  We build an efficient and unitary (hence stable) method for the solution of
the semi-classical Schr\"odinger equation subject with explicitly
time-dependent potentials. The method is based on a combination of the
Zassenhaus decomposition (Bader, Iserles, Kropielnicka & Singh 2014) with the
Magnus expansion of the time-dependent Hamiltonian. We conclude with numerical
experiments.

Numerical Analysis