Quantum Mechanics and Computational Materials Science¶

Section 1: Quantum Mechanics¶

1. Numerical Solution of the Schrödinger Equation for a 1D Quantum Well
2. Numerical Solution of the Schrödinger Equation for a Double Square Well Potential
3. Avoided Crossings in a 1D Asymmetric Quantum Well
4. Shooting Method to Solve the Time-Independent Schrödinger Equation
5. Numerical Solution of the 1D Time-Dependent Schrödinger Equation by the Split Operator Fourier Transform (SOFT) Method
6. Numerical Solution of the 1D Time-Dependent Schrödinger Equation For Nuclear Evolution On Multiple Electronic Potential Energy Surfaces Via The Multiple Split Operator Fourier Transform (MSOFT) Method.

Section 2: Band Theory of Crystals¶

1. Fourier Transforms and Plane-Wave Expansions
2. Brillouin Zone
3. Free-Electron Bandstructure
4. Density of States
5. Norm-conserving Pseudopotentials

Section 3: Molecule and Lattice Vibration¶

1. Molecule Vibrations
2. Phonons in 1D
3. Phonons in 2D

Section 4: Molecular Dynamics¶

1. Verlet Integration

Section 5: Statistical Mechanics¶

1. Monte Carlo Calculation of π
2. Monte Carlo Simulations to Sample the Canonical Distribution
3. Ising Model in 2D
4. Random Diffusion in 2D