AP 50A is the first half of a year-long, team- and project-based introduction to physics focusing on the application of physics to real-world problems. The AP 50A and B sequence, designed for engineering and physics concentrators, is equivalent in content and rigor to a standard calculus-based introductory physics course sequence. Lectures and exams are replaced by interactive, hands-on, and collaborative learning activities that will not only help you master physics concepts and hone your scientific reasoning and problem-solving skills, but also grow your capacity for self-directed learning and develop your collaborative skills.

Course Content: Kinematics, mechanics, waves

AP 50B is the second half of a year-long, team- and project-based introduction to physics focusing on the application of physics to real-world problems. The AP 50A and B sequence, designed for engineering and physics concentrators, is equivalent in content and rigor to a standard calculus-based introductory physics course sequence. Lectures and exams are replaced by interactive, hands-on, and collaborative learning activities that will not only help you master physics concepts and hone your scientific reasoning and problem-solving skills, but also grow your capacity for self-directed learning and develop your collaborative skills.

Course Content: Electromagnetism and optics

The physics of crystalline solids and their electric, magnetic, optical, and thermal properties. Designed as a first course in solid-state physics. Topics: free electron model; Drude model; the physics of crystal binding; crystal structure and vibration (phonons); x-ray diffraction; electrons in solids (Bloch theorem) and electronic band structures; metals and insulators; semiconductors (and their applications in pn junctions and transistors); magnetism; superconductivity.

Select topics in materials chemistry, focusing on chemical bonds, crystal chemistry, organic and polymeric materials, hybrid materials, surfaces and interfaces, self-assembly, electrochemistry, biomaterials, and bio-inspired materials synthesis.

Single-molecule biophysics is a vibrant research field within the Quantitative Biology umbrella that has grown substantially over the past ~30 years. The impact of single-molecule biophysics has been significant in terms of not only the experimental and theoretical methods that have been developed, but also the scientific insights in biological and soft matter science that these tools have generated. This new course will cover the motivation behind single-molecule measurements in biology and, for the majority of the time, focus on discussing state-of-the-art experimental and computational techniques in single-molecule measurements as well as the key biological discoveries that they have enabled.

This course covers theoretical background and practical hands-on applications of modern computational atomistic methods used to understand and design properties of advanced functional materials. Topics include classical interatomic potentials and machine learning methods, quantum first-principles electronic structure models based on wave functions and density functional theory, Monte Carlo sampling and molecular dynamics simulations of phase transitions and free energies, fluctuations and transport properties. Applications include atomistic and electronic effects in materials for energy conversion and storage, catalysis, alloys, polymers, and low-dimensional materials.

The course introduces various aspects of quantum science, including quantum computing, quantum simulation, quantum communication and quantum metrology. It will particularly focus on the presentation of different experimental platforms currently used in the field and include superconducting qubits, trapped ions, neutral atoms, defects in solids, photons, among others. The course will cover an introduction of the general goals and essential prerequisites for these platforms; it will elucidate their operational principles and highlight some of their most significant and recent achievements, as well as the main challenges in their development.

Basic principles of statistical physics with applications including: the equilibrium properties of classical and quantum gases; phase diagrams, phase transitions and critical points, as illustrated by the gas-liquid transition and simple magnetic models; Bose-Einstein condensation.

This course focuses on the modern applications of Statistical Mechanics. We will learn the basics of information theory, coding and compression. We will next learn about Bayesian Inference, priors and maximizing entropy, which will naturally lead us to regularization and compressed sensing. We will then cover learning: support vector machines, vc dimension, supervised, reinforcement and unsupervised learning. These topics, which build on each other, will be taught using examples in the primary literature with an emphasis on applying the framework we develop. Applications will be taught through problems in genomics, neuroscience, geophysics, and engineering.

Lectures and laboratory instruction on transmission electron microscopy (TEM) and Cs corrected, aberration-correction microscopy and microanalysis. Lab classes include; diffraction, dark field imaging, X-ray spectroscopy, electron energy-loss spectroscopy, atomic imaging, materials sample preparation, polymers, and biological samples.

AP295a is an introductory graduate level course in solid-state physics. Lattices and symmetries. Phonons and electronic structure of crystals. Metals, semiconductors, and insulators will be covered. Electrical, optical, and thermal properties of solids will be treated based on an atomic scale picture and using the independent electron approximation. Additional topics selected from the integer quantum hall effect, an introduction to topological insulators with edge states and the theory of interacting electrons.

A course on the application of the principles of many-particle quantum mechanics to the properties of solids. The objective is to make students familiar with the tools of second quantization and diagrammatic perturbation theory, while describing the theory of the electron liquid, the BCS theory of superconductivity, and theory of magnetism in metals and insulators. Modern topics on correlated electron systems will occupy the latter part of the course.

Concepts of condensed matter physics are applied to the science and technology of beyond-CMOS devices, in particular, mesoscale, low-dimensional, and superconducting devices. Topics include: quantum dots/wires/wells and two-dimensional (2D) materials; optoelectronics with confined electrons; conductance quantization, Landauer-Buttiker formalism, and resonant tunneling; magneto oscillation; integer and fractional quantum Hall effects; Berry phase and topology in condensed matter physics; various Hall effects (anomalous, spin, valley, etc.); Weyl semimetal; topological insulator; spintronic devices and circuits; collective electron behaviors in low dimensions and applications; Cooper-pair boxes and superconducting quantum circuits.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

This course is an introduction to the foundations of quantum mechanics, with specific focus on the basic principles involved in the control of quantum systems. Experimental foundations of quantum mechanics. Superposition principle, Schrödinger’s equation, eigenvalue and time dependent problems, wave packets, coherent states; uncertainty principle. One dimensional problems: double well potentials, tunneling and resonant tunneling; WKB approximation. Hermitian operators and expectation values; time evolution and Hamiltonian, commutation rules, transfer matrix methods. Crystals, Bloch theorem, superlattices. Angular momentum, spin, Pauli matrices. Coherent interaction of light with two-level systems. Quantization of the EM field, spontaneous and stimulated emission; qubits, entanglement, teleportation. Taking this course meets the quantum mechanics core course requirement for the Applied Physics model programs.

The focus is on the foundations of optics/photonics and on some of its most important modern developments and applications. Powerful and widely used computational tools will be developed in the sections. Topics to be covered: Maxwell's equations, Free space optics. Reflection, refraction, polarization (Jones Calculus and Stokes parameters); interference and diffraction. Light-matter interaction, dispersion and absorption. Guided wave optics (including optical fibers). Perturbation and couple mode theory, transfer matrix methods; numerical methods. Optical resonators.  Photonic crystals. Near-field optics. Metal optics and Plasmonics. Metamaterials and Metasurfaces.

This course is an introduction to the foundations of quantum mechanics, with specific focus on the basic principles involved in the control of quantum systems. Experimental foundations of quantum mechanics. Superposition principle, Schrödinger’s equation, eigenvalue and time dependent problems, wave packets, coherent states; uncertainty principle. One dimensional problems: double well potentials, tunneling and resonant tunneling; WKB approximation. Hermitian operators and expectation values; time evolution and Hamiltonian, commutation rules, transfer matrix methods. Crystals, Bloch theorem, superlattices. Angular momentum, spin, Pauli matrices. Coherent interaction of light with two-level systems. Quantization of the EM field, spontaneous and stimulated emission; qubits, entanglement, teleportation.

Taking this course meets the quantum mechanics core course requirement for the Applied Physics model programs.