ABSTRACT
The technical development of short pulse laser devices has lead to a growth of the interest in time resolved processes governed by the nonrelativistic Schrodinger equation. Most conventional tests of quantum theory are based on energy calculations or steady state probability fluxes. The new computer generations are able to handle large numbers of data fast and accurately. Special integration methods like Crank-Nicholson or the split operator methods are required. The peculiarities of quantum theory in the time domain and its main consequences can be understood from such models. The usual Born-Oppenheimer approximation is presented as a time independent approach giving energy eigenvalues. The chapter discusses all the approximations necessary to neglect the static corrections to the Born-Oppenheimer approximation. It provides some of the important features of the Wigner representation of the density matrix. Quantum aspects enter through the initial conditions that all Wigner functions derive from state vectors and their ensembles.
