Faculty of Arts & Sciences

This is the second term of a two-semester introductory sequence that uses a combination of analytic and numerical methods to understand physical systems, to analyze experimental data, and to compare data to models. Topics include electrostatics and magnetostatics, electromagnetic fields, optics [all topics illustrated with applications to current technological and societal challenges], and an introduction to the physics of many-body systems and their aggregate properties such as entropy, temperature and pressure. The course is aimed at second year students who have an interest in pursuing a concentration in the sciences and/or engineering. The course structure includes lecture, discussion and laboratory components.

Electricity and magnetism. Topics include electrostatics, electric currents, magnetic field, electromagnetic induction, Maxwell's equations, electromagnetic radiation, and electric and magnetic fields in materials.

Newtonian mechanics and special relativity for students with good preparation in physics and mathematics at the level of the advanced placement curriculum. Topics include oscillators damped and driven and resonance (how to rock your car out of a snow bank or use a swing), an introduction to Lagrangian mechanics and optimization, symmetries and Noether's theorem, special relativity, collisions and scattering, rotational motion, angular momentum, torque, the moment of inertia tensor (dynamic balance), gravitation, planetary motion, and a quantitative introduction to some of the mind-bending ideas of modern cosmology like inflation and dark energy.

Open to selected concentrators in Physics, Chemistry and Physics, and other fields who wish to do supervised reading and studying of special topics in physics. Ordinarily such topics do not include those covered in a regular course of the Department. Honor grades in Physics 15 and a number of intermediate-level courses are ordinarily required. The student must be accepted by a member of the faculty.

This course will introduce cosmology, the study of the large-scale evolution of the universe. Topics include the expanding universe; Friedmann-Robertson-Walker metrics; the evolution of the matter, radiation, and vacuum energy of the universe over time; evidence for dark matter; the Cosmic Microwave Background and its role in determining cosmological parameters; Big-Bang Nucleosynthesis; inflation and how it seeded the universe today; and the formation of structures like galaxies.

Applies elementary physics to the real world and fundamental phenomena, introducing estimation and calculational techniques that are commonly used by research physicists when addressing new problems. Emphasis is on developing physical intuition and the ability to do order-of-magnitude calculations. New physical concepts are introduced as necessary. Example topics: the Big Bang and searches for Earth-like exoplanets; material properties and phase transitions; masers, lasers, and the global positioning system; magnetic resonance imaging and physiology of major organs; Earth properties & human energy use. Example estimation techniques: dimensional analysis, commonly used concepts such as diffusion and the Bloch model, scaling laws, and symmetries and conservation laws.

This course presents the underlying physics of modern medical diagnostic imaging techniques. We will explore the physics of diagnostic imaging from a unified electromagnetics' viewpoint ranging from a simple mapping of radiation attenuation coefficients in X-ray, to resonance absorption in a nuclear magnetic resonance (NMR) induced inhomogeneously broadened RF absorber. The bulk of the course will focus on the powerful technique of NMR imaging. Flexibility exists to vary the depth of each area depending on background and experience of the students.

Living organisms use sensory systems to inform themselves of the sights, sounds, and smells of their surrounding environments. Sensory systems are physical measuring devices, and are therefore subject to certain limits imposed by physics. Here we will consider the physics of sensory measurement and perception, and study ways that biological systems have solved their underlying physical problems. We will discuss specific cases in vision, olfaction, and hearing from a physicist's point of view.

Introduction to nonrelativistic quantum mechanics: uncertainty relations; Schrodinger equation; Dirac notation; matrix mechanics; one-dimensional problems including particle in box, tunneling, and harmonic oscillator; angular momentum, hydrogen atom, spin, Pauli principle; time-independent perturbation theory; scattering.

This course will review the role of symmetries in quantum mechanics. Topics include atomic and molecular symmetries, crystallographic symmetries, spontaneous symmetry breaking and phase transitions, geometrical Berry phases, topological aspects of condensed matter systems. Mathematical basics of group theory will be taught as needed to give students an understanding of the topics covered.

Fundamental ideas of classical mechanics including contact with modern work and applications. Topics include Lagrange's equations, the role of variational principles, symmetry and conservation laws, Hamilton's equations, Hamilton-Jacobi theory and phase space dynamics. Applications to celestial mechanics, quantum mechanics, the theory of small oscillations and classical fields, and nonlinear oscillations, including chaotic systems presented.

Includes the use of coherent electromagnetic radiation to probe and control atomic systems, use of traps to isolate atoms, molecules, and elementary particles for studies of ultracold quantum degenerate matter and precision tests of the standard model; resonance methods. Goals of course include acquainting student with these and other modern research topics while providing the foundations of modern atomic, molecular and optical physics research.

Introduction to thermal physics and statistical mechanics: basic concepts of thermodynamics (energy, heat, work, temperature, and entropy), classical and quantum ensembles and their origins, and distribution functions. Applications include the specific heat of solids, black body radiation; classical and quantum gases; magnetism; phase transitions; propagation of heat and sound.

This course gives a grounding in condensed matter physics, with an emphasis on solid state materials of practical utility. We give a physical & quantitative introduction to crystal structure, band structure, electrons, phonons, thermal properties, optical properties, and magnetic properties. We cover materials including metals, insulators, semiconductors, and superconductors. We include discussion of experimental techniques employed to measure material properties.

A survey of black holes focusing on the deep puzzles they present concerning the relations between general relativity, quantum mechanics and thermodynamics. Topics include: causal structure, event horizons, Penrose diagrams, the Kerr geometry, the laws of black hole thermodynamics, Hawking radiation, the Bekenstein-Hawking entropy/area law, the information puzzle, microstate counting and holography. Parallel issues for cosmological and deSitter event horizons will also be discussed.

Introduction to functional analytic methods relevant for problems in quantum and statistical physics. Properties of linear transformations on Hilbert space. Generators of continuous groups and semigroups. Properties of Green's functions and matrices. Uniqueness and non-uniqueness of ground states and equilibrium states. Heat kernel methods. Index theory, invariants, and related algebraic structure. The KMS condition and its consequences.

An introduction to electronic circuit design intended to develop circuit intuition and debugging skills through daily design exercises, discussion and hands-on lab exercises. The approach is intensely practical, minimizing theory. Moves quickly from passive circuits to discrete transistors, then concentrates on operational amplifiers, used to make a variety of circuits including integrators, oscillators, regulators, and filters. The digital half of the course treats analog-digital interfacing, emphasizes the use of microcontrollers and programmable logic devices (PLDs).

Three experimental projects are selected representing condensed matter, atomic, nuclear, and particle physics. Examples: experiments on pulsed nuclear magnetic resonance, microwave spectroscopy, optical tweezers, and non-linear optics, optical pumping, Raman scattering, scattering of laser light, nitrogen vacancies in diamond, neutron activation of radioactive isotopes, Compton scattering, relativistic mass of the electron, recoil free gamma-ray resonance, lifetime of the muon, studies of superfluid helium, positron annihilation, superconductivity, the quantum Hall effect, properties of semiconductors. The facilities of the laboratory include several computer controlled experiments as well as computers for analysis.

Basic course in nonrelativistic quantum mechanics. Review of wave functions and the Schrodinger Equation; Hilbert space; the WKB approximation; central forces and angular momentum; electron spin; measurement theory; the density matrix; perturbation theory.

Introduction to relativistic quantum field theory. This course covers quantum electrodynamics. Topics include canonical quantization, Feynman diagrams, spinors, gauge invariance, path integrals, ultraviolet and infrared divergences, renormalization and applications to the quantum theory of the weak and gravitational forces.

Introduction to some of the tools for studying the exact nonperturbative dynamics of supersymmetric gauge theories, supergravity, and gauge/gravity duality.

Basic principles of statistical physics and thermodynamics, with applications including: the equilibrium properties of classical and quantum gases, phase transitions and critical phenomena, as illustrated by the liquid-gas transition and simple magnetic models. Universality, scaling and renormalization group. Introduction to non-equilibrium physics.

Introduction to strongly interacting soft condensed matter and biophysical systems. We begin with the physics of cells and related single molecule experiments on bio-polymers such as DNA, RNA and proteins. A major part of the course will then focus on genetic engineering, and the non-equilibrium statistical dynamics of genetic circuits and neural networks.

Introduction to physics of quantum information, with emphasis on ideas and experiments ranging from quantum optics to condensed matter physics. Background and theoretical tools will be introduced. The format is a combination of lectures and class presentations.

Explores an emerging interface involving strongly correlated systems in atomic and condensed matter physics. Topics include bosonic and fermionic Hubbard models, strongly interacting systems near Feshbach resonances, magnetism of ultracold atoms, quantum spin systems, low dimenstional systems, non-equilibrium coherent dynamics.

Introduction to quantum optics and modern atomic physics. The basic concepts and theoretical tools will be introduced. Topics will include coherence phenomena, non-classical states of light and matter, atom cooling and trapping and atom optics. The second of a two-term subject sequence that provides the foundations for contemporary research.

A selection of topics from current areas of research on string theory.

Electrical, optical, thermal, magnetic, and mechanical properties of solids will be treated based on an atomic scale picture and using the independent electron approximation. Metals, semiconductors, and insulators will be covered, with possible special topics such as superconductivity.

Hands-on, experienced-based course for graduate students on teaching and communicating physics, conducted through practice, observation, feedback, and discussion. Departmental rules for teaching fellows, section and laboratory teaching, office hours, assignments, grading, and difficult classroom situations.