### Description

This course covers key topics in the use of quantum mechanics in many modern applications in science and technology, introduces core advanced concepts such as spin, identical particles, the quantum mechanics of light, the basics of quantum information, and the interpretation of quantum mechanics, and covers the major ways in which quantum mechanics is written and used in modern practice. It follows on directly from the QMSE-01 "Quantum Mechanics for Scientists and Engineers" course and is also accessible to others who have studied some quantum mechanics at the equivalent of a first junior or senior college-level physics quantum mechanics course. All of the material for the QMSE-01 course is also provided as a resource. The course should prepare participants well to understand quantum mechanics as it is used in a wide range of current applications and areas and provide a solid grounding for deeper studies of specific more advanced areas.

## Course syllabus

**Quantum mechanics in crystals**

Crystal structures, the Bloch theorem that simplifies quantum mechanics in crystals, and other useful concepts for understanding semiconductor devices, such as density of states, effective mass, quantum confinement in nanostructures, and important example problems like optical absorption in semiconductors, a key process behind all optoelectronics.

**Methods for one-dimensional problems**

How to understand and calculate tunneling current. The transfer matrix technique, a very simple and effective technique for calculating quantum mechanical waves and states.

**Spin and identical particles**

The purely quantum mechanical idea of spin, and how to represent and visualize it. The general ideas of identical particles in quantum mechanics, including fermions and bosons, their properties and the states of multiple identical particles.

**Quantum mechanics of light**

Representing light quantum mechanically, including the concept of photons, and introducing the ideas of annihilation and creation operators.

**Interaction of different kinds of particles**

Describing interactions and processes using annihilation and creation operators for fermions and bosons, including the important examples of stimulated and spontaneous emission that correctly explain all light emitters, from lasers to light bulbs.

**Mixed states and the density matrix**

Introducing the idea of mixed states to describe how quantum mechanical systems interact with the rest of the complex world around us, and the notation and use of the density matrix to describe and manipulate these.

**Quantum measurement and quantum information**

Introducing the no-cloning theorem, quantum cryptography, quantum entanglement and the basic ideas of quantum computing and teleportation, and returning to the idea of measurement in quantum mechanics, including the surprising results of Bell's inequalities.

**Interpretation of quantum mechanics**

A brief introduction to some of the different approaches to the difficult problem of understanding what quantum mechanics really means!

## Prerequisites

The course is designed to build on a first course on quantum mechanics at the junior or senior college level, so students should have at least that background. The material here is specifically matched to follow on from the Stanford Online QMSE-01 "Quantum Mechanics for Scientists and Engineers" class, and all the material from that class is provided as background in the online course materials here. No additional background beyond that class is presumed here.

## Course Staff

**David Miller**is the W. M. Keck Foundation Professor of Electrical Engineering and, by Courtesy, Professor of Applied Physics, both at Stanford University. He received his B. Sc. and Ph. D. degrees in Physics in Scotland, UK from St. Andrews University and Heriot-Watt University, respectively. Before moving to Stanford in 1996, he worked at AT&T Bell Laboratories for 15 years. His research interests have included physics and applications of quantum nanostructures, including invention of optical modulator devices now widely used in optical fiber communications, and fundamentals and applications of optics and nanophotonics. He has received several awards and honorary degrees for his work, holds over 70 US Patents, is a Fellow of many major professional societies in science and engineering, including IEEE, APS, OSA, the Royal Society of London, and the Royal Society of Edinburgh, and is a member of both the National Academy of Sciences and the National Academy of Engineering in the US. He has taught quantum mechanics at Stanford for more than 10 years to a broad range of students ranging from physics and engineering undergraduates to graduate engineers and scientists in many disciplines.