Efficient methods for time-dependence in semiclassical Schr\"odinger   equations
  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. 
Philipp Bader, Arieh Iserles, Karolina Kropielnicka, Pranav Singh
math.NA