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Year: ### 2009-10

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. 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.

Requisite: A working knowledge of high-school algebra, geometry and trigonometry. Limited to 20 students. Spring semester. Professor Hunter.

Beginning with the roots of the principle of relativity in the work of Galileo and Newton, the course will discuss Einstein's Special Theory of Relativity in quantitative detail. The eighteenth- and nineteenth-century developments in electrodynamics and optics will be explored along the way. A qualitative outline of general relativity will be presented. The next topic will be the study of the structure of matter and forces on the small scale and the challenges posed by the quantum theory that best describes the microworld. The last topic of the semester will be the application of relativity and quantum physics to the early universe. The approach will be elementary but rigorous. The course is designed for the non-specialist audience; no advanced mathematics or prior physics will be required. The work will include readings and regular problem sets as well as a few essays. High school algebra and geometry will however be used extensively in class and in the problem sets.

Spring semester. Professor Jagannathan.

This course explores how computation can be used effectively to solve problems arising in scientific disciplines. It will provide insight into how numerical methods work, and how and where to apply them. Topics include numerical integration, solving systems of equations and differential equations, root finding, the fast Fourier transform, random number generation, curve fitting, error estimation, and simulation of physical systems. We will emphasize ways of constructing correct, efficient algorithms and of implementing those algorithms well. No previous programming experience is required, but quantitative aptitude is essential. Students will be expected to learn the basics of programming in the first few weeks and will do substantial programming throughout the semester.

Requisite: Mathematics 11 or consent of the instructor. Fall semester. STINT Fellow Carlsund-Levin.

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. Fall semester: Professors Bourgeois and Darnton. Spring semester: Professors Darnton and Jagannathan.

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. Fall semester: Professors Hall and Bourgeois. Spring semester: Professors Friedman and Loinaz.

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. Fall semester. Professor Hunter.

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. Spring semester. Professor Hall.

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. Fall semester. Professor Friedman.

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. Spring semester. Professors Friedman and Hunter.

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 and Physics 17/24 or consent of the instructor. Fall semester. Professor Loinaz.

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. Spring semester. Professor Darnton.

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. Fall semester. Professor Loinaz.

(Offered as Physics 46 and Chemistry 46.) How do the physical laws that dominate our lives change at the small length and energy scales of individual molecules? What design principles break down at the sub-cellular level and what new chemistry and physics becomes important? We will answer these questions by looking at bio-molecules, cellular substructures, and control mechanisms that work effectively in the microscopic world. How can we understand both the static and dynamic shape of proteins using the laws of thermodynamics and kinetics? How has the basic understanding of the smallest molecular motor in the world, ATP synthase, changed our understanding of friction and torque? We will explore new technologies, such as atomic force and single molecule microscopy that have allowed research into these areas. This course will address topics in each of the three major divisions of Biophysics: bio-molecular structure, biophysical techniques, and biological mechanisms.

Requisite: Chemistry 12, Physics 16/23, Physics 17/25, Biology 19 or evidence of equivalent coverage in pre-collegiate courses. Omitted 2009-10. Professor Darnton.

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. Fall semester. Professor Hall.

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. Spring semester. Professor Loinaz.

(Also Physics 57.) Taking off from an exploration of the Standard Model of elementary particles, and the physics of particle and radiation detection, this course will cover topics in the young field of Particle Astrophysics. This field bridges the fields of elementary particle physics and astrophysics and investigates processes in the universe using experimental methods from particle physics. An emphasis will be placed on current experiments and the scientific literature. Topics covered will include cosmic rays, neutrinos, the development of structure in the early universe, big bang nucleosynthesis, and culminate with our modern understanding of the nature of dark matter and dark energy in the expanding universe.

Requisite: Physics 48 or consent of instructor. Omitted 2009-10.

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.

Fall semester. The Department.

Independent Reading Course. A full course.

Fall semester.