Upper-Division

Topics in quantum physics including the Schrodinger equation; angular momentum and spin; the Pauli exclusion principle; and quantum statistics. Applications in multi-electron atoms and molecules, and in solid-state, nuclear, and particle physics.

Particle dynamics in one, two, and three dimensions. Conservation laws. Small oscillations, Fourier series and Fourier integral solutions. Phase diagrams and nonlinear motions, Lagrange's equations, and Hamiltonian dynamics.

Examines electrostatics, including the electric field, potential, solutions to Laplace's and Poisson's equations, and work and energy; electricity in matter (conductors, dielectrics); magnetostatics, including the magnetic field and vector potential, Ampere's and Faraday's laws; magnetism in matter; and Maxwell's equations.

Examines electromagnetic waves, including absorption and dispersion, reflection and transmission, and wave guides; conservation laws and gauge invariance; time-dependent vector and scalar potentials and application to radiation of charges and antennae; and electrodynamics and relativity.

Consequences of the first and second laws of thermodynamics, elementary statistical mechanics, thermodynamics of irreversible processes.

This course applies efficient numerical methods to the solutions of problems in the physical sciences which are otherwise intractable. Examples will be drawn from classical mechanics, quantum mechanics, statistical mechanics, and electrodynamics. Students apply a high-level programming language, such as Python, to the solution of physical problems and develop appropriate error and stability estimates.

Infinite series, topics in linear algebra including vector spaces, matrices and determinants, systems of linear equations, eigenvalue problems and matrix diagonalization, tensor algebra, and ordinary differential equations.

Fourier series and transforms, Dirac-delta function, Green's functions, series solutions of ordinary equations, Legendre polynomials, Bessel functions, sets of orthogonal functions, and partial differential equations.

Complex functions, complex analysis, asymptotic series and expansions, special functions defined by integrals, and probability and statistics. (Formerly offered as PHYS 116B.)

Statistical properties polymers; scaling behavior, fractal dimensions; random walks, self avoidance; single chains and concentrated solutions; dynamics and topological effects in melts; polymer networks; sol-gel transitions; polymer blends; application to biological systems; computer simulations will demonstrate much of the above. Students cannot receive credit for this course and PHYS 240.

The standard model of particle physics; physics beyond the standard model; neutrino physics; the early universe; dark matter and dark energy; selected topics in general relativistic cosmology and high-energy astrophysics. (Formerly Nuclear and Particle Astrophysics.)

Demonstration of phenomena of classical and modern physics. Development of a familiarity with experimental methods. Special experimental projects may be undertaken by students in this laboratory.

Individual experimental investigations of basic phenomena in atomic, nuclear, and solid state physics.

Introduction to the techniques of modern observational astrophysics at optical and radio wavelengths through hands-on experiments. Offered in some academic years as a multiple-term course: PHYS 135A in fall and PHYS 135B in winter, depending on astronomical conditions.

Introduction to techniques of modern observational astrophysics at optical and radio wavelengths through hands-on experiments. Intended primarily for juniors and seniors majoring or minoring in astrophysics. Offered in some academic years as single-term course PHYS 135 in fall, depending on astronomical conditions.

Introduction to techniques of modern observational astrophysics at optical and radio wavelengths through hands-on experiments. Intended primarily for juniors and seniors majoring or minoring in astrophysics. Offered in some academic years as single-term PHYS 135 in fall, depending on astronomical conditions.

Application of advanced optical techniques to the study of problems in astrophysics, physics, chemistry, biology, and engineering. Techniques include interferometry, Fourier optics, adaptive optics, optical tweezers, photon correlation spectroscopy, optical pumping, laser spectroscopy, and more.

Basic principles and mathematical techniques of nonrelativistic quantum mechanics: Schrodinger equation and Dirac notation; one-dimensional systems, including the free particle and harmonic oscillator; three-dimensional problems with spherical symmetry; angular momentum; hydrogen atom; spin; identical particles and degenerate gases.

Approximation methods in nonrelativistic quantum mechanics: time-independent perturbation theory (non-degenerate and degenerate) and addition of angular momenta; variational methods; the WKB approximation; time-dependent perturbation theory and radiation theory; scattering theory.

Review of linear algebra. Includes basic concepts in quantum mechanics including quantum states, measurements, operators, entanglement, entanglement entropy, "no cloning" theorem, and density matrices; classical gates, reversible computing, and quantum gates; several quantum algorithms including Deutsch's algorithm, Simon's algorithm, Shor's algorithm, and the Grover algorithm; quantum error correction; and quantum key distribution and teleportation.

Review of select topics in statistical physics including information theory, entropy, coupled systems, phase transitions, and symmetry breaking. Introduction to multivariate algorithms, with an emphasis on their foundations in statistical physics and classical mechanics. Notebooks, data preparation, cross-validation, supervised and unsupervised learning. Practical considerations for training and optimizing neural networks and related tools. (Formerly offered as Neural Networks, Statistical Physics and Computing.)

Quantum mechanics in solid-state materials plays a fundamental role in the development of quantum computation and sustainable technologies, as well as the search for fundamental physics beyond the Standard Model. This course introduces the quantum physics of semiconductors and low-dimensional materials (such as graphene), with emphasis on applications to transistors for logic operations, p-n junctions for photovoltaic cells and particle detection, as well as quantum dots for qubits. (Formerly Applications of Solid State Physics.)

The fundamentals of quantum materials are revamped by incorporating the geometric Berry phase and the topology of quantum wave functions. The traditional solid-state phenomena of superconductivity and magnetism are taught from a cutting-edge topological perspective, to understand phenomena such as the quantum Hall effect and emergent Majorana fermions. Applications of topological quantum materials range from spintronics to quantum information and computation. (Formerly offered as PHYS 155, Solid State Physics.)

Provides a practical knowledge of analog electronics that experimentalists generally need in research, including basic circuits with bipolar and field-effect transistors, op-amps, comparators, oscillators, and voltage regulators. It assumes no previous knowledge of electronics but includes twice-weekly lectures with some homework assignments, including small circuit simulations done using PSpice. However, with the aid of the instructor and teaching assistant, the students are expected to learn mainly through the construction, debugging, and analysis of small electronics projects.

Special relativity is reviewed. Curved space-time, including the metric and geodesics, are illustrated with simple examples. The Einstein equations are solved for cases of high symmetry. Black-hole physics and cosmology are discussed, including recent developments.

Physical principles and techniques used in biology: X-ray diffraction; nuclear magnetic resonance; statistics, kinetics, and thermodynamics of macromolecules; viscosity and diffusion; DNA/RNA pairing; electrophoresis; physics of enzymes; biological energy conversion; optical tweezers.

Develops the writing skills necessary to prepare professional publications: how to structure a physics article; write for a specific audience with clarity, precision, and concision; and deliver a short informal presentation. Additionally, students become familiar with the peer review process and the ethics of the publication process.

Designed to provide upper-division undergraduates with an opportunity to work with students in lower division courses, leading discussions, reading and marking submissions, and assisting in the planning and teaching of a course. Prerequisite(s): excellent performance in major courses; instructor approval required; enrollment restricted to senior physics majors.

Teaching of a lower-division seminar under faculty supervision. (See PHYS 42.) Prerequisite(s): upper-division standing; submission of a proposal supported by a faculty member willing to supervise.

Independent research for seniors conducted under the supervision of a faculty mentor. Students develop a written research proposal, thesis outline, and introductory material. Prerequisite(s): Entry Level Writing and Composition requirements. Enrollment is restricted to senior applied physics, physics, and physics (astrophysics) majors.

Independent research for seniors conducted under the supervision of a faculty mentor. Students prepare an oral presentation of their results, and they submit a written senior thesis on their research topic. Prerequisite(s): Entry Level Writing and Composition requirements. Enrollment is restricted to senior applied physics, physics, and physics (astrophysics) majors.

Students submit petition to sponsoring agency.

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