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
Seminar 2, Getting started
Seminar 3, Coupled Quantum Wells and the Kronig-Penney model
- 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/A2x2
Seminar 4, 1D Hydrogen Atom and H2 Molecule Ion
- 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 5,6, 1D Solid Hydrogen
- Solve the He-ion problem numerically.
- Calculate the approximate bond length of the hydrogen molecule ion.
- 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.