Physics

This course is a one-semester journey across cosmological history, from the beginning of time to something akin to its end. We will explore the origin of inanimate physical structures (the cosmos as a whole, as well as that of galaxies, stars, planets, particles, atoms and complex molecules), the origin of life (replicating molecules, the first cells, as well as more complex life forms), the origin of mind (self-reflective conscious awareness) and the origin of culture (language, myth, religion, art, and science). We will then consider what science in particular tells us about the very far future, where we will encounter the likely demise of all complex matter, all life and all consciousness. In the face of such disintegration we will examine the nature of value and purpose. We will recognize that the deepest understanding of reality emerges from blending all of the accounts we discuss—from the reductionist to the humanist to the cosmological—and only through such amalgamation can we fully grasp the long-standing human search for meaning.

The proposed independent study is a one-semester course that is in dialogue with the Origins
and Meaning, Physics UN1111. Students in the independent study will further explore various
issues raised in Origins and Meaning by (a) meeting once per week with the instructor, (b)
completing a selection of readings and viewings, and (c) completing an end-of-term writing
assignment.

Prerequisites: some basic background in calculus or be concurrently taking MATH UN1101 Calculus I. The accompanying laboratory is PHYS UN1291-UN1292 The course will use elementary concepts from calculus. The accompanying laboratory is PHYS UN1291 - UN1292. Basic introduction to the study of mechanics, fluids, thermodynamics, electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics.

Prerequisites: some basic background in calculus or be concurrently taking MATH UN1101 Calculus I. The accompanying laboratory is PHYS UN1291-UN1292 The course will use elementary concepts from calculus. The accompanying laboratory is PHYS UN1291 - UN1292. Basic introduction to the study of mechanics, fluids, thermodynamics, electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

Corequisites: MATH UN1101 Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics. Corequisite: MATH UN1101 or the equivalent.

Corequisites: MATH UN1101 Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics. Corequisite: MATH UN1101 or the equivalent.

Corequisites: MATH UN1101 Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics. Corequisite: MATH UN1101 or the equivalent.

Prerequisites: PHYS UN1402 PHYS W1402. Corequisites: MATH V1201 or the equivalent. Classical waves and the wave equation, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, applications to atomic physics.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494.

Prerequisites: Corequisite: MATH UN1102 Calculus II or equivalent. Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, introduction to special relativity and relativistic kinematics. The course is preparatory for advanced work in physics and related fields.

This class is an introduction to classical mechanics. Our goal is to develop an understanding of the principles underlying motion and how they apply to a wide variety of systems. The course will emphasize topics that help both to understand and to predict behavior in the world around us, highlighting when possible its relevance in medical & biological contexts.

Corequisites: Calculus I or the equivalent  

Fundamental laws of mechanics. Kinematics, Newtons laws, work and energy, conservation laws, collisions, rotational motion, oscillations, gravitation.  PLEASE NOTE: Students who take PHYS BC2001 may not get credit for PHYS BC2009 or PHYS BC2010.

PHYS BC2010 Mechanics - Lecture Only is required as a pre- or co-requisite for this lab.

Fundamental laws of mechanics. Kinematics, Newton's laws, work and energy, conservation laws, collisions, rotational motion, oscillations, gravitation.  This is a calculus-based class. Familiarity with derivatives and integrals is needed.

Prerequisites: PHYS UN1402 or PHYS UN1602 Corequisite: MATH UN1202 or equivalent. Classical waves and the wave equation, geometrical optics, interference and diffraction, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, the harmonic oscillator. The course is preparatory for advanced work in physics and related fields.

Prerequisites: Advanced Placement in physics and mathematics, or the equivalent, and the instructor's permission. (A special placement meeting is held during Orientation.) This accelerated two-semester sequence covers the subject matter of PHYS UN1601, PHYS UN1602 and PHYS UN2601, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, PHYS UN3081, in the following year.

Prerequisites: Physics BC2002 or the equivalent. Corequisites: Calculus III. Nonlinear pendula, transverse vibrations-elastic strings, longitudinal sound waves, seismic waves, electromagnetic oscillations - light, rainbows, haloes, the Green Flash; polarization phenomena - Haidingers Brush, Brewsters angle, double refraction, optical activity; gravity - capillary waves; interference, diffraction, lenses - mirrors.  PLEASE NOTE: Students who take PHYS BC3001 may not receive credit for PHYS BC3010.

Prerequisites: general physics, and differential and integral calculus. Electrostatics and magnetostatics, Laplace's equation and boundary-value problems, multipole expansions, dielectric and magnetic materials, Faraday's law, AC circuits, Maxwell's equations, Lorentz covariance, and special relativity.

A detailed study of a selected field of active research in physics. The motivation, techniques, and results obtained to the present, as well as the difficulties and unsolved problems. For Physics majors only. Priority given to seniors; juniors by permission of the instructor.

Prerequisites: phys UN2601 or phys un2802 Primarily for junior and senior physics majors; other majors must obtain the instructors permission. Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.

Prerequisites: phys UN2601 or phys un2802 Primarily for junior and senior physics majors; other majors must obtain the instructors permission. Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.

Prerequisites: phys UN2601 or phys un2802 Primarily for junior and senior physics majors; other majors must obtain the instructors permission. Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.

Prerequisites: PHYS UN3003 or PHYS UN3007 May be taken before or concurrently with this course. A sequence of experiments in solid-state electronics, with introductory lectures.

Classical electromagnetic wave phenomena via Maxwells equations, including: (i) Michaelson and Fabry-Perot Interferometry, as well as a thin-film interference and elementary dispersion theory; (ii) Fraunhofer Diffraction (and a bit of Fresnel); (iii) Wireless Telegraphy I: AM Radio Receivers; and (iv) Wireless Telegraphy II: AM Transmitters. Last two labs pay homage to relevant scientific developments in the period 1875-1925, from the discovery of Hertzian waves to the Golden Age of Radio. Complements PHYS W3008 Electromagnetic Waves and Optics.

Prerequisites: the written permission of the faculty member who agrees to act as supervisor, and the director of undergraduate studies permission. Readings in a selected field of physics under the supervision of a faculty member. Written reports and periodic conferences with the instructor.

Prerequisites: Permission of the departmental representative required. For specially selected students, the opportunity to do a research problem in contemporary physics under the supervision of a faculty member. Each year several juniors are chosen in the spring to carry out such a project beginning in the autumn term. A detailed report on the research is presented by the student when the project is complete.

Prerequisites: Permission of the departmental representative required. For specially selected students, the opportunity to do a research problem in contemporary physics under the supervision of a faculty member. Each year several juniors are chosen in the spring to carry out such a project beginning in the autumn term. A detailed report on the research is presented by the student when the project is complete.

Prerequisites: PHYS UN3003 and PHYS UN3007 and differential and integral calculus; linear algebra; or the instructor's permission. This course will present a wide variety of mathematical ideas and techniques used in the study of physical systems. Topics will include: ordinary and partial differential equations; generalized functions; integral transforms; Green’s functions; nonlinear equations, chaos, and solitons; Hilbert space and linear operators; Feynman path integrals; Riemannian manifolds; tensor analysis; probability and statistics. There will also be a discussion of applications to classical mechanics, fluid dynamics, electromagnetism, plasma physics, quantum mechanics, and general relativity.

Prerequisites: PHYS UN3003 and PHYS UN3007 Formulation of quantum mechanics in terms of state vectors and linear operators. Three dimensional spherically symmetric potentials. The theory of angular momentum and spin. Identical particles and the exclusion principle. Methods of approximation. Multi-electron atoms.

Prerequisites: PHYS GU4021 or the equivalent. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism.

Prerequisites: (PHYS GU4021 and PHYS GU4022) In this course, we will learn how the concepts of quantum mechanics are applied to real physical systems, and how they enable novel applications in quantum optics and quantum information. We will start with microscopic, elementary quantum systems – electrons, atoms, and ions - and understand how light interacts with atoms. Equipped with these foundations, we will discuss fundamental quantum applications, such as atomic clocks, laser cooling and ultracold quantum gases - a synthetic form of matter, cooled down to just a sliver above absolute zero temperature. This leads us to manybody quantum systems. We will introduce the quantum physics of insulating and metallic behavior, superfluidity and quantum magnetism – and demonstrate how the corresponding concepts apply both to real condensed matter systems and ultracold quantum gases. The course will conclude with a discussion of the basics of quantum information science - bringing us to the forefront of today’s quantum applications.

The “Quantum Physics Lab” will give students in the Quantum Science and Technology Masters program hands-on experience in quantum physics and its applications. Students will work in small groups on several distinct experiments through the semester. Each experimental project might last for 3-4 weeks, comprising the steps outlined in the Program below. Initial experimental offerings include: a quantum optics (entangled photon) platform, a Josephson junction experiment, a nitrogen vacancy (NV) center for direct manipulation of quantum states, along with experiments on nuclear magnetic resonance, quantum conductance and the quantum Hall effect. We expect to add additional experiments in the near future.

Students will observe and measure fundamental quantum behaviors, reinforcing material they are learning in the Masters lecture courses, while simultaneously being introduced to forefront technology that will be the basis of the second “quantum revolution” that could eventually lead to revolutionary applications in electronics, computing, energy technology and medical devices.    

Program:

1 x 230 min lab meeting per week (small group work)

Background research on selected experiments, and associated physics and instrumentation

Data analysis, discussions with instructor and teaching assistants

Project writeups and presentations

Prerequisites: a strong undergraduate background in E-M and classical mechanics. Qualified undergraduates may be admitted with the instructors permission. The basic physics of high energy astrophysical phenomena. Protostars, equations of stellar structure; radiative transfer theory; stellar nucleosynthesis; radiative emission processes; equations of state and cooling theory for neutron stars and white dwarfs, Oppenheimer-Volkoff equation; Chandrasekhar limit; shocks and fluids; accretion theory for both disks and hard surfaces; black hole orbits and light bending.

Prerequisites: PHYS W4021-W4022-W4023, or their equivalents. Fundamentals of statistical mechanics; theory of ensembles; quantum statistics; imperfect gases; cooperative phenomena.

Prerequisites: PHYS W4021-W4022, or their equivalents. The fundamental principles of quantum mechanics; elementary examples; angular momentum and the rotation group; spin and identical particles; isospin; time-independent and time-dependent perturbation theory.

Prerequisites: PHYS G6037 or the equivalent. The elementary particles and their properties; interactions of charged particles and radiation with matter; accelerators, particle beams, detectors; conservation laws; symmetry principles; strong interactions, resonances, unitary symmetry; electromagnetic interactions; weak interactions; current topics.

Recent progress in control of atoms with lasers has led to creating the coldest matter in the universe, constructing ultra precise time and frequency standards, and capability to test high energy theories with tabletop experiments. This course will cover the essentials of atomic physics including the resonance phenomenon, atoms in magnetic and electric fields, and light-matter interactions. These naturally lead to line shapes and laser spectroscopy, as well as to a variety of topics relevant to modern research such as cooling and trapping of atoms. It is recommended for anyone interested in pursuing research in the vibrant field of atomic, molecular, and optical (AMO) physics, and is open to interested students with a one year background in quantum mechanics. Both graduate students and advanced undergraduates are welcome.

Prerequisites: PHYS W3008 or its equivalent. Fundamentals of electromagnetism from an advanced perspective with emphasis on electromagnetic fields in vaccum with no bounding surfaces present. A thorough understanding of Maxwells equations and their application to a wide variety of phenomena. Maxwells equations (in vacuum) and the Lorentz force law - noncovariant form. Scalar and vector potentials, gauge transformations. Generalized functions (delta functions and their derivatives), point changes. Fourier transforms, longitutdinal ad transverse vector fields. Solution of Maxwells equations in unbounded space for electrostatics and magnetostatics with given charge and current sources. Special relativity, Loretnz transformations, 4-momentum, relativistic reactions. Index mechanics of Cartesian tensor notation. Covariatn formulation of Maxwells equations and the Lorentz force law, Lorentz transformation properties of E and B. Lagrangian density for the electromagnetic field, Langrangian density for the Proca field. Symmetries and conservation laws, Noethers theorem. Field conservation laws (energy, linear momentum, angular momentum, stress tensor). Monochromatic plane wave solutions of the time-dependent source-free Maxwell equations, elliptical polarization, partially-polarized electromagnetgic waves, Stokes parameters. Solution of the time-dependent Maxwell equations in unbounded space with given chare and current sources (retarded and advanced solutions). Properties of electromagnetic fields in the radiaion zone, angular distribution of radiated power, frequency distribution of radiated energy, radiation form periodic and non-periodic motions. Radiation from antennas and antenna arrays. Lienard-Wiechert fields, the relativistic form of the Larmor radiation forumla, synchrotron radiation, bremsstrahlung, undulator and wiggler radiation. Electric dipole and magnetic dipole radiation. Scattering of electromagnetic radiation, the differential scattering cross-section, low-energy and high-energy approximations, scattering from a random or periodic array of scatterers. Radiation reaction force, Feynman-Wheeler theoryy. The macroscopic Maxwell equations (spatial averaging to get P, M, D, H). Convolutions, linear materials (permittivity, permeability, and conductivity), causality, analytics continuation, Kramers-Kronig relations. Propagation of monochromatic plane waves in isotropic and non-isotropic linear materials, ordinary ad extraordinary waves. Cherenkov radiation, transition radiation.

Prerequisites: PHYS G6037-G6038. Relativistic quantum mechanics and quantum field theory.