  Time dependent Schr\"odinger equations with conservative force field U
commonly constitute a major challenge in the numerical approximation,
especially when they are analysed in the semiclassical regime. Extremely high
oscillations originate from the semiclassical parameter, and call for
appropriate methods. We propose to employ a combination of asymptotic
Zassenhaus splitting with time adaptivity. While the former turns the
disadvantage of the semiclassical parameter into an advantage, leading to
highly efficient methods with low error constants, the latter enables to choose
an optimal time step and to speed up the calculations when the oscillations
subside. We support the results with numerical examples.
