Physics and Astronomy; Pre-Engineering
(For 2016–2017 academic year)
Professors Aveni, Balonek, Galvez
Associate Professors Bary, Crotty, J. Levine, Parks, Segall (Chair)
Assistant Professors Metzler, Tseng
Visiting Assistant Professor Jones
A student should select a 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 others pursue careers in teaching, business (often technology-based), management, medicine, and other areas.
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.
Major Program in 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. PHYS 205, Mathematical Methods for Physics, is also required and is normally taken concurrently with PHYS 233. 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.
Major Program in Astronomy-Physics 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; PHYS 205, 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.
Minor Programs in Physics or Astronomy
The minor in physics requires PHYS 131, 232, 233, and two additional physics courses, 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, physics 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 3.33 must be achieved in all upper-level courses required for honors.
See “Honors and Awards: Physics and Astronomy” in Chapter VI.
Credit for PHYS 111 will be granted to students who score 4 or 5 on the AP Physics 1 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 2 exam or 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. In particular, summer courses taken with the expectation of transfer credit must be pre-approved by the department well in advance of enrollment.
International Exam Transfer Credit
Transfer credit and/or placement appropriate to academic development of a student may be granted to incoming first year students who have achieved a score on an international exam (e.g., A-Levels, International Baccalaureate) that indicates a level of competence equivalent to the completion of a specific course in the department. Requests should be directed to the department chair. Any such credit may not be used to fulfill the university areas of inquiry requirement, but may count towards the major.
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 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.
Preparation for Graduate School
Students intending to pursue graduate studies in physics, astronomy, or engineering should discuss their plans with their major advisers as early as possible. 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.
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.”
The department administers the physical science and astrogeophysics majors and serves as a home department for students in these programs.
Course Offerings: Physics
PHYS courses count toward the Natural Sciences and Mathematics area of inquiry 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
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, but not necessarily offered every year.
111/111L Fundamental Physics I
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. Students are not eligible to take PHYS 111 after having completed PHYS 431. The required credit-bearing laboratory PHYS 111L must be taken concurrently with PHYS 111. Offered in the fall only.
112/112L Fundamental Physics II
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
E. Galvez, 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. Prerequisites: secondary school physics and math, and for continuing students, co-registration with MATH 111. Offered in the fall only. (Formerly PHYS 120/120L, General Physics I.)
205 Mathematical Methods of Physics
A one-semester introduction to the mathematical methods of physics, with an emphasis on applications and how these methods are used to approach various problems. The course will cover topics such as ordinary differential equations, complex numbers and Euler’s equation, linear systems, Fourier series, Fourier transforms, computational techniques, series expansions, cylindrical and spherical coordinate systems, vector differentiation, divergence and curl, integration methods and multi-dimensional integrals. These topics will be brought to bear on physical problems such as the damped and driven oscillator, coupled oscillators, electric dipoles, beat frequencies, electromagnetic waves and electrostatic boundary-value problems. As of the fall 2016 term, this course replaces the four course sequence PHYS 201-204. Offered in the fall only.
232/232L Introduction to Mechanics
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 and integral 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. 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. (Formerly PHYS 121/121L, General Physics II.)
233/233L Introduction to Electricity and Magnetism
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. Students are not eligible to take this course after having completed PHYS 431. The required credit-bearing laboratory PHYS 233L must be taken concurrently with PHYS 233. 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. (Formerly PHYS 122/122L, General Physics III.)
304/304L Physical Optics
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. Prerequisites: PHYS 201–204 and PHYS 233 (formerly PHYS 122). Offered in the spring only, in alternate years. (Formerly PHYS 404.)
310, 410 Advanced Topics and Experiments
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
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. Prerequisite: PHYS 233 (formerly PHYS 122). Pre- or corequisites: PHYS 201–204. Offered in the spring only. (Formerly PHYS 216.)
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. Prerequisite: PHYS 233 (formerly PHYS 122) or permission of instructor. Offered in the spring only. (Formerly PHYS 282/282L.)
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 182 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
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. Prerequisite: PHYS 334 (formerly PHYS 216). Offered in the fall only, in alternate years. (Formerly PHYS 302.)
A study of Maxwell’s equations and their applications to topics in electrostatics and electrodynamics, including electromagnetic waves. Prerequisites: PHYS 201–204. Offered in the spring only, in alternate years. (Formerly PHYS 303.)
433 Thermodynamics and Statistical Mechanics
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. Prerequisite: PHYS 334 (formerly PHYS 216). Offered in the fall only, in alternate years. (Formerly PHYS 372.)
434/434L Quantum Mechanics
An introduction to the theory and formalism of quantum mechanics. This course addresses the philosophical and mathematical foundations of the theory. It develops the linear algebraic formulation using spins, photon and atoms; and cover topics that include time evolution, angular momentum, the harmonic oscillator, the Schrodinger equation, entanglement, and quantum information. A series of associated laboratories (PHYS 434L) gives students vivid examples of quantum mechanical principles. Prerequisite: PHYS 334 (formerly PHYS 216). Offered in the spring only, in alternate years. (Formerly PHYS 371/371L.)
451/451L Computational Mechanics
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. Prerequisite: PHYS 334 (formerly PHYS 216). Offered in the fall only, in alternate years. (Formerly PHYS 402.)
453 Solid State Physics
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. Prerequisite: PHYS 334 (formerly PHYS 216). Offered in the fall only, in alternate years. (Formerly PHYS 420.)
456 Relativity and Cosmology
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. Prerequisite: PHYS 334 (formerly PHYS 216). Not offered every year. (Formerly PHYS 422.)
458 Real-time Nonlinear Dynamics and Chaos
This course is crosslisted as MATH 458. For course description, see “Mathematics: Course Offerings.” (Formerly PHYS 407.)
291, 391, 491 Independent Study
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.
Course Offerings: Astronomy
ASTR courses count toward the Natural Sciences and Mathematics area of inquiry requirement, unless otherwise noted.
101 Solar System Astronomy
T. Balonek, J. Bary
An introductory course dealing with the exploration of the solar system through ground-based observations and spacecraft missions. Topics include motions of solar system objects, properties of the solar system, origin and evolution of the solar system, uncovering the nature of objects in our solar system through comparative planetology, detection techniques and characteristics of planets orbiting other stars, and the possibility of life elsewhere in the universe. Evening observing and Ho Tung Visualization Lab sessions supplement lectures. Offered in the fall only.
102 Stars, Galaxies, and the Universe
An introductory course that explores our modern view of the universe. Building on several basic observational techniques and physical principles, this course demystifies the science of astronomy and illuminates the evidence that establishes our physical understandings of stars and planetary systems, galaxies, and the universe. This course seeks evidence-based answers to questions including: Of what stuff are stars made? What powers the Sun and other stars? How do stars and planetary systems form and evolve? Do other Earth-like planets exist? What determines the distribution and nature of galaxies in the universe? How did the universe begin and what is its future? Ho Tung Visualization Lab and observing sessions supplement lectures. Offered in spring only.
165 How Old Is the Universe
The last 20 years is often characterized as the Golden Age of modern astronomy due to the number of paradigm-shifting discoveries that have revolutionized our vision and understanding of the universe. This introductory-level course explores several of these ground-breaking discoveries in great detail by focusing on the physical concepts and observations as well as the historical narrative that traces the progression of the scientific endeavor that made these discoveries possible. This course is distinctly different from ASTR 101 and 102, and allows for the interested non-science student to delve more deeply into the many discoveries that lead us to conclude that the universe is 13.77 +/– 0.059 billion years old; a number, by cosmological standards, that is staggeringly precise. No prior course work in physics, astronomy, or mathematics is required for this course.
210 Intermediate Astronomy and Astrophysics
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
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. This course is crosslisted as ANTH 230. (Formerly ASTR 130.)
312/312L Astronomical Techniques
A laboratory course introducing students to basic astronomical observations, 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. 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. (Formerly ASTR 212/212L.)
313 Planetary Science
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. 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. (Formerly ASTR 320.)
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. Prerequisite: PHYS 334 (formerly PHYS 216) or permission of instructor. Offered in the spring only, in alternate years. (Formerly ASTR 314.)
416 Galactic and Extragalactic Astronomy
Study of the astronomical techniques, methods, and fundamental 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. Prerequisite: PHYS 233 (formerly PHYS 122). Offered in the spring only, in alternate years. (Formerly ASTR 316.)