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# Quantum Mechanics for Scientists and Engineers

## About This Course

This 9 week course aims to teach quantum mechanics to anyone with a reasonable college-level understanding of physical science or engineering. Quantum mechanics was once mostly of interest to physicists, chemists and other basic scientists. Now the concepts and techniques of quantum mechanics are essential in many areas of engineering and science such as materials science, nanotechnology, electronic devices, and photonics. This course is a substantial introduction to quantum mechanics and how to use it. It is specifically designed to be accessible not only to physicists but also to students and technical professionals over a wide range of science and engineering backgrounds.

## Course syllabus

**Introduction to quantum mechanics**

How quantum mechanics is important in the everyday world, the bizarre aspects and continuing evolution of quantum mechanics, and how we need it for engineering much of modern technology.

**Schroedinger’s wave equation**

Getting to Schroedinger’s wave equation. Key ideas in using quantum mechanical waves — probability densities, linearity. The "two slit" experiment and its paradoxes.

**Getting "quantum" behavior**

The "particle in a box", eigenvalues and eigenfunctions. Mathematics of quantum mechanical waves.

**Quantum mechanics of systems that change in time**

Time variation by superposition of wave functions. The harmonic oscillator. Movement in quantum mechanics — wave packets, group velocity and particle current.

**Measurement in quantum mechanics**

Operators in quantum mechanics — the quantum-mechanical Hamiltonian. Measurement and its paradoxes — the Stern-Gerlach experiment.

**Writing down quantum mechanics simply**

A simple general way of looking at the mathematics of quantum mechanics — functions, operators, matrices and Dirac notation. Operators and measurable quantities. The uncertainty principle.

**The hydrogen atom**

Angular momentum in quantum mechanics — atomic orbitals. Quantum mechanics with more than one particle. Solving for the the hydrogen atom. Nature of the states of atoms.

**How to solve real problems**

Approximation methods in quantum mechanics.

## Prerequisites

The course is approximately at the level of a first quantum mechanics class in physics at a third-year college level or above, but it is specifically designed to be suitable and useful also for those from other science and engineering disciplines.

The course emphasizes conceptual understanding rather than a heavily mathematical approach, but some amount of mathematics is essential for understanding and using quantum mechanics. The course presumes a mathematics background that includes basic algebra and trigonometry, functions, vectors, matrices, complex numbers, ordinary differential and integral calculus, and ordinary and partial differential equations.

In physics, students should understand elementary classical mechanics (Newton’s Laws) and basic ideas in electricity and magnetism at a level typical of first-year college physics. (The course explicitly does not require knowledge of more advanced concepts in classical mechanics, such as Hamiltonian or Lagrangian approaches, or in electromagnetism, such as Maxwell’s equations.) Some introductory exposure to modern physics, such as the ideas of electrons, photons, and atoms, is helpful but not required.

The course includes an optional and ungraded “refresher” background mathematics section that reviews and gives students a chance to practice all the necessary math background background. Introductory background material on key physics concepts is also presented at the beginning of the course.

## Course Staff

### David Miller

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 Laboratores 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, is a Fellow of many major professional societies in science and engineering, including the Royal Society of London, 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.

## Frequently Asked Questions

### Required text

The text “Quantum Mechanics for Scientists and Engineers” (Cambridge, 2008) is recommended for the course, though it is not required. It follows essentially the same syllabus, has additional problems and exercises, allows you to go into greater depth on some ideas, and also contains many additional topics for further study.

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