pre- or corequisites:
PHYS 201–204. Offered in the spring only.
336/336L Electronics C. Herne, Staff
A comprehensive treatment of basic electronics. The course covers analog and digital electronics. The analog section includes DC and AC circuits, filters, diodes, transistors, and operational amplifiers. The digital section includes combinational and sequential logic, integrated circuits, and interfacing. Two class meetings per week. Each meeting is a lecture followed by a laboratory session. The required credit-bearing laboratory PHYS 336L must be taken concurrently with
PHYS 336. (Formerly
PHYS 282/282L.) Prerequisite:
PHYS 233 (formerly
PHYS 122) or permission of instructor. Offered in the spring only.
350 Biophysics R. Metzler
An introduction to biological physics including a survey of topics such as diffusion, Brownian motion, non-Newtonian fluids, self-assembly, cooperativity, bioenergetics, and nerve impulses, as well as experimental techniques and analytical approaches. Students first develop the interdisciplinary knowledge needed to address biophysical questions. The course then focuses on the reading, presentation, and critique of current biophysics research literature. Although challenging in its breadth, this course is intended to be accessible to juniors and seniors majoring in physics, chemistry, or biology. Prerequisites:
MATH 111, and
BIOL 212 or any physics course, or permission of instructor. Offered in the spring only, in alternate years. This course is crosslisted as
BIOL 350.
431 Classical Mechanics P. Crotty
A detailed study, using vector calculus, of important problems in the mechanics of particles and extended bodies including a derivation of Lagrange’s and Hamilton’s equations and other advanced topics. (Formerly
PHYS 302.) Prerequisite:
PHYS 334 (formerly
PHYS 216). Offered in the fall only, in alternate years.
432 Electromagnetism M.E. Parks
A study of Maxwell’s equations and their applications to topics in electrostatics and electrodynamics, including electromagnetic waves. (Formerly
PHYS 303.) Prerequisites:
PHYS 201-204. Offered in the spring only, in alternate years.
433 Thermodynamics and Statistical Mechanics K. Segall
An introduction to the physical concepts underlying the formalism of thermal physics. Emphasis is on the role and meaning of entropy in physical systems and processes. Topics include black body radiation, liquid helium, superconductivity, negative temperature, and the efficient use of energy. (Formerly
PHYS 372.) Prerequisite:
PHYS 334 (formerly
PHYS 216). Offered in the fall only, in alternate years.
434/434L Quantum Mechanics E. Galvez, Staff
A study of elementary quantum mechanics. This course briefly reviews the history and philosophy of quantum mechanics and develops solutions to one-dimensional problems such as the quantum harmonic oscillator. The course then presents the general mathematical formulation of the theory, generalized uncertainty relations, and the matrix formulation of quantum theory. Further applications to spherically symmetric systems such as the hydrogen atom are also developed. A series of associated laboratories (
PHYS 434L) gives students vivid examples of quantum mechanical principles. (Formerly
PHYS 371/371L.) Prerequisite:
PHYS 334 (formerly
PHYS 216). Offered in the spring only, in alternate years.
451/451L Computational Mechanics P. Crotty
This course investigates general algorithms and their implementation for the exploration of problems in classical and quantum mechanics. Applications range widely from solar system dynamics and chaotic systems to particles in general quantum potentials. Fourier analysis, including the fast Fourier transform, and its application to the understanding of physical systems and data analysis, are also studied. In addition to graded homework assignments and exams, each student undertakes a major numerical project of his or her choice. The required credit-bearing laboratory
PHYS 451L must be taken concurrently with
PHYS 451. (Formerly
PHYS 402.) Prerequisite:
PHYS 334 (formerly
PHYS 216). Offered in the fall only, in alternate years.
453 Solid State Physics Staff
Several important properties of matter in its solid form are examined. The ordered, crystalline nature of most solids is used as a starting point for understanding condensed material and as a basis for introducing the band theory of solids. The course investigates thermal, electrical, and magnetic properties of metals, semiconductors, and insulators. (Formerly
PHYS 420.) Prerequisite:
PHYS 334 (formerly
PHYS 216). Offered in the fall only, in alternate years.
456 Relativity and Cosmology P. Crotty
At the beginning of the 20th century, Einstein’s discovery of the Special and General Theories of Relativity revolutionized understanding of space and time. This course studies both theories; the emphasis is on General Relativity, including cosmology and the study of black holes. (Formerly
PHYS 422.) Prerequisite:
PHYS 334 (formerly
PHYS 216). Not offered every year.
458 Real-time Nonlinear Dynamics and Chaos
This course is crosslisted as
MATH 458 (formerly
MATH 407). For course description, see “Mathematics: Course Offerings.” (Formerly
PHYS 407.)
291, 391, 491 Independent Study Staff
These courses are especially suitable for qualified students who wish to undertake the study of advanced topics in physics and astronomy. Prerequisite: permission of department chair and prior arrangement with faculty sponsor.
ASTR courses count toward the Natural Sciences and Mathematics area of inquiry/distribution requirement, unless otherwise noted.
101 Solar System Astronomy T. Balonek
An introductory course dealing with the large-scale environment in the vicinity of Earth. Motions of solar system objects, properties of the solar system, its origin, and the possibility of intelligent life in the universe are discussed. Observing and Ho Tung Visualization Lab sessions supplement lectures. Offered in the fall only.
102 Stars, Galaxies, and the Universe J. Bary
An introductory course dealing with the motions and physical characteristics of the sun, stars, and galaxies, including such modern topics as solar effects upon the Earth, stellar explosions, and theories of the origin of the universe. Observing and Ho Tung Visualization Lab sessions supplement lectures. Offered in the spring only.
210 Intermediate Astronomy and Astrophysics J. Bary
A discussion of the fundamental physical principles of astronomy and astrophysics emphasizing topics of current interest such as stellar structure, evolution, neutron stars, black holes, and the interstellar medium. Prerequisites:
MATH 111, 112, and co-registration in
PHYS 233 (formerly
PHYS 122). Offered in the fall only, in alternate years.
230 Astronomy in Culture A. Aveni
This course deals with the development of astronomy and, in a more general sense, with the relationship between the natural world and people in different societies and walks of life. The course examines the role of the sky in shaping religions and political ideologies in various kinds of cultures, among them hunter-gatherers, agrarian societies, and dynasties. Specific goals of the course include 1) gaining familiarization with the sky as seen with the naked eye, 2) understanding how various ways of comprehending the sky shapes a society’s world view, and 3) examining where cross-cultural parallels exist by seeking out the similarities and differences between the development of techno-assisted Western science and the so-called “ethno-sciences” in other cultures, both ancient and contemporary. Lectures are accompanied by sessions in the planetarium of the Ho Tung Visualization Lab, as well as out of doors, weather permitting. (Formerly
ASTR 130.) This course is crosslisted as
SOAN 230.
312/312L Astronomical Techniques T. Balonek
A laboratory course introducing students to basic astronomical observations, and methods of data acquisition and reduction using the university’s 16-inch telescope, CCD electronic camera, and image-processing workstation. Students are instructed in methods of astronomical imaging including detector calibration and atmospheric effects; in fundamentals of photometric reductions, including obtaining a light curve for a selected variable star; and in astronomical spectroscopy and spectral classification.
ASTR 312L must be taken concurrently with
ASTR 312. (Formerly
ASTR 212/212L.) Prerequisite:
PHYS 232 (formerly
PHYS 121) or
MATH 112 or an astronomy course or permission of instructor. Offered in the fall only, in alternate years.
313 Planetary Science J. Levine
Study of the solar system with emphasis on physical processes. Topics include formation of the solar system, planets, moons, asteroids, comets, meteorites, orbital mechanics, tides, atmospheric structure, planetary surfaces and interiors, impact cratering, and rings. Although challenging in breadth, this course is intended to be accessible to juniors and seniors majoring in physics, astronomy-physics, astrogeophysics, chemistry, or geology. (Formerly
ASTR 320.) Prerequisites:
PHYS 232 (formerly
PHYS 121), or any two
GEOL courses and
MATH 111, or permission of instructor. Offered in the fall only, in alternate years.
414 Astrophysics J. Bary
A study of stellar atmospheres and interiors, this course develops a fundamental understanding of stars and their evolution from the application of several basic principles found in atomic physics, electricity and magnetism, Newtonian mechanics, and statistical mechanics. Topics include fusion processes, reaction rates, stellar structure, the formation of spectral lines, opacity and optical depth effects, and radiative processes in the interstellar medium. (Formerly
ASTR 314.) Prerequisite:
PHYS 334 (formerly
PHYS 216) or permission of instructor. Offered in the spring only, in alternate years.
416 Galactic and Extragalactic Astronomy T. Balonek
Study of the astronomical techniques, methods, and basic data relating to the Milky Way Galaxy and objects located outside our galaxy, such as normal galaxies, radio galaxies, and quasars. Topics include galactic stellar populations, large-scale structure and rotation of the galaxy, the structure and content of other galaxies, galaxy classification, clusters of galaxies, active galactic nuclei, quasars, and the large-scale structure of the universe. The physical processes responsible for the radio, infrared, visual, and x-ray radiation from these objects are studied in detail. (Formerly
ASTR 316.) Prerequisite:
PHYS 233 (formerly
PHYS 122). Offered in the spring only, in alternate years.