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Single-step propagators for calculation of time evolution in quantum systems with arbitrary interactions. (English) Zbl 1348.81229

Summary: 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 in closed-form, which could be used for the numerical solving of the problem with any prescribed accuracy. We demonstrate the applicability of the proposed approach by considering a quantum problem with non-separable time-dependent Hamiltonian: the propagation of an electron in focused electromagnetic field with vortex electric field component.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81-08 Computational methods for problems pertaining to quantum theory
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References:

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