1. Many-Body problems - Introduction to remainder of course
   • The many-body wavefunction for electrons
     • The general form of the wavefunction discussed in lecture 7
     • Reminder of the simplification in the Hartree-Fock Approximation
     • How can we do better - how to include correlations?
     • The idea is a correlated wavefunction like that for the H₂ molecule discussed in Thijssen, 12.2.
     • This leads up to the use of Monte Carlo methods
   • Idealized many-body problems - examples
     • The Hubbard model model for electrons
     • Simplest example: Heitler-London theory for H₂
     • Spin models - Ising, Heisenberg
     • The key point is that the size of the Hilbert space grows as a factorial of the number of possible states for one particle
     • Exact solutions only possible for very restricted numbers of single body orbitals, and limited numbers of particles in systems
     • Configuration interaction methods in chemistry
     • Monte Carlo methods sample large spaces by random methods
     • Lanczos methods are efficient methods to find lowest eigenstates of enormous matrices

Next time: Monte Carlo methods for Quantum Problems: Thijssen Chapt. 12