  The semiclassically scaled time-dependent multi-particle Schr\"odinger
equation describes, inter alia, quantum dynamics of nuclei in a molecule. It
poses the combined computational challenges of high oscillations and high
dimensions. This paper reviews and studies numerical approaches that are robust
to the small semiclassical parameter. We present and analyse variationally
evolving Gaussian wave packets, Hagedorn's semiclassical wave packets,
continuous superpositions of both thawed and frozen Gaussians, and Wigner
function approaches to the direct computation of expectation values of
observables. Making good use of classical mechanics is essential for all these
approaches. The arising aspects of time integration and high-dimensional
quadrature are also discussed.
