9. Energy. We will develop the concept of energy from a Physics perspective. We will introduce the various forms that energy can take and discuss the mechanisms by which it can be generated, transmitted, and transformed. The law of conservation of energy will be introduced both as a useful tool, and as an example of a fundamental physical law. The environmental and financial costs and benefits of various methods of energy generation and consumption will be discussed. Demonstrations and hands-on laboratory experiences will be an integral part of the course.
Requisite: A working knowledge of high-school algebra, geometry and trigonometry. The course is intended for non-science majors and not for students who have either completed or intend to complete the equivalent of Physics 17 or Chemistry 10. Limited to 20 students. Second semester. Professor to be named.
11. Light, Color and Vision. We will examine the phenomena of light, color, and vision from the points of view of physics, physiology and neuroscience. We will also see how these phenomena affect visual perception and are manipulated by artists including painters and theater designers. The course will treat the reflection, refraction, diffraction and interference of light along with optical instruments, modern quantum theories of light, and lasers. We will also discuss optical illusions and natural light phenomena such as rainbows and glories.
First semester. Omitted 2007-08.
15. Scientific Computing. (Also Computer Science 15.) See Computer Science 15.
Requisite: Mathematics 11. First semester. Professors Hall and L. McGeoch.
16. Introductory Physics I: Mechanics and Wave Motion. The course will begin with a description of the motion of particles and introduce Newton’s dynamical laws and a number of important force laws. We will apply these laws to a wide range of problems to gain a better understanding of them and to demonstrate the generality of the framework. The important concepts of work, mechanical energy, and linear and angular momentum will be introduced. The unifying idea of conservation laws will be discussed. The study of mechanical waves permits a natural transition from the dynamics of particles to the dynamics of waves, including the interference of waves. Additional topics may include fluid mechanics and rotational dynamics. Three hours of lecture and discussion and one three-hour laboratory per week.
Requisite: Mathematics 11. First semester: Professor to be named. Second semester: Professor to be named.
17. Introductory Physics II: Electromagnetism and Optics. Most of the physical phenomena we encounter in everyday life are due to the electromagnetic force. This course will begin with Coulomb’s law for the force between two charges at rest and introduce the electric field in this context. We will then discuss moving charges and the magnetic interaction between electric currents. The mathematical formulation of the basic laws in terms of the electric and magnetic fields will allow us to work towards the unified formulation originally given by Maxwell. His achievement has, as a gratifying outcome, the description of light as an electromagnetic wave. The course will consider both ray-optics and wave-optics descriptions of light. Laboratory exercises will emphasize electrical circuits, electronic measuring instruments, optics and optical experiments. Three hours of lecture and discussion and one three-hour laboratory per week.
Requisite: Physics 16 or 23. First semester: Professors Jagannathan and Zajonc. Second semester: Professor to be named.
20. Quantum Challenges. The puzzles of quantum mechanics have challenged physicists and philosophers alike. Working from the original writings of the founders of quantum mechanics such as Planck, Bohr, Einstein, Heisenberg, and Schrödinger, as well as from the work of more recent authors, we will explore the revolutionary ideas of quantum mechanics and their philosophical implications. We will also discuss experimental confirmation of the extraordinary predictions of quantum mechanics and the current and future application of quantum effects. In particular we will treat wave-particle duality, the uncertainty principle, the concept of the photon, particle identity, quantum entanglement, the Einstein-Podolsky-Rosen effect, macroscopic quantum effects and the measurement problem. While there are no prerequisites, the course will make use of high school mathematics and physics.
23. The Newtonian Synthesis: Dynamics of Particles and Systems, Waves. The idea that the same simple physical laws apply equally well in the terrestrial and celestial realms, called the Newtonian Synthesis, is a major intellectual development of the seventeenth century. It continues to be of vital importance in contemporary physics. In this course, we will explore the implications of this synthesis by combining Newton’s dynamical laws with his Law of Universal Gravitation. We will solve a wide range of problems of motion by introducing a small number of additional forces. The concepts of work, kinetic energy, and potential energy will then be introduced. Conservation laws of momentum, energy, and angular momentum will be discussed, both as results following from the dynamical laws under restricted conditions and as general principles that go well beyond the original context of their deduction. Newton’s laws will be applied to a simple continuous medium to obtain a wave equation as an approximation. Properties of mechanical waves will be discussed. Four hours of lecture and discussion and one three-hour laboratory per week.
Requisite: Mathematics 11. First semester. Professor Hunter.
24. The Maxwellian Synthesis: Dynamics of Charges and Fields, Optics. In the mid-nineteenth century, completing nearly a century of work by others, Maxwell developed an elegant set of equations describing the dynamical behavior of electromagnetic fields. A remarkable consequence of Maxwell’s equations is that the wave theory of light is subsumed under electrodynamics. Moreover, we know from subsequent developments that the electromagnetic interaction largely determines the structure and properties of ordinary matter. The course will begin with Coulomb’s Law but will quickly introduce the concept of the electric field. Moving charges and their connection with the magnetic field will be explored. Currents and electrical circuits will be studied. Faraday’s introduction of the dynamics of the magnetic field and Maxwell’s generalization of it will be discussed. Laboratory exercises will concentrate on circuits, electronic measuring instruments, and optics. Four hours of lecture and discussion and one three-hour laboratory per week.
Requisite: Mathematics 12 and Physics 16 or 23. Second semester. Professor to be named.
25. Modern Physics. The theories of relativity (special and general) and the quantum theory constituted the revolutionary transformation of physics in the early twentieth century. Certain crucial experiments precipitated crises in our classical understanding to which these theories offered responses; in other instances, the theories implied strange and/or counterintuitive phenomena that were then investigated by crucial experiments. After an examination of the basics of Special Relativity, the quantum theory, and the important early experiments, we will consider their implications for model systems such as a particle in a box, the harmonic oscillator, and a simple version of the hydrogen atom. We will also explore the properties of nuclei and elementary particles, study lasers and photonics, and discuss some very recent experiments of interest in contemporary physics. Three class hours per week.
Requisite: Mathematics 12 and Physics 17 or 24. First semester. Professor Friedman.
26. Intermediate Laboratory. A variety of classic and topical experiments will be performed. In the area of fundamental constants, we will undertake a measurement of the speed of light, a determination of the ratio of Planck’s constant to the charge of the electron through the study of the photoelectric effect, and an experiment to obtain the charge-to-mass ratio of the electron. We will study the wave nature of the electron through a diffraction experiment. An experiment to measure optical spectra and another on gamma ray spectra will reveal the power of spectroscopy for exploring the structure of matter. Other experiments such as nuclear magnetic resonance, quantized conductance in nanocontacts, and properties of superconductors will give students an opportunity to experience laboratory practice in its contemporary form. Emphasis will be placed on careful experimental work and data-analysis techniques. One meeting a week of discussion plus additional, weekly self-scheduled laboratory work.
Requisite: Physics 25 or consent of the instructor. Second semester. Professor to be named.
27. Methods of Theoretical Physics. The course will present the mathematical methods frequently used in theoretical physics. The physical context and interpretation will be emphasized. Topics covered will include vector calculus, complex numbers, ordinary differential equations (including series solutions), partial differential equations, functions of a complex variable, and linear algebra. Four class hours per week.
Requisite: Mathematics 12 or consent of the instructor. First semester. Professor Jagannathan.
28. Intermediate Optics. Recent years have seen breathtaking advances in the field of optics, with technologies that achieve secure communication across long distances at extremely high speeds and systems that produce light with nonclassical properties. Optics is also one of the oldest disciplines of physics, with a rich history that stretches into antiquity. This course will explore the relationship between optics and other branches of physics, including electromagnetic and quantum theory, focusing in particular on the properties of light, its interaction with matter, and how it is manipulated and controlled in optical systems, from lenses and mirrors to the most recent developments in lasers and electro-optics. Three class hours per week, with occasional laboratory meetings.
Requisite: Physics 17 or 24, or consent of the instructor. Second semester. Professor to be named.
30. Statistical Mechanics and Thermodynamics. The basic laws of physics governing the behavior of microscopic particles are in certain respects simple. They give rise both to complex behavior of macroscopic aggregates of these particles, and more remarkably, to a new kind of simplicity. Thermodynamics focuses on the simplicity at the macroscopic level directly, and formulates its laws in terms of a few observable parameters like temperature and pressure. Statistical Mechanics, on the other hand, seeks to build a bridge between mechanics and thermodynamics, providing in the process, a basis for the latter, and pointing out the limits to its range of applicability. Statistical Mechanics also allows one to investigate, in principle, physical systems outside the range of validity of Thermodynamics. After an introduction to thermodynamic laws, we will consider a microscopic view of entropy, formulate the kinetic theory, and study several pertinent probability distributions including the classical Boltzmann distribution. Relying on a quantum picture of microscopic laws, we will study photon and phonon gases, chemical potential, classical and degenerate quantum ideal gases, and chemical and phase equilibria. Three class hours per week.
Requisite: Physics 25 or consent of the instructor. Second semester. Professor to be named.
43. Dynamics. This course begins with the foundation of classical mechanics as formulated in Newton’s Laws of Motion. We then use Hamilton’s Principle of Least Action to arrive at an alternative formulation of mechanics in which the equations of motion are derived from energies rather than forces. This Lagrangian formulation has many virtues, among them a deeper insight into the connection between symmetries and conservation laws. From the Lagrangian formulation we will move to the Hamiltonian formulation and the discussion of dynamics in phase space, exploring various avenues for the transition from the classical to the quantum theory. We will study motion in a central force field, the derivation of Kepler’s laws of planetary motion from Newton’s law of gravity, two-body collisions, and physics in non-inertial reference frames. Other topics may include the dynamics of driven, damped oscillators, and non-linear dynamics of chaotic systems. Three class hours per week.
Requisite: Physics 27 or consent of the instructor. First semester. Professor Friedman.
47. Electromagnetic Theory I. A development of Maxwell’s electromagnetic field equations and some of their consequences using vector calculus. Topics covered include: electrostatics, steady currents and static magnetic fields, time-dependent electric and magnetic fields, and the complete Maxwell theory, energy in the electromagnetic field, Poynting’s theorem, electromagnetic waves, and radiation from time-dependent charge and current distributions. Three class hours per week.
Requisite: Physics 17 or 24 and Physics 27 or consent of the instructor. First semester. Professor Hall.
48. Quantum Mechanics I. Wave-particle duality and the Heisenberg uncertainty principle. Basic postulates of Quantum Mechanics, wave functions, solutions of the Schroedinger equation for one-dimensional systems and for the hydrogen atom. Three class hours per week.
Requisite: Physics 25 and Physics 43 or consent of the instructor. Second semester. Professor to be named.
52. Electromagnetic Theory II. This course is a continuation of Physics 47. We will focus on applications of Maxwell’s equations to radiation and waves. We will consider radiation in free space, in bounded media, and in atomic systems. Three hours per week.
Second semester. Professor to be named.
53. Quantum Mechanics II. This course is a continuation of Physics 48. We will study variational methods, semiclassical approximations, time-dependent perturbation theory, non-relativistic scattering theory, and the quantization of the radiation field. Three class hours per week.
76. Quantum Information, Quantum Measurement and Quantum Computing. Quantum mechanics is well known for its counterintuitive and seemingly paradoxical predictions. Despite its failure to give us a clear, intuitive picture of the world, the theory is remarkably successful at predicting the outcomes of experiments, although those predictions are probabilistic rather than deterministic. Because of its unparalleled success, the thorny issues about the theory’s foundations were often ignored during its first 50 years. Recent advances in both theory and experiment have again brought these issues to the fore. This course will review some of the most interesting and intriguing facets of quantum mechanics, as well as the theory’s potential applications to information science and computing. Topics to be covered will include the Schrodinger cat paradox and the quantum measurement problem; Bell’s inequalities, entanglement and related phenomena that establish the "weirdness" of quantum mechanics; secure communication using quantum cryptography; and how quantum computers (if built) can solve certain problems much more efficiently than classical ones. We will also explore recent experiments in which quantum phenomena appear on the macroscopic scale and some of the philosophical conundrums raised by those results.
Requisite: Physics 25 or 35 or consent of the instructor. . Omitted 2007-08.
77. Senior Departmental Honors. Individual, independent work on some problem, usually in experimental physics. Reading, consultation and seminars, and laboratory work.
Designed for Honors candidates, but open to other advanced students with the consent of the Department. First semester. The Department.
78, 78D. Senior Departmental Honors. Same description as Physics 77. A single or double course.
Requisite: Physics 77. Second semester. The Department.
97, 97H, 98, 98H. Special Topics. Independent Reading Course. Full or half course.
First and second semesters.