This is a self-guided review of undergraduate-level quantum mechanics, that will be useful for the core HetSys training modules, and is designed to be completed at your own pace.

Objectives

By the end of this session you should be able to:

Appreciate an introduction to Quantum Mechanics and the origin of the Schrödinger Equation. Be able to use Quantum Mechanics to describe the electron states of the hydrogen atom. Know the origin of the n,l,m and s quantum numbers and be able to use the Pauli exclusion principle to explain the Periodic Table. Be familiar with the free-electron model of a metal.

The material presented here is not intended to be rigorous, but may rather be considered as a pragmatic quick-start guide to the level of understanding of QM expected of students enrolled on this course.

1. Here is an excellent introduction to QM written by David Morin of Harvard University. It explains how particles have wavelike properties which are governed by the Schrödinger Equation. The article gives some historical context and the key ideas underpinning QM including the Heisenberg Uncertainty Principle. It explains where the Schrödinger Equation comes from and goes through some illustrative examples such as a particle in a potential well and a particle tunnelling through a potential barrier. It describes the quantisation of energy levels and the nature of the wave solutions.
2. Here is short overview to complement the information above.
3. The quantum mechanics of a hydrogen atom with its electron moving around a proton is an important case to study. It provides useful insights and gives the starting point for models of other atoms and the structure of the periodic table. This wikipedia page provides a starting point and these notes (part 1) and (part 2) gives some further detail.
4. These notes also describe the free electron model of metals which is another important case study to build up intuition. Some introduction into how the electrons move in a crystalline solid can be found here.
5. Some other suitable introductory reference materials are listed here: H D Young and R A Freedman, University Physics, Pearson; AIM Rae, Quantum Mechanics, IOP; P.C.W. Davies and D.S. Betts, Quantum Mechanics, Chapman and Hall 1994; F. Mandl, Quantum Mechanics, John Wiley 1992.

There is a self-assessment test and solutions available to gauge your progress. If you feel sufficiently up-to-date on the material outlined above, feel free to complete the test now! Otherwise, follow the links given above and then complete the test.

Acknowledgement: Some of this online material is taken from

https://scholar.harvard.edu/files/david-morin/files/waves_quantum.pdf

https://en.wikipedia.org/wiki/Hydrogen_atom

https://courses.warwick.ac.uk/modules/2022/PX262-15