This course provides an introduction to simulation methods for quantum systems. Starting from the one-body problem, a special emphasis is on quantum many-body problems, where we cover both approximate methods (Hartree-Fock, density functional theory) and exact methods (exact diagonalization, matrix product states, and quantum Monte Carlo methods).

Computer simulation methods in statistical physics. Classical Monte-Carlo-simulations: finite-size scaling, cluster algorithms, histogram-methods, renormalization group. Application to Boltzmann machines. Simulation of non-equilibrium systems.Molecular dynamics simulations: long range interactions, Ewald summation, discrete elements, parallelization.

General structure of quantum theory: Hilbert spaces, states and observables, equations of motion, Heisenberg uncertainty relation, symmetries, angular momentum addition, EPR paradox, Schrödinger and Heisenberg picture.Applications: simple potentials in wave mechanics, scattering and resonance, harmonic oscillator, hydrogen atom, and perturbation theory.