Course Number

Course Title

Description

Introduces mechanics of motion. Designed for concentrators in sciences other than physics-including premedical students. PHYS0030 applies algebra, geometry, trigonometry and analytic geometry. Students with a strong background in calculus should consider taking PHYS0050 or 0070 instead. Consists of lectures and laboratory.

Recommended: MATH0090 or MATH0100.

This course introduces the fundamental elements of electrical and magnetic phenomena, optics and wave optics, as well as selected modern physics topics.  Materials are introduced through lectures, workshops and laboratory exercises.  The topics covered include: the electric force, field and potentials, circuits and circuit elements, magnetic fields and magnetic phenomena, induction, electromagnetic waves, optics, interference and diffraction, wave-particle duality and the photoelectric effect, and radioactivity.  The course is taught at a level that assumes familiarity with algebra and trigonometry, but no calculus.  Students with a strong background in calculus should consider taking PHYS0060 instead. 

Recommended: PHYS0030 or a strong background in high-school level mechanics.

PHYS0050 provides a calculus-based introduction to classical Newtonian mechanics intended for science concentrators. Topics include: linear and rotational motion, Newton’s laws, conservation of energy and momentum, gravitation, fluids, oscillations, and simple harmonic motion. It emphasizes the conceptual understanding of the principles of physics and the development of the calculation skills needed to apply these principles to the physical universe.

Physics 0070 covers the topics of Newtonian Mechanics emphasizing fundamental principles underlying mechanical phenomena and developing mathematical approaches for applying them.  As such, it introduces students to the general approach employed to describe physical phenomena even beyond mechanics. The presentation presumes preparation of a year or more of mechanics and a year of calculus.

Flat Earth to Quantum Uncertainty: On the

Nature and Meaning of Scientific Explanation

In this class, students will explore how physics has affected our view of the cosmos, of ourselves as human beings, as well as our view of the relation of mathematical or physical structures to 'truth' or 'reality.’

This course, aimed at both students in the humanities and sciences, will explore the myriad surprising ways that jazz music is connected to modern physics. No background in physics, mathematics or music is required, as all of these foundational concepts and tools will be introduced.

This course is a first course in astronomy and astrophysics, serving as the preferred gateway for students considering a physics concentration in the astronomy track.  The course introduces the sky and the tools needed to study celestial objects, and ranges then from stars, galaxies, clusters and the largest scales, to the universe' evolution, and returns to solar system formation, exoplanets and SETI.  Significant evening lab and problem sets are at a higher level than the outreach course PHYS0220, as is the associated assumed math and physics understanding.

This class is an introduction to electrodynamics, the theory of electricity and magnetism. The course covers electrostatics (the electric field, electric potential, conductors and boundary value problems), special relativity (the fields of moving charges), magnetostatics (electric currents vector potential), electromagnetic induction and an introduction to Maxwell’s equations (including wave solutions) as well as electric and magnetic fields in matter. The course also provides a basic introduction to AC and DC circuits. 

Prerequisites are multivariable calculus (MATH0180, MATH0200 or MATH0350), and either PHYS0040, PHYS0060 or PHYS0160. APMA0350 is also useful albeit not required.

Linear algebra and vector spaces: inverses, determinants, unitary matrices, inner products, diagonalization, eigenvectors, eigenvalues. Fourier series and transforms. Ordinary differential equations: homogeneous and inhomogeneous first order and second order equations, power series methods. Partial differential equations: separation of variables, Green’s functions. Complex analysis: analytic functions, singularities, calculus of residues. More advanced topics.

Prerequisites: Multivariable Calculus

An introduction to the principles of quantum mechanics and their use in the description of the electronic, thermal, and optical properties of materials. Primarily intended as an advanced science course in the engineering curriculum. Open to others by permission.

Prerequisites: ENGN0040, APMA0340 or equivalents.

This course is focused on the physics of galaxies and systems of galaxies, and on the processes that lead to the production of high energy photons, cosmic rays, and gravitational waves.  Topics include structure of the Milky Way and other galaxies, the physics underlying their appearance and evolution, galaxy interactions and active galactic nuclei, particle acceleration mechanisms, synchrotron, free-free and Compton radiation, and sources of neutrinos and gravitational waves.   PHYS0470 must, at a minimum, be taken to concurrently, and PHYS0270 or instructor’s permission is required.  In addition, mathematics through MATH0200 or MATH0350 is strongly encouraged.

This course covers modern relativistic cosmology and the theory of structure formation through the observations and theoretical framework of special and general relativity.  Topics covered include cosmological observations of the expansion of the Universe, general relativity, Friedmann-Robertson-Walker-Lemaitre cosmologies, the thermal evolution of the Universe, primordial nucleosynthesis, recombination and the Cosmic Microwave Background, structure formation and growth of perturbations, and modern measurements of cosmological parameters. 

Prerequisites: PHYS0160 or the equivalent, and mathematics at the level of MATH0190.

The necessary framework for Quantum mechanics is developed carefully and used to link and explain both the older and newer experimental phenomena of modern physics. This is the first of a two-semester sequence.  In P-1410, the main focus is on 1-D quantum physics, leaving 3-D to P-1420. The course has been taught in recent years following the approach of Sakurai, but at a junior-level, e.g., adopting the text by Townsend. The mathematics that we will use includes basic calculus. Linear transformations on complex vector space serve as essential tools for describing quantum physics.

Prerequisites: PHYS 0500 and 0560; and MATH 0520, 0540 or PHYS 0720; or approved equivalents.

Building on the foundation of PHYS0470, this course applies Maxwell’s equations to study some of the key phenomena and applications of time-dependent electromagnetism: electromagnetic waves, radiation, and special relativity.

Prerequisites: Include lower level electromagnetic theory, vector calculus and basic differential equations. 

The course aims to help physics students learn basic of thermodynamics and develop microscopic understanding of it based on elementary statistical mechanics.  That is, the concepts of thermodynamics and statistical mechanics are introduced from a unified view. Students will develop understanding and importance of quantities such as entropy, negative temperature, and behavior of quantum gases. The emphasis is on real-world applications.  

Prerequisites: PHYS070; PHYS0160; PHYS0500

The course aims to help PhD and MSc students learn experimental methods and develop experimental and scientific communication abilities in major areas of modern physics. We discuss the application of the scientific method. Four major experiments are conducted during the semester. Students develop skills including observing and measuring physical phenomena, analyzing and interpreting data (primarily using Python notebooks) clearly identifying and including possible sources of errors, and also reaching conclusions and publishing experimental results. Students also learn scientific presentation skills and how to read published results and references with appropriate judgment. 

Prerequisites: Note that this course is intended for PhD and MSc students. Undergraduates do not typically have sufficient time available in their schedule to take this course.

Students in the course will learn both the foundations of classical mechanics, including Lagrangian and Hamiltonian formulations, as well as applications of classical mechanics to physically important and illustrative systems including orbital motion, motion in rotating frames, chaos, waves, fluid dynamics and solitons.   

Prerequisites: Classical mechanics at the undergraduate level, including Lagrangian mechanics. Multivariable calculus, and linear ordinary and partial differential equations.  Willingness and ability to learn and use Python for some simple computational simulations.

Wave description of particles.  Wave mechanics and the Schrodinger equation.  Fundamental principles and postulates.  Symmetry transformations.  Time evolution and stationary states.  Theory of angular momentum. Advanced topics: Quantum information, Superfluidity, and other topics if time permits. 

Prerequisites:  Knowledge of basic undergraduate Hamiltonian Mechanics and Electromagnetism as well as a comfortable familiarity with standard Modern Physics. 

The course on Advanced Quantum Mechanics will deal with advanced quantum mechanical  concepts  and their applications. This is based on the use Feynman’s path integral quantization method which will be reviewed at an advanced level. The techniques developed will involve Feynman  diagrammatics, Semiclassical approximations and Non-perturbative methods. A particular attention is paid to fermionic systems with a detailed  discussion of Quantization for  Dirac, Majorana and Supersymmetric particles. And Grassman integration. Advanced Quantum Mechanics also provides  the prerequisite knowledge for the course on Quantum Field Theory (PHYS2300) and these two courses are organized as a sequence. The course involves a bi-weekly set of lectures, related HW sets, weekly discussion meetings and a final study where each student selects a topic of their research  interest. The prerequisites are Math Methods and Quantum Mechanics (at advanced undergraduate level).

1. Feynman Path Integral Quantization; Correlation Functions, Semi-classical methods, Feynman Diagrams, Summing over Topologies*

2. Relativistic Systems; Sum over Relativistic Paths, Klein-Gordon Equation, Interacting Feynman Diagrams

3.Fermionic Systems; Dirac and Majorana Equations, Supersymmetry

4. Quantum Electrodynamics; Divergences, Renormalization

Advanced methods in quantum field theory. The course focuses on nonperturbative approaches to quantum field theory, including conformal field theory, large N methods, Wilsonian renormalization, solitons, instantons and other topological defects. 

The course provides an introduction to Solid State physics. We discuss free electrons, band theory, crystalline symmetries, semiconductors, magnetism and topological band theory. Students are expected to be familiar with quantum mechanics and statistical mechanics.

This is an advanced graduate course on many body quantum theory. The subject is extremely broad and the exact topics will be chosen according to the interests of the class. The topics can include the theory of topological insulators and the general theory of interacting quantum particles. 

Prerequisites: A working knowledge of quantum mechanics and statistical mechanics.

Course Number

Course Title

Description

Introduces mechanics of motion. Designed for concentrators in sciences other than physics-including premedical students. PHYS0030 applies algebra, geometry, trigonometry and analytic geometry. Students with a strong background in calculus should consider taking PHYS0050 or PHYS0070 instead. Consists of lectures and laboratory.

Recommended: MATH0090 or MATH0100.

This course introduces the fundamental elements of electrical and magnetic phenomena, optics and wave optics, as well as selected modern physics topics.  Materials are introduced through lectures, workshops and laboratory exercises.  The topics covered include: the electric force, field and potentials, circuits and circuit elements, magnetic fields and magnetic phenomena, induction, electromagnetic waves, optics, interference and diffraction, wave-particle duality and the photoelectric effect, and radioactivity.  The course is taught at a level that assumes familiarity with algebra and trigonometry, but no calculus.  Students with a strong background in calculus should consider taking PHYS0060 instead.  PHYS0030 or a strong background in high-school level mechanics is strongly recommended.

This course provides a calculus-based introduction to the principles and phenomena of electricity, magnetism, optics, and the concepts of modern physics. It is intended for science concentrators and emphasizes the conceptual understanding of the principles of physics and the development of the calculation skills needed to apply these principles to the physical universe.

Prerequisite: PHYS0050.

The course will cover the significant developments in the detection and characterization
of extra-solar planetary systems in the past almost 30 years. We will study the techniques for detecting planets outside of our solar system, the properties of the exoplanets discovered so far, and the prospects for future discoveries, with an emphasis on the search for "Earth-analogues" and the implications for astrobiology.

Over the last 30 years there has been a revolution in our understanding of planets.
The first exoplanet was discovered in 1988 and today we know of thousands of planets
outside of our solar system. The wide variety of planets and planetary configurations has given us new insights into planetary formation and characteristics. Many of the things we took for granted when we had only the solar system to describe turned out not to be true. Amazingly, even without seeing most of these planets directly, we can understand their composition, climate and likelihood for hosting life. In this course, we will introduce these new discoveries and explore how our understanding of planets, habitable worlds, and the search for life in the Universe has changed as a result of these discoveries.

This course will introduce students to the fundamental laws that govern energy and its use. Physical concepts will be discussed in the context of important technological applications of energy.  The physical concepts include mechanical energy, thermodynamics, the Carnot cycle, electricity and magnetism, quantum mechanics, and nuclear physics. The technological applications include wind, hydro, and geothermal energy, engines and fuels, electrical energy transmission and storage, solar energy and photovoltaics, nuclear reactors, and biomass.

This course is a mathematically rigorous introduction to special relativity, waves, and quantum mechanics. It is the second in a 3-semester sequence for those seeking the strongest foundation in physics and is also suitable for students better served by an introduction to modern physics rather than electromagnetism.

Prerequisites: PHYS0050 or PHYS0070 (note that neither ENGN0030 nor AP Physics is adequate).  MATH0180 or MATH0200 is recommended.

A conceptual introduction to basic ideas and observations in astronomy.  Topics include: the properties of light; the observed sky; the historical development of astronomical ideas; the properties and lifecycles of stars; black holes; galaxies; and the evolution of the Universe as a whole ("cosmology").  Particular emphasis is placed on the physical laws governing astronomical objects and systems.  The material is covered at a more basic level than PHYS0270.  Basic algebra and trigonometry will be used, but no experience with calculus is necessary.  The course includes evening laboratory sessions.

We will cover classical mechanics at a more sophisticated level and introduce new framework, i.e., Lagrangian and Hamiltonian mechanics, that could simplify solving mechanics problems and will be useful later in other advanced physics classes such as quantum mechanics.

Prerequisites: Lower level mechanics, calculus and basic knowledge of solving differential equations, in particular, second order differential equations with constant coefficients. 

This course teaches quantum mechanics through experiment, provides insight into modern physics and some important historical background. In addition, this course develops laboratory and data analysis skills, exposes students to relatively modern experimental research techniques, and gives students feeling for how experiments are designed.  It is a writing course that develops scientific writing skills. At the same time, the presentation component develops oral communication skills.

Prerequisites: Undergraduate level PHYS0070 Minimum Grade of S and Undergraduate level PHYS0160 Minimum Grade of S or Undergraduate level PHYS0050 Minimum Grade of S and Undergraduate level PHYS0060 Minimum Grade of S and Undergraduate level PHYS0470 Minimum Grade of S.

Review of Special Relativity.
 The Formalism of Tensors.
 Einstein’s Equations.
 The Schwarzschild Solution. Experimental Tests of General Relativity. More General Black Holes. Gravitational Waves. More advanced topics.

Prerequisites: PHYS0470, PHYS0500

This course represents the second part of a comprehensive course on Quantum Mechanics. It deals with nontrivial quantum mechanical concepts and applications. Feynman’s path integral quantization is reviewed first as a complement to the standard operator quantization of Heisenberg and Schrodinger. The equivalence of the three methods is demonstrated. This is followed with study of Symmetries in one and two-body systems. Angular momenta and the spectra of Hydrogen and Helium are discussed in detail. Perturbation theory techniques are formulated and a study of Scattering is given. Discussion of Identical Particles and Statistics concludes the course.  

This course provides hands-on experience with some of the experimental techniques of modern physics and, in the process, to deepen the understanding of the relations between experiment and theory. The students will do six experiments on phenomena whose discoveries led to major advances in physics.  For many of the experiments, you would have won a Nobel Prize if you had been the first to do it.

Prerequisites: PHYS0470, PHYS0500 and PHYS0560; and MATH0520, MATH0540 or PHYS0720; or approved equivalents. WRIT

An introduction to scientific computing applied to physical science problems. This course is a general survey of numerical methods with an emphasis on the use of those methods to better understand physical systems. Topics include numerical solution of differential equations, chaotic systems, statistical modeling, molecular dynamics, and Monte Carlo simulations.

Prerequisites: PHYS0070, PHYS0160 (or PHYS0050, PHYS0060) and PHYS2070; MATH0180 and MATH0200 or MATH0350. 

PHYS 1970B

Topics in  Optics

An introduction to string theory at an upper undergraduate level. Topics covered include special relativity, symmetries and Noether's theorem, nonrelativistic strings, relativistic particles and strings, string quantization and gauge fixing, electrodynamics in various dimensions, supersymmetry, and selected advanced topics.

Prerequisite PHYS0470 and corequisite PHYS1410.

PHYS

1970G

This is a course on topology in physics which does a minimal amount of elementary topology. The major topic is the theory underlying the recently discovered materials called topological insulators and what makes them different from ordinary or trivial insulators. The experimental situation is also reviewed. 

Prerequisites: Some knowledge and interest in physics and mathematics. No specific courses are required but a reasonably flexible mind prepared to listen to strange new ideas is essential.

The course aims to help PhD and MSc students learn experimental methods and develop experimental and scientific communication abilities in major areas of modern physics. We discuss the application of the scientific method. Four major experiments are conducted during the semester. Students develop skills including observing and measuring physical phenomena, analyzing and interpreting data (primarily using Python notebooks) clearly identifying and including possible sources of errors, and also reaching conclusions and publishing experimental results. Students also learn scientific presentation skills and how to read published results and references with appropriate judgment. 

Prerequisites: None (Note that this course is intended for PhD and MSc students. Undergraduates do not typically have sufficient time available in their schedule to take this course)

Electrostatics of conductors and dielectrics. Boundary value problems. Magnetostatics. Maxwell’s equations and macroscopic electromagnetism. Conservation laws in electrodynamics. Electromagnetic waves and wave propagation. Special relativity. Relativistic particles and electromagnetic fields.  Electromagnetic radiation. Other topics if time permits. 

Prerequisites: PHYS2030 and knowledge of basic undergraduate Electromagnetism.

The second semester of a rigorous full-year graduate quantum mechanics course. Two areas will be emphasized: (1) Essential tools of quantum mechanics, including addition of angular momentum, perturbation and scattering theory, and an introduction to relativistic quantum mechanics. (2) Key results of quantum mechanics such as the solution of the hydrogen atom, Fermi’s golden rule, and the spontaneous decay of excited states of atoms.

Prerequisites: Quantum mechanics at the undergraduate level, and at the level of PHYS2050. Multivariable calculus, and linear ordinary and partial differential equations, linear algebra. Willingness and ability to learn and use Python for some simple computational quantum science.

This graduate course in general relativity and cosmology will cover the principles of Einstein's general theory of relativity, differential geometry, the first order formulation of general relativity (Einstein-Cartan theory), experimental tests of general relativity and black holes.  The second half of the course will focus on relativistic cosmology with a focus on its interface with field theory.

This course provides a graduate level introduction to the foundations of classical and quantum statistical mechanics with applications to ideal gases (including the magnetic properties of electron gases and Bose-Einstein condensation), interacting systems, and phase transitions, including an introduction to the renormalization group and scaling at continuous phase transitions.

Prerequisites: thermodynamics, statistical mechanics and quantum mechanics.

This course provides a comprehensive introduction to modern elementary particle physics for graduate and senior undergraduate students. The focus of the course is the detailed description of the Standard Model of particle physics, which has proven remarkably successful in describing the properties and behavior of elementary particles and fields. Topics of current interest, new developments, and outstanding problems are be highlighted. Special attention is devoted to experimental methods, which resulted in most significant discoveries in particle physics.

Prerequisites: Introductory Quantum Mechanics (PHYS0560, or PHYS1410, or equivalent).

This class is a graduate course on the big-bang cosmological model. The course covers three distinct areas: The homogeneous universe (kinematics, dynamics, big bang nucleosynthesis, production of relic particles, baryogenesis/leptogenesis), the inhomogeneous universe (inflation, linear perturbation theory of the growth of fluctuations, cosmic microwave background, large scale structure, statistical measures), and non-linear evolution of collision-less fluids (spherical collapse, excursion sets, the N-body problem). 

Pre-requisites are graduate courses in electrodynamics, classical, quantum and statistical mechanics as well as general relativity. A basic knowledge of the Standard Model of particle physics is assumed as well as computational skills that involve the solution of coupled partial differential equations. 

An introduction to the quantum theory of fields. Topics include scalar field theory, quantum electrodynamics, path integrals, perturbation theory and an introduction to renormalization.

This course aims to provide a basic introduction to the elements of group theory most commonly encountered in physics, including discrete groups, Lie groups and Lie algebras.  The course will place a particular emphasis on characters and the representation theory of Lie algebras. Students should have a solid background in linear algebra, and some exposure to quantum mechanics may be helpful.

Advanced topics in solid state physics. The course concentrates on collective phenomena and puts heavy emphasis on the concept of quasiparticles in condensed matter physics. We cover kinetic theory of gases, Fermi liquid theory, superfluids and superconductors. Students are expected to be familiar with the basic solid state physics and with quantum mechanics. 

An introduction to scientific computing applied to physical science problems. This course is a general survey of numerical methods with an emphasis on the use of those methods to better understand physical systems. Topics include numerical solution of differential equations, chaotic systems, statistical modeling, molecular dynamics, and Monte Carlo simulations.

Prerequisites: PHYS0070, PHYS0160 (or PHYS0050, PHYS0060) and PHYS2070; MATH0180 and MATH0200 or MATH0350.