Theoretical predictions from a 1D model of a solid:
Bandstructure, defects, interfaces and quantum wells

Seminar series given at the University of Pretoria by Matthias Schmidt in 2014.
Time: Wednesdays, 16:00. Venue: Department of Physics, Computer Lab

The seminar series addresses post-graduate and PhD students with a background in solid state physics. It is aimed to provide insight into the quantum mechanics of electronic states in solids within the band theory. Thereby the capabilities of the most simple model of a solid, the one-dimensional linear chain of Coulomb wells, are fully exploited. The seminar series starts with the basic aspects of a numerical Schrödinger equation solver. Simple well-known quantum mechanical problems like an electron in a potential well or the harmonic oscillator are treated and the Kronig-Penney model is discussed.
Then the atomic states of the 1D hydrogen atom are calculated. The example of the 1D hydrogen molecule ion is used to explain chemical bonding. In the next step a hydrogen crystal is constructed by aligning Coulomb wells periodically. Thereby the formation of bands from atomic states is studied. Finally localised electronic states in solids introduced by perturbations of the crystal potential (defects, surfaces, interfaces, etc.) are calculated.
The seminars are intended to be interactive. The source code of the computer program will be provided to the participants such that the they can reproduce the examples presented and simulate their own quantum mechanical problems.