  We propose and develop a general method of numerical calculation of the wave
function time evolution in a quantum system which is described by Hamiltonian
of an arbitrary dimensionality and with arbitrary interactions. For this, we
obtain a general n-order single-step propagator, which could be used for the
numerical solving of the problem with any prescribed accuracy. We demonstrate
an applicability of the proposed approach by considering a propagation of an
electron in focused electromagnetic field with vortex electric field component.
