**Adrian E. Feiguin**

- Schödinger's Equation
- Variational Methods

- The Hartree-Fock method
- The Born-Oppenheimer approximation
- The helium atom
- A program for the helium ground-state
- Many electron systems and the Slater determinant
- Hartree-Fock theory
- Matrix form of the Hartree-Fock equations

- Density Functional Theory
- Introduction
- Functionals and functional derivatives
- The Coulomb (Thomas-Fermi) functional
- Hohenberg-Kohn theorems
- DFT formalism and derivation of the Kohn-Sham equations
- The local density approximation - LDA
- More about exchange
- Solution to the Kohn-Sham equations
- Pros and Cons of the DFT

- Methods for band-structure calculations
- The tight-binding approximation
- General case: Linear Combination of Atomic Orbitals
- Plane Waves
- The Pseudopotential Method
- The cellular (Wigner-Seitz) method
- The Muffin-tin potential
- The Augmented plane-wave method (APW)
- The LAPW method
- Adding electron-electron interactions

- Random sequences
- Pseudo-random number generators
- Testing for randomness and uniformity
- Non-uniform random distributions
- von Neumann rejection
- Random walk methods: the Metropolis algorithm

- Monte Carlo integration

- Monte Carlo Simulation
- The Canonical Ensemble
- The Metropolis algorithm
- The Ising model
- Simulation of the 2D Ising model
- Metropolis algorithm
- Measuring observables
- The Ising phase transition

- Quantum Monte Carlo
- Variational Monte Carlo
- World Line Monte Carlo
- Determinantal (or Auxiliary Field) Monte Carlo
- Projector Monte Carlo
- Sign problem revisited

- Bibliography
- About this document ...

Adrian E. Feiguin 2009-11-04