ABOUT THIS COURSE
This 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.
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.
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 will include “refresher” resources for the required mathematics and physics background.