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

TL;DR

This paper introduces a general numerical method for simulating quantum system dynamics using single-step propagators of arbitrary order, applicable to complex Hamiltonians with various interactions.

Contribution

It develops a universal n-order single-step propagator method for accurate quantum wave function evolution calculations in systems with arbitrary Hamiltonians.

Findings

Successfully applied to electron propagation in focused electromagnetic fields.

Demonstrates high accuracy and flexibility of the method.

Applicable to quantum systems with complex interactions.

Abstract

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.