The design of efficient numerical methods, which produce an accurate approximation of the solutions, for solving time-dependent Schrodinger equation in the semiclassical regime, where the Planck constant epsilon is small, is a formidable mathematical challenge. In this paper a new method is shown to construct exponential splitting schemes for linear time-dependent Schrodinger equation with a linear potential. The local discretization error of the two time-splitting methods constructed here is O(max{Delta t(3), Delta t(5)/epsilon}), while the well-known Lie-Trotter splitting scheme and the Stra...
