(non committing list, by logical order)
BASICS:
States: the probability function/matrix (rho).
The representation of two level system.
The representation of a particle using Wigner function.
Wigner-Weyl formalism and the Weyl formula.
EIGENSTATES:
The Hamiltonian, Invariance, Symmetries
Galilei and gauge invariance
Time reversal invariance
Banded matrices (Wigner/Anderson models)
Random matrix theory and Quantum Chaos
STATIONARY PROBLEMS:
The resolvent [Green function] and perturbation theory
Scattering theory in the S matrix approach
Current via a lead (Landauer, pumping).
DYNAMICS:
Wavepacket dynamics
Theory of driven systems
Linear response theory (Kubo formula)
Adiabatic processes, Berry phase
Born-Oppenheimer approximation
Small systems under the influence of dissipation: Formalism
Unitary evolution and Path integrals
Feynman-Vernon Formalism
Master equations
Dissipation and Decoherence
Small systems under the influence of dissipation: Applications
Two level system - The spin boson model
Multi level system - Pauli Eq.
Damped particle - Fokker-Plank Eq.
Reaction rate theory, Kramer