Nanosecond wave-packet propagation with the Split-Operator Technique

We investigate the grid propagation of quantum mechanical wave packets for propagation times of several nanoseconds using the ''Split-Operator Technique''. The vibrational motion of a diatomic molecule is chosen as a numerical example. For the systems under investigation the propagation time is several thousand times larger than the vibrational period. Physical properties calculated as a function of time show only small numerical errors. Even for time-steps which are chosen too big to keep the error in the phase of the wavefunction small, surprisingly good results can be obtained in the average.