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

Single-step Propagators for calculation of time evolution in quantum systems with arbitrary interactions