A216 Quantum Mechanics I, preferably also A217 Quantum Mechanics II

Companion course to A218 Condensed Matter

Advanced course in Quantum Mechanics, based on recent theoretical and experimental advances. Evolution in Hilbert space and quantum bits; conditional quantum dynamics; quantum simulations; quantum Fourier transform and quantum search algorithms; ion-trap and NMR experiments; quantum noise and master equations; Hilbert space distances; Von Neumann entropy; Holevo bound; entanglement as a physical resource; quantum cryptography; lab: quantum eraser, interaction free measurement.

A216 Quantum Mechanics I, and A217 Quantum Mechanics II

companion course to A203 Advanced Optics, A210 Advanced Quantum Mechanics, A273 Ultracold Quantum Gases

Advanced level course in atomic physics. Progress in laser control of atoms has led to the creation of Bose-Einstein condensates, ultrafast time and frequency standards and the ability to develop quantum technologies. In this course we will cover the essentials of atomic physics including resonance phenomena, atoms in electric and magnetic fields, and light-matter interactions. This leads to topics relevant in current research such as laser cooling and trapping.

Either A202 Fluid Dynamics or B13 Fluid Mechanics

The interface between engineering and miniaturization is among the most intriguing and active areas of inquiry in modern technology. The aim of this course is to illuminate and explore microfluidics as an interdisciplinary research area, with an emphasis on emerging microfluidics disciplines, including molecular assembly to bulk and device level scales, with applications in novel materials synthesis, bio-microtechnology and nanotechnology.

In this course, students will learn basic principles of electrochemistry with a particular focus on redox behavior of transition metals including metalloproteins. Modern research in application of transition metal complexes for renewable energy storage and production will be highlighted and discussed in detail, including metal-catalyzed water oxidation, proton reduction and CO2 reduction processes. The course will provide practical training in voltammetric techniques and spectroelectrochemistry, and analysis and simulation of cyclic voltammetry data.

In this course, students will learn basic principles of nucleic acid chemistry and engineering through lectures and discussions. The students will then use the basic knowledge to deepen their understanding of the current research in the field of nucleic acid chemistry and engineering. Finally, the students will design, construct, and characterize functional nucleic acids in the laboratory while learning basic experimental skills to manipulate nucleic acids.

Materials chemistry is emerging as an interdisciplinary field that involves knowledge from diverse science and engineering research fields. The recent public attention and enthusiasm on nanoscience and nanotechnology not only underscores the importance of interdisciplinary research, but also highlights the promises of materials chemistry. The development of modern chemistry allows chemists to precisely control the three-dimension arrangement of many atoms for developing novel materials.

Students who take the course are expected to be familiar with general topics in Classical Mechanics, Electrodynamics and Calculus.

This is a two-term graduate course that covers most of the essential topics of modern nonrelativistic quantum mechanics. The course is primarily intended for graduate students with background in Physics.

Students who take the course are expected to be familiar with general topics in Classical Mechanics, Electrodynamics and Calculus. This course requires a pass in Quantum Mechanics I.

This is a two-term graduate course that covers most of the essential topics of modern nonrelativistic quantum mechanics. The course is primarily intended for graduate students with background in Physics.

Students are required to have basic understanding of quantum mechanics (e.g., A216 QM I and A217 QM II), and basic concepts of statistics.

Condensed matter physics is both old fashioned (originated from solid state physics in 1950’s or even metal physics in 1920’s) and also new style (with emphasis on collective behaviour, symmetry, and topological conditions). Over the past century, this sub-field of physics has grown into a monstrous size with various ramifications such that any offered perspective would always be partial and biased. Here this class will be served at the introduction level, and at a few places, I will try to demonstrate how to evolve from fundamental concepts to perspectives of advanced topics.

Prerequisites: Maxwell’s equations in differential form. Solving Maxwell’s equations to obtain electromagnetic waves. Linear algebra of vectors and matrices.

We begin by introducing tensors in non-relativistic physics. We then give an overview of Special Relativity, and discuss the special nature of gravity as an “inertial force”. With this motivation, we develop the differential geometry necessary to describe curved spacetime and the geodesic motion of free-falling particles. We then proceed to Einstein’s field equations, which we analyze in the Newtonian limit and in the linearized limit (gravitational waves).