# 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

## Homework

**Seminar 2, Getting started**
- Install
`solidsim` on your computer.
- 'Play' with
`solidsim` and solve the finite quantum well problem.
- Calculate the angular frequency of an harmonic oscillator analytically.
*V(x)*=0.5eV/A^{2}*x*^{2}

**Seminar 3, Coupled Quantum Wells and the Kronig-Penney model**
- Play with the harmonic oscillator. Change
*x* steps and *x* range in order to see the effect on the accuracy of the
calculated states and wave-functions.
- What happens to the bandgaps in the Kronig-Penney model if the lattice constant is increased? Modify the
`solidsim` file
provided and run `solidsim`!

**Seminar 4, 1D Hydrogen Atom and H**_{2} Molecule Ion
- Solve the He-ion problem numerically.
- Calculate the approximate bond length of the hydrogen molecule ion.

**Seminar 5,6, 1D Solid Hydrogen**
- Calculate a hydrogen-like crystal with a lattice constant of a=5 and charge 0.5.
- What is the effect on the bandgaps?
- Simulate the hydrogen crystal for at least three different cutoff potentials.
- Calculate the effective mass for one of the bands in dependence of the cutoff potential.