Cornell University Registrar

Lasers have had an enormous impact on communications, medicine, remote sensing, and material processing. This course reviews the properties of light that are essential to understanding the underlying principles of lasers and these photonic technologies. There also is a strong, hands-on laboratory component in which the students build and operate a nitrogen laser and participate in several demonstration experiments such as holography, laser processing of materials, optical tweezers, and fiber optics.

Lecture/laboratory course designed to introduce first-year students to some of the ideas and concepts of nanoscience and nanotechnology with stronger emphasis on nanobiotechnology in the spring semester. Topics include nanoscience and nanotechnology-what they are and why they are of interest; atoms and molecules; the solid state; surfaces; behavior of light and material particles when confined to nanoscale dimensions; scanning tunneling microscopy (STM), atomic force microscopy (AFM), scanning electron microscopy (SEM); microelectromechanical systems (MEMS) design; basic micromachining and chemical synthesis methods, i.e., top-down and bottom-up approaches to nanofabrication; how to manipulate structures on the nanoscale; physical laws and limits they place on the nanoworld; some far-out ideas. In the laboratory, students construct a simple STM to record atomic resolution images; learn through hands on experience the basic workings of an SEM; use a MEMS computer-aided design software package to model the entire manufacturing sequence of a simple MEMS device, examine the simulated behavior of the device and compare it with real behavior; investigate the optical properties of quantum dots and the unexpected properties of fluids that flow through narrow channels.

Second in a three semester introductory physics sequence. Explores quantitative modeling of the physical world through a study of electricity and magnetism. More mathematical and abstract than a typical introductory electricity and magnetism course. Topics include electrostatics, behavior of matter in electric fields, circuits, magnetic fields, Faraday's law, AC circuits, and electromagnetic waves. Makes substantial use of vector calculus. At the level of Electricity and Magnetism by Purcell.

Introduces the physics of biological macromolecules (e.g., proteins, DNA, RNA) to students of the physical sciences or engineering who have little or no background in biology. The macromolecules are studied from three perspectives. First, the biological role or function of each class of macromolecules is considered. Second, a quantitative description of the physical interactions that determine the behavior of biomolecular systems. An introduction is provided to probability and statistical methods used to describe the behavior of biological systems. Finally, techniques that are commonly used to probe these systems, with an emphasis on biotechnology applications, are discussed.

This course examines the physical hardware of quantum information processing, quantum communication, and quantum sensing technologies. Topics include an analysis of qubit attributes and an introduction to the operational principles of physical qubits. Specific systems will include photonic circuits, trapped ions, superconducting quantum circuits, isolated solid-state spins and quantum dots.

An introduction to quantum computing for students who have not necessarily had prior exposure to quantum mechanics. This course is intended for physicists, electrical engineers, and computer scientists. Topics include: foundational algorithmic building blocks and quantum algorithms; variational quantum algorithms (for physics simulation and for combinatorial optimization); quantum machine learning; basic physics of quantum computing hardware implementation. There will be substantial programming exercises implementing quantum algorithms to run on simulators and quantum computers in the cloud.

Covers review of vector analysis, tensor calculus, Dirac Delta functions, complex variable theory, Cauchy-Rieman conditions, complex Taylor and Laurent series, Cauchy integral formula and residue techniques, conformal mapping, calculus of variations, Fourier Series.

Newtonian mechanics, especially with dissipative forces; objects rotating around a constant direction and possibly translating, using both torque and energy; coupled and damped-driven linear oscillations and an introduction to nonlinear systems; an introduction to variational calculus; Lagrangian and Hamiltonian formalism for generalized coordinates; central-force motion and a brief introduction to scattering; non-inertial reference systems; 3D motion of rigid bodies. (At the level of Classical Dynamics by Marion and Thornton and Classical Mechanics by John Taylor).

Intermediate-level course on electromagnetic theory with a focus on statics. Vector calculus, electrostatics, conductors, dielectric materials, boundary conditions, solutions to Laplace's equation, magnetostatics, quasistatic conditions, Maxwell equations, Poynting theorem, Maxwell Stress tensor, EM wave, polarization, energy, momentum. Emphasis is on developing proficiency with analytical techniques and intuitive understanding of fundamental electromagnetism.

Applied Group Theory. Focus is on the symmetry of geometrical objects, both as abstract objects (up to an isomorphism) and embedded in a physical space (up to a conjugation) such as the Crystallographic Groups. Topics will include: Group Actions (on Sets & Vector Spaces), Numbers & Groups, Permutations & the Symmetric Group, Orbit-Stabilizer Theorem, Regular Objects in 2d/3d & the Platonic solids, applications to problems in physics.

Second course in theory of electromagnetism: Magnetic materials, Faraday's law, Maxwell equations, electromagnetic waves, reflection and transmission, guided waves, and radiation.

Introductory course in quantum mechanics. Topics include Schrodinger's equation and the statistical interpretation of the wavefunction, potentials in 1 to 3 dimensions, Dirac notation and Hilbert space, ladder operators for harmonic potentials and angular momentum, exact solutions for the hydrogen atom and spin systems. Emphasis is on developing both an intuitive understanding of quantum mechanics and how to apply it rigorously.

Continuation of AEP 3610 covering more advanced material in quantum mechanics. Topics include operator formalism and matrix representation, angular momentum and spin, the hydrogen atom, techniques for solving Schrodinger's equation including perturbation theory, two- and three-level systems, interaction with radiation, and identical particles.

Practical electronics as encountered in a scientific or engineering research/development environment. Analyze, design, build, and test circuits using discrete components and integrated circuits. Analog circuits: resistors, capacitors, operational amplifiers, feedback amplifiers, oscillators, comparators, passive and active filters, diodes, and transistor switches and amplifiers. Digital circuits: combinational and sequential logic (gates, flipflops, registers, counters, timers), analog to digital (ADC) and digital to analog (DAC) conversion, signal averaging, and computer architecture and interfacing. Additional topics may include analog and digital signal processing, light wave communications, transducers, noise reduction techniques, and computer-aided circuit design. At the level of Art of Electronics by Horowitz and Hill.

A hands-on introduction to modern applied physics computer-aided experimental design with weekly laboratory-based problem solving culminating in the development and use of an automated laser scanning microscope system. Students learn fundamentals of the theory and practice of computer-aided control of equipment and data acquisition in an applied physics laboratory. Topics include introductory optical microscopy, analog-to-digital conversion and digital-to-analog conversion, hardware timing, error in digital systems, discrete Fourier analysis and sampling theorem. Data analysis is performed primarily using MATLAB or Python and instrument interfacing is using LabVIEW and serial communication protocols. (No prior knowledge of LabVIEW is required; LabVIEW basics will be learned through weekly laboratory activities rather than by formal instruction.) This course means to introduce students to the practice of scientific and engineering R&D, which includes stages of design, experimentation, and the communication of knowledge gained. Students will develop effective writing and communication skills both as a tool for practicing engineering design and for the dissemination of knowledge through a formal article.

Introduces the fundamental concepts of nuclear science and engineering, including nuclear structure, radioactivity, nuclear reactions and the interaction of neutrons, charged particles, x-rays and gamma-rays with matter. Discusses the neutron chain reaction and its control in the core of a fission reactor. Different reactor designs are introduced and discussed along with their safety features. Other topics include radiation shielding and aspects of the nuclear fuel cycle, including isotope separation, fuel reprocessing, waste disposal and sustainability

Covers Fourier and Laplace transforms, ordinary and partial differential equations, separation of variables, Method of Frobenius, Laplace transform techniques. Green's functions, wave and diffusion equations, Solutions to Laplace's Equation, Hermitian Operators, Sturm-Liouville operators, Bessel functions, Legendre Polynomials, spherical harmonics.

Quantum statistical basis for equilibrium thermodynamics, microcanonical, canonical and grand canonical ensembles, and partition functions. Classical and quantum ideal gases, paramagnetic and multiple-state systems. Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics and applications. Introduction to systems of interacting particles. At the level of Introductory Statistical Mechanics by Bowley and Sanchez.

Covers integral equations, Friedholm equations, kernels, complex variable theory, branch points and cuts, Riemann sheets, method of steepest descent, method of constant phase, tensors, contravariant and covariant representations, group theory, matrix representations, class and character.

Intro to elasticity (including stress and strain tensors and their linear relations for isotropic materials), very brief intro to plastic deformation, fluid properties and some hydrostatics, conservation laws with applications (including pipes), dimensional analysis, vorticity, ideal flow (including forms of Bernoulli equations and potential flow), flow past objects (including boundary layers, drag, lift, and model aerofoils), instabilities, a brief introduction to turbulence (including Reynolds stress from time averaging), some topics in compressible flow (including choking and shock waves).

Introduction to Numerical computation (e.g., derivatives, integrals, differential equations, matrices, boundary-value problems, FFT's, Monte Carlo methods) as applied to engineering physics problems that cannot be solved analytically (e.g., chaotic systems, three-body problem, electrostatic fields, quantum energy levels). C/C++ computer programming required (some Matlab, Python, etc.). Some prior exposure to programming assumed but no previous experience with C/C++ assumed.

Introduction to the fundamentals of the interaction of laser light with matter, including a survey of phenomena and photonic devices based on these processes with relevance to modern science and technology. Topics include the origins of optical nonlinearities, propagation of laser beams and ultrashort pulses, harmonic generation, parametric amplification, nonlinearly guided waves and self-focusing, solitons, spontaneous and stimulated scattering, optical resonance and two-level atoms, multiphoton processes, and ultra-intense laser-matter interactions.

Introductory Senior-level course on electromagnetic and optical metamaterials. The properties of matter can be molded and tailored on subwavelength spatial scales yielding 'metamaterials' with properties very different from naturally occurring materials, thereby opening up new directions for applications. The course introduces the electromagnetic and optical properties of surface plasmons and polaritons, artificial magnetic materials, negative-index materials, nanostructured optical materials, etc. The course also discusses the applications of these materials in diverse areas including electromagnetic cloaking and invisibility, stealth technologies, optical super-lensing, bio-chemical sensing, conformal optics, meta-surfaces, and non-reciprocal devices.

Introduction to the physics of crystalline solids. Covers crystal structures; diffraction; electronic states and density functional theory; lattice vibrations; and metals, insulators, and semiconductors. Covers optical properties, magnetism, and superconductivity as time allows. The majority of the course addresses the foundations of the subject, but time is devoted to modern and/or technologically important topics such as quantum size effects. At the level of Introduction to Solid State Physics by Kittel or Solid State Physics by Ashcroft and Mermin.

Overview of the diversity of modern biophysical experimental techniques used in the study of biophysical systems at the molecular, cellular, and population level. Emphasis is placed on groundbreaking methods behind recent Nobel Prizes and other techniques likely to be encountered in cutting-edge research and industry. Topics include: 1) super-resolution, multi-photon, and single molecule microscopy, 2) crystallography and structural biology methods used to characterize DNA, RNA, proteins, cells, tissues, 3) microfluidics, lab-on-a-chip, and single cell culture techniques, 4) molecular dynamics simulations, stochastic modeling, and physical models of a cell, and 5) next-generation sequencing, protein engineering, synthetic biology, genome editing, and other experimental techniques at the intersection of applied physics and biological engineering.

Hardware that exploits quantum phenomena can dramatically alter the nature of computation. Though constructing a general purpose quantum computer remains a formidable technological challenge, there has been much recent experimental progress. In addition, the theory of quantum computation is of interest in itself, offering new perspectives on the nature of computation and information, as well as providing novel insights into the conceptual puzzles posed by quantum theory. This course is intended for physicists, unfamiliar with computational complexity theory or cryptography, and for computer scientists and mathematicians with prior exposure to quantum mechanics. Topics include: simple quantum algorithms, error correction, cryptography, teleportation, and uses of quantum computing devices either currently available or to be available in the near future.

Introduction to the physical principles and various engineering aspects underlying power generation by controlled fusion. Topics include: fuels and conditions required for fusion power and basic fusion-reactor concepts, fundamental aspects of plasma physics relevant to fusion plasmas and basic engineering problems for a fusion reactor, and an engineering analysis of proposed magnetic and/or inertial confinement fusion-reactor designs.

Laboratory or theoretical work in any branch of engineering physics under the direction of a member of the faculty. The study can take a number of forms; for example, design of laboratory apparatus, performance of laboratory measurements, computer simulation or software developments, theoretical design and analysis. Details TBD with respective faculty member.

Laboratory or theoretical work in any branch of engineering physics under the direction of a member of the faculty. The study can take a number of forms; for example, design of laboratory apparatus, performance of laboratory measurements, computer simulation or software developments, theoretical design and analysis. A written report, an oral presentation and at least a grade of A- is required for successful completion of the Engineering Physics honors requirement.

Covers review of vector analysis, tensor calculus, Dirac Delta functions, complex variable theory, Cauchy-Rieman conditions, complex Taylor and Laurent series, Cauchy integral formula and residue techniques, conformal mapping, calculus of variations, Fourier Series.

Covers Fourier and Laplace transforms, ordinary and partial differential equations, separation of variables, Method of Frobenius, Laplace transform techniques. Green's functions, wave and diffusion equations, Solutions to Laplace's Equation, Hermitian Operators, Sturm-Liouville operators, Bessel functions, Legendre Polynomials, spherical harmonics.

Quantum statistical basis for equilibrium thermodynamics, microcanonical, canonical and grand canonical ensembles, and partition functions. Classical and quantum ideal gases, paramagnetic and multiple-state systems. Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics and applications. Introduction to systems of interacting particles. At the level of Introductory Statistical Mechanics by Bowley and Sanchez.

Covers integral equations, Friedholm equations, kernels, complex variable theory, branch points and cuts, Riemann sheets, method of steepest descent, method of constant phase, tensors, contravariant and covariant representations, group theory, matrix representations, class and character.

An introduction to quantum computing for students who have not necessarily had prior exposure to quantum mechanics. This course is intended for physicists, electrical engineers, and computer scientists. Topics include: foundational algorithmic building blocks and quantum algorithms; variational quantum algorithms (for physics simulation and for combinatorial optimization); quantum machine learning; basic physics of quantum computing hardware implementation. There will be substantial programming exercises implementing quantum algorithms to run on simulators and quantum computers in the cloud.

Newtonian mechanics, especially with dissipative forces; objects rotating around a constant direction and possibly translating, using both torque and energy; coupled and damped-driven linear oscillations and an introduction to nonlinear systems; an introduction to variational calculus; Lagrangian and Hamiltonian formalism for generalized coordinates; central-force motion and a brief introduction to scattering; non-inertial reference systems; 3D motion of rigid bodies. (At the level of Classical Dynamics by Marion and Thornton and Classical Mechanics by John Taylor).

Intro to elasticity (including stress and strain tensors and their linear relations for isotropic materials), very brief intro to plastic deformation, fluid properties and some hydrostatics, conservation laws with applications (including pipes), dimensional analysis, vorticity, ideal flow (including forms of Bernoulli equations and potential flow), flow past objects (including boundary layers, drag, lift, and model aerofoils), instabilities, a brief introduction to turbulence (including Reynolds stress from time averaging), some topics in compressible flow (including choking and shock waves).

Introduction to Numerical computation (e.g., derivatives, integrals, differential equations, matrices, boundary-value problems, FFT's, Monte Carlo methods) as applied to engineering physics problems that cannot be solved analytically (e.g., chaotic systems, three-body problem, electrostatic fields, quantum energy levels). C/C++ computer programming required (some Matlab, Python, etc.). Some prior exposure to programming assumed but no previous experience with C/C++ assumed.

Introduction to the fundamentals of the interaction of laser light with matter, including a survey of phenomena and photonic devices based on these processes with relevance to modern science and technology. Topics include the origins of optical nonlinearities, propagation of laser beams and ultrashort pulses, harmonic generation, parametric amplification, nonlinearly guided waves and self-focusing, solitons, spontaneous and stimulated scattering, optical resonance and two-level atoms, multiphoton processes, and ultra-intense laser-matter interactions.

Can an electric vehicle be made cheaper than a gasoline one with comparable range? How much of our energy needs can be supplied by solar energy? What is the maximum efficiency of a solar cell? Graduate-level analysis of renewable energy devices and materials that you will likely encounter in research or advanced industrial settings, with a goal of understanding their ultimate limits, current efficiencies and opportunities for improvement. The main emphasis is on electrical energy creation, conversion and storage devices - Solar Cells, Fuel Cells, Batteries, Supercapacitors and Thermoelectrics, which are areas of current research at Cornell.

Introduction to the physics of crystalline solids. Covers crystal structures; diffraction; electronic states and density functional theory; lattice vibrations; and metals, insulators, and semiconductors. Covers optical properties, magnetism, and superconductivity as time allows. The majority of the course addresses the foundations of the subject, but time is devoted to modern and/or technologically important topics such as quantum size effects. At the level of Introduction to Solid State Physics by Kittel or Solid State Physics by Ashcroft and Mermin.

A self-contained pedagogical introduction to Groups acting-on things like sets, modules, vector spaces, manifolds, and other groups, and to the Morphisms and Equivariant Functions between them. The course will intertwine ideas on the Structure of (mostly finite-order) Groups with those on their Representation, making judicious use of Equivalence Relations throughout. In contrast to the usual pedagogy, we will organize the course around the question of where do groups live in physics. Specific examples will vary from year to year but include: Translational and Rotational Symmetry - Isometry, orbits & stabilizers; gauges, wavefunctions, & boundary conditions - U(1) and its finite-order Cyclic subgroups, Character Theory & the Group Algebra; Bloch & Wannier Functions - Morphisms b/w group actions, Pontryagin Duality; Molecules & Bonding - Point Groups, Permutation& Induced Reps; Selection Rules & Tensors - Irreps & Schur's Lemma; Spin-1/2 and Angular Momentum - Complex Numbers, Quaternions, Projective Spaces, groups acting on n-Spheres & Covers.

Intermediate-level course on electromagnetic theory with a focus on statics. Vector calculus, electrostatics, conductors, dielectric materials, boundary conditions, solutions to Laplace's equation, magnetostatics, quasistatic conditions, Maxwell equations, Poynting theorem, Maxwell Stress tensor, EM wave, polarization, energy, momentum. Emphasis is on developing proficiency with analytical techniques and intuitive understanding of fundamental electromagnetism.

Applied Group Theory. Focus is on the symmetry of geometrical objects, both as abstract objects (up to an isomorphism) and embedded in a physical space (up to a conjugation) such as the Crystallographic Groups. Topics will include: Group Actions (on Sets & Vector Spaces), Numbers & Groups, Permutations & the Symmetric Group, Orbit-Stabilizer Theorem, Regular Objects in 2d/3d & the Platonic solids, applications to problems in physics.

Second course in theory of electromagnetism: Magnetic materials, Faraday's law, Maxwell equations, electromagnetic waves, reflection and transmission, guided waves, and radiation.

Introductory course in quantum mechanics. Topics include Schrodinger's equation and the statistical interpretation of the wavefunction, potentials in 1 to 3 dimensions, Dirac notation and Hilbert space, ladder operators for harmonic potentials and angular momentum, exact solutions for the hydrogen atom and spin systems. Emphasis is on developing both an intuitive understanding of quantum mechanics and how to apply it rigorously.

Continuation of AEP 5610 covering more advanced material in quantum mechanics. Topics include operator formalism and matrix representation, angular momentum and spin, the hydrogen atom, techniques for solving Schrodinger's equation including perturbation theory, two- and three-level systems, interaction with radiation, and identical particles.

Overview of the diversity of modern biophysical experimental techniques used in the study of biophysical systems at the molecular, cellular, and population level. Emphasis is placed on groundbreaking methods behind recent Nobel Prizes and other techniques likely to be encountered in cutting-edge research and industry. Topics include: 1) super-resolution, multi-photon, and single molecule microscopy, 2) crystallography and structural biology methods used to characterize DNA, RNA, proteins, cells, tissues, 3) microfluidics, lab-on-a-chip, and single cell culture techniques, 4) molecular dynamics simulations, stochastic modeling, and physical models of a cell, and 5) next-generation sequencing, protein engineering, synthetic biology, genome editing, and other experimental techniques at the intersection of applied physics and biological engineering.

Overview of the diversity of modern biophysical experimental techniques used in the study of biophysical systems at the molecular, cellular, and population level. Emphasis is placed on groundbreaking methods behind recent Nobel Prizes and other techniques likely to be encountered in cutting-edge research and industry. Topics include: 1) super-resolution, multi-photon, and single molecule microscopy, 2) crystallography and structural biology methods used to characterize DNA, RNA, proteins, cells, tissues, 3) microfluidics, lab-on-a-chip, and single cell culture techniques, 4) molecular dynamics simulations, stochastic modeling, and physical models of a cell, and 5) next-generation sequencing, protein engineering, synthetic biology, genome editing, and other experimental techniques at the intersection of applied physics and biological engineering.

Topics include plasma state; motion of charged particles in fields; drift-orbit theory; coulomb scattering, collisions; ambipolar diffusion; elementary transport theory; two-fluid and hydromagnetic equations; plasma oscillations and waves, CMA diagram; hydromagnetic stability; and elementary applications to space physics, plasma technology, and controlled fusion.

Graduate-level introduction to the tools used to image and probe optical, electronic, chemical, and mechanical properties at the atomic and nano scales.

Independent study under the direction of a member of the university faculty. Students participate in an independent research project through work on a special problem related to their field of interest. A formal and complete research report is required.

Special topics in applied science, with focus on areas of applied physics and engineering that are of current interest. Subjects chosen are presented in a seminar format by the students. A major goal of this course is to provide training and experience planning, preparing, and presenting proposals, progress reports, technical talks, and research papers.

Special topics in applied science, with focus on areas of applied physics and engineering that are of current interest. Subjects chosen are presented in a seminar format by the students. A major goal of this course is to provide training and experience planning, preparing, and presenting proposals, progress reports, technical talks, and research papers.

Hardware that exploits quantum phenomena can dramatically alter the nature of computation. Though constructing a general purpose quantum computer remains a formidable technological challenge, there has been much recent experimental progress. In addition, the theory of quantum computation is of interest in itself, offering new perspectives on the nature of computation and information, as well as providing novel insights into the conceptual puzzles posed by quantum theory. This course is intended for physicists, unfamiliar with computational complexity theory or cryptography, and for computer scientists and mathematicians with prior exposure to quantum mechanics. Topics include: simple quantum algorithms, error correction, cryptography, teleportation, and uses of quantum computing devices either currently available or to be available in the near future.

Thesis research for applied physics graduate students.