Physics

Professors: Jeffrey Dunham, Robert Prigo (on leave 2008-09), Stephen Ratcliff, P. Frank Winkler (on leave WT & Spring term), Richard Wolfson; Associate Professor: Susan Watson; Assistant Professor: Noah Graham. Department Coordinator: Amy Comes

Physics is the fundamental science; it leads to our most basic understanding of the natural world and of human technological achievements. The physics program at Middlebury is designed to integrate physics into the liberal arts curriculum, as well as to provide challenging courses and research opportunities for students majoring in physics. Courses and student research activities in astronomy are also part of the physics program.
     Course offerings reflect the needs of three categories of students: (1) those majoring in physics; (2) those majoring in another science who need a basic introduction to physics and the analytical skills it provides; and (3) those majoring in areas outside the sciences, who seek to explore the concepts of physics with a minimum of mathematics.
     Courses designed especially for nonscience students are PHYS 0155 (Introduction to the Universe), PHYS 0101 (Physical Reality and Human Thought), PHYS 0104 (Chaos, Complexity, and Self-Organization), and first-year seminars. Students majoring in the sciences, and others who desire a more analytical approach to physics, usually take the two-semester introductory physics sequence PHYS 0109-0110, and the winter term course PHYS 0111. In addition, they may elect more advanced courses at the 0200-level or above.
     Students in premedical and other preprofessional programs requiring two semesters of physics should take PHYS 0109 and PHYS 0110; other 0100-level physics courses are not acceptable.  Such students are advised to take the Winter Term course PHYS 0111 also.
     For those majoring in physics, we offer a broad range of courses that emphasize a variety of topics in physics while building both theoretical understanding and experimental skills. Middlebury physics majors apply their education in a wide variety of careers. Some pursue graduate work in physics and related fields. Others find their physics degrees valuable in engineering, medicine, business, law, teaching, government service, and other pursuits. The physics program is designed to serve the needs of both those intending advanced study in physics and those for whom formal work in physics will end with the Middlebury degree.
     The physics department encourages its majors to study abroad to gain experience at international research facilities, learn different national styles of scientific practice, improve language proficiency, and pursue academic interests outside of physics. Upper-level physics courses taken abroad may be eligible for physics course credit upon approval of the department chair; students are strongly encouraged to obtain this approval before going abroad.
     Physics majors interested in obtaining high school physics teaching certification should notify the teacher education program preferably no later than the middle of their sophomore year. 
     Required for the Major in Physics: The major program consists of eight required physics courses: PHYS 0109, PHYS 0110, PHYS 0201, PHYS 0202, PHYS 0212, PHYS 0301, PHYS 0321, and the winter term course, PHYS 0111, that is offered each year and serves as a bridge between PHYS 0109 and PHYS 0110; a minimum of two electives; and the senior program. Electives may be chosen from physics courses at the 0200-level and above except that one upper-level physics course taken in an off-campus physics program, or chosen from the following list of Middlebury College courses, may be substituted: MATH 0225, MATH 0302, MATH 0325, CSCI 0201, CHEM 0351, CHEM 0352. Mathematics at least through the level of MATH 0122 is also required; this requirement may be satisfied either at Middlebury or through appropriate pre-college courses in calculus. Independent study courses such as PHYS 0500 may not be used for elective credit. In addition to the courses listed below, courses that satisfy the elective requirement in physics are occasionally offered during the winter term.
     Prospective majors must begin the physics sequence no later than the sophomore year. Starting in the first year allows more flexibility in the choice of courses and thesis topics. Students planning graduate work in physics should elect as many as possible of PHYS 0221 (Electronics for Scientists), PHYS 0330 (Analytical Mechanics), PHYS 0350 (Statistical Mechanics), and PHYS 0401 (Quantum Mechanics). In addition, MATH 0200, MATH 0225, and PHYS 0302 (Electromagnetic Waves) are strongly recommended for those anticipating graduate study. Most physics majors will find computer programming skills through the level of CSCI 0201 extremely valuable.
     Senior Program: The major program culminates with a two-unit senior thesis. The thesis involves a significant piece of experimental or theoretical research. Thesis topics in recent years have included work in astrophysics, condensed matter physics, laser spectroscopy, biophysics, physics education, environmental applications, plasma physics, quantum computing, and nuclear magnetic resonance.
     Departmental Honors: A minimum grade average of B in physics courses is required of all honors candidates. Honors in physics is awarded primarily on the basis of excellent senior thesis work, combined with depth and excellence of coursework in physics. A student's overall accomplishments in the department, including teaching assistantships and leadership, are also considered in the awarding of honors.
     Required for the Minor in Physics: The minor in physics consists of at least five courses, two of which must be PHYS 0109 and PHYS 0110. At least one of the others is to be chosen from among PHYS 0201 and PHYS 0202; any two additional PHYS courses, including those offered during winter term, complete the minor.
     Pre-Engineering: Some students study physics with the intent of eventually doing engineering, either through a 3-2 program or in graduate school. Students who pursue a physics major en route to a 3-2 engineering degree should take the same eight-course sequence outlined above, and one elective chosen from physics courses at the 0200-level and above; they must complete a one- or two-unit thesis project representing a cohesive presentation of significant experimental and/or theoretical work. A one-unit project must be carried out over the fall or spring term. Four-year pre-engineering students take the normal physics major and choose electives in consultation with the pre-engineering adviser.
     Advanced Placement: Students who seek advanced placement in physics should take the College Board AP examinations. Credit for PHYS 0109 and/or PHYS 0110 is given to students who achieve a score of 4 or 5 on the Physics C: Mechanics and/or Physics C: Electricity and Magnetism examination, respectively. One AP credit is given to students who take the Physics B examination and achieve scores of 4 or 5, but such students are advised to begin their study of physics with PHYS 0109.

PHYS 0101 Physical Reality and Human Thought (Spring)
This course for nonscience students will explore major ideas that shape our understanding of physical reality. The course will focus on the developments of modern physics, particularly relativity and quantum theory. The physical content of these ideas will be emphasized in a nonmathematical way, and their philosophical implications discussed. Tracing the historical development of physical theories will convey a sense of the evolutionary and revolutionary aspects of scientific progress. The course concludes with contemporary attempts to understand the evolution of the universe in terms of the most fundamental physical principles. (Not open to students who have completed PHYS 0201.) 3 hrs. lect., 1 hr. disc. SCI DED (J. Dunham)

PHYS 0104 Chaos, Complexity, and Self-Organization (Not offered 2008-09)
A paradigm shift has occured throughout the natural sciences in recent years. Our understanding of the strict determinism of the Newtonian world-view has been revised in surprising and fruitful new ways, providing an outlook that emphasizes the fundamental significance of open, evolving systems.  This course explores recent work on chaos, fractals, complexity, and self-organization.  Ideas from these fields suggest new ways of thinking about life and mind, and how they arise as emergent phenomena from a physical world of dead and mindless fundamental particles interacting through aimless fundamental forces.  We will also explore the influence of these basic ideas on the humanities and the social sciences.  Although the course is largely nonmathematical, students should be willing to use elementary high school algebra. 3 hrs. lect. SCI DED

PHYS 0109 Newtonian Physics (Fall, Spring)
This course examines motion as it occurs throughout the universe. Topics covered include inertia, force, Newton's laws of motion, work and energy, linear momentum, collisions, gravitation, rotational motion, torque, angular momentum, and oscillatory motion. Emphasis is on practical applications in physics, engineering, the life sciences, and everyday life. Laboratory work and lecture demonstrations illustrate basic physical principles. (Students in PHYS 0109 should be enrolled concurrently in MATH 0121 or MATH 0122 or have completed a high school or college calculus course.) 3 hrs. lect., 3 hrs. lab. SCI DED (fall: R. Wolfson; spring: S. Watson)

PHYS 0110 Electricity and Magnetism (Fall, Spring)
The physical principles of electricity and magnetism are developed and applied to the electrical structure of matter and the electromagnetic nature of light. Practical topics from electricity and magnetism include voltage, current, resistance, capacitance, inductance, and AC and DC circuits. Laboratory work includes an introduction to electronics and to important instruments such as the oscilloscope. (PHYS 0109; MATH 0122 concurrent or prior) 3 hrs. lect., 3 hrs. lab. SCI DED (fall: S. Ratcliff; spring: N. Graham)

PHYS 0111 Thermodynamics, Fluids, Wave Motion, and Optics (Winter)
This lecture and laboratory course covers concepts from classical physics which are not included in PHYS 0109 and PHYS 0110, and serves as a bridge between those two courses. Topics include thermal properties of matter, thermodynamics, fluid mechanics, wave motion, sound, and geometrical and physical optics. This course is strongly recommended for all students otherwise required to take PHYS 0109 and PHYS 0110 as part of a major or of a premedical program, and is required for physics majors. (PHYS 0109 or equivalent) SCI DED (Staff)

PHYS 0155 An Introduction to the Universe (Fall)
Our universe comprises billions of galaxies in a rapidly expanding fabric. How did it begin? Will it expand forever, or how may it end? How do the stars that compose the galaxies evolve from their births in clouds of gas, through the tranquility of middle age, to their often violent deaths? How can scientists even hope to answer such cosmic questions from our vantage point on a small planet, orbiting a very ordinary star? Are there other planets, orbiting other stars, where intelligent beings may be pondering similar issues? This introductory astronomy course, designed for nonscience majors, will explore these and other questions. Students will also become familiar with the night sky, both as part of our natural environment and as a scientific resource, through independent observations and sessions at the College Observatory. The approach requires no college-level mathematics, but students should expect to do quantitative calculations using scientific notation and occasionally to use elementary high-school algebra. (Students may not receive credit for both PHYS 0155 and PHYS 0165.) 3 hrs. lect., 2 hrs. lab./disc. SCI DED (F. Winkler)

PHYS 0165 Physics in the Universe (Fall)
This introduction to the phenomena and physical principles of the universe follows a similar syllabus to that of PHYS 0155, but with an added emphasis on analytical material. Principles of Newtonian mechanics are applied to the motions of planets, stars, and galaxies; statistical techniques help in understanding structures ranging from the interiors of stars to clusters of galaxies; and quantum principles are used to understand the radiation we receive from cosmic sources and the physical processes at work there. 3 hrs. lect., 3.5 hrs. lab./disc. (PHYS 0109 or equivalent) (Students may not receive credit for both PHYS 0155 and PHYS 0165.) SCI DED  (F. Winkler)

PHYS 0201 Relativity and Quantum Physics (Fall)
This course probes a number of areas for which classical physics has provided no adequate explanations. Topics covered include Einstein's special relativity, quantization of atomic energy levels and photons, the atomic models of Rutherford and Bohr, and wave-particle duality. (PHYS 0109, MATH 0122; PHYS 0110 concurrent or prior) 3 hrs. lect. SCI DED (S. Ratcliff)

PHYS 0202 Quantum Physics and Applications (Spring)
This course introduces quantum theory and statistical mechanics, and explores the Heisenberg uncertainty principle, the Schrödinger wave equation, and wave mechanics. These techniques are then applied to atomic, molecular, nuclear, and elementary particle systems. (PHYS 0201; PHYS 0212 concurrent or prior) 3 hrs. lect. SCI DED (J. Dunham)

PHYS 0212 Applied Mathematics for the Physical Sciences (Spring)
This course concentrates on the methods of applied mathematics used for treating the partial differential equations that commonly arise in physics, chemistry, and engineering. Topics include differential vector calculus, Fourier series, and other orthogonal function sets. Emphasis will be given to physical applications of the mathematics. Both analytic and numerical methods are employed. This course is a prerequisite for all 0300- and 0400-level physics courses. (MATH 0122; PHYS 0110 concurrent or prior) 4.5 hrs. lect. DED (S. Ratcliff)

PHYS 0221 Electronics for Scientists (Fall)
An introduction to modern electronic circuits and devices, emphasizing both physical operation and practical use. Transistors and integrated circuits are considered in both analog and digital applications. Examples and laboratory experiments stress measurement and control applications in the physical and biological sciences. Students will gain hands-on familiarity with the design, use, and troubleshooting of electronic instrumentation. (PHYS 0110 or by waiver) 3 hrs. lect., 3 hrs. lab. SCI DED (Staff)

PHYS 0261 Observational Astronomy and Data Analysis (Not offered 2008-09)
An introduction to the concepts and techniques of acquiring and analyzing astronomical data, including celestial coordinates, digital image processing, statistical analysis, photometric systems, and spectroscopy. The College Observatory telescopes and CCD camera systems will be used extensively in laboratory work. (PHYS 0110 and PHYS 0155, or PHYS 0165) 3 hrs. lect., 3 hrs. lab. SCI

PHYS 0301 Intermediate Electromagnetism (Fall)
The unified description of electricity and magnetism is one of the greatest triumphs of physics. This course provides a thorough grounding in the nature of electric and magnetic fields and their interaction with matter. Mathematical techniques appropriate to the solution of problems in electromagnetism are also introduced. The primary emphasis is on static fields, with the full time-dependent Maxwell equations and electromagnetic waves introduced in the final part of the course. (PHYS 0212) 3 hrs. lect. (N. Graham)

PHYS 0302 Electromagnetic Waves (Not offered 2008-09)
Maxwell's theory of the electromagnetic field provides the basis of our understanding of the nature of light, radio waves, infrared radiation, X-rays, and other forms of electromagnetic radiation. This course examines the behavior of electromagnetic waves starting from Maxwell's equations, the fundamental laws of electromagnetism. Topics include wave propagation in different materials; reflection and refraction at interfaces; applications in space communications, optics, and other fields; and relativistic electrodynamics. (PHYS 0301) 3 hr. lect.

PHYS 0321 Experimental Techniques in Physics (CW) (Fall)
This course will cover the design and execution of experiments, and the analysis and presentation of data, at an advanced level. Laboratory experiments will be chosen to illustrate the use of electronic, mechanical, and optical instruments to investigate fundamental physical phenomena, such as the properties of atoms and nuclei and the nature of radiation. Skills in computer-based data analysis and presentation will be developed and emphasized. This course satisfies the College writing requirement. (PHYS 0201 and PHYS 0202 and PHYS 0212; MATH 0200 recommended) 3 hrs. lect., 3 hrs. lab. (J. Dunham, S. Watson)

PHYS 0330 Analytical Mechanics (Spring)
An intermediate-level course in the kinematics and dynamics of particles and rigid body motion. The topics will include: analysis and application of Newton's law of mechanics; the concepts of work, energy, and power; energy conservation; momentum and momentum conservation; torque, angular momentum, and angular momentum conservation; oscillatory motion; and central-force motion. Lagrange's and Hamilton's formulations of classical mechanics will be introduced with emphasis placed on developing problem-solving strategies and techniques. (PHYS 0109 and PHYS 0212, or by waiver; MATH 0200 recommended) 3 hrs. lect. (S. Ratcliff)

PHYS 0340 Introduction to Solid State Physics (Spring)
In this course, the properties of solids are shown to arise naturally from their atomic composition and their structure. Elementary quantum mechanics, electromagnetism, and statistical mechanics are invoked to explore fundamental properties of crystalline solids, including their classification as metals, insulators, semiconductors, and semimetals. Topics covered include crystal structure and diffraction; crystal vibrations; electrical and thermal conduction; and the response of solids to external electric and magnetic fields. (PHYS 0202 and PHYS 0212) 3 hrs. lect. (S. Watson)

PHYS 0350 Statistical Mechanics (Not offered 2008-09)
The course opens with a review of classical thermodynamics and continues with an examination of the fundamental concepts of probability, statistics, and distribution functions. These topics are followed by in-depth discussion of the concepts of energy, energy quantization, and the application of these concepts to the modeling of macroscopic systems. The remainder of the course is a study of statistical mechanics and its application to a variety of classical and quantum systems. Topics covered include statistical thermodynamics, Maxwellian distributions, imperfect gases, equipartition theorem, quantum statistics, heat capacities of solids, electromagnetic radiation, and ideal quantum gases. (PHYS 0202 and PHYS 0212) 3 hrs. lect.

PHYS 0360 Topics in Contemporary Physics (Spring)
This course explores an area of current interest in physics. The topic varies from year to year, depending on faculty and student interest. The emphasis is on thorough exploration of a contemporary field of physics accessible to students with an intermediate undergraduate physics background. Students will be consulted before selection of the course topic, and a detailed description will be provided before fall term registration. (PHYS 0202 and PHYS 0212; additional prerequisites may be imposed.) (R. Wolfson)

PHYS 0401 Quantum Mechanics (Fall)
A fundamental course in quantum mechanics aimed at understanding the mathematical structure of the theory and its application to physical phenomena at the atomic and nuclear levels. Topics include the basic postulates of quantum mechanics, operator formalism, Schrödinger equation, one-dimensional and central potentials, angular momentum and spin, perturbation theory, and systems of identical particles. (PHYS 0202 and PHYS 0212; MATH 0200 recommended) 3 hrs. lect. (N. Graham)

PHYS 0402 Advanced Quantum Mechanics (Not offered 2008-09)
This course emphasizes realistic atomic and nuclear structure calculations using techniques from perturbation theory and angular momentum coupling. A major goal is complete calculations of the fine structure, hyperfine structure, and Lamb shift for the hydrogen atom in the presence of perturbing fields. The electromagnetic field is quantized and used to calculate transition rates and angular distributions for simple radiating systems. Nuclear magnetic resonance and blackbody radiation receives extended treatment. (PHYS 0301 and PHYS 0401) 3 hrs. lect.

PHYS 0500 Independent Study and Special Topics (Fall, Winter, Spring)
(Approval required) (Staff)

PHYS 0705 Senior Research and Thesis (Fall, Winter, Spring)
Independent research in the fall, winter, and spring terms culminating in a written thesis (two units total). (Approval required) (Staff)