Topics: self-adjoint operators, Eigen function expansion, simple model system, linear algebra, BRA-Ket notation, formal developments, harmonic oscillators, coherent state, quantum mechanics, angular momentum, stationary perturbations, perturbation theory, scattering off potentials, density of state, time-independent perturbation, perturbation, path integrals, polarizability tensor, electromagnetic coupling, Lagrangian field theory, Non-relativistic Quantum Field Theory, Maxwell field, relativistic quantum fields, spinor QED