Classical numerical integrators for wave-packet dynamics

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Abstract
Gray and Verosky have recently studied the reformulation of the N‐state matrix representation of the time‐dependent Schrödinger equation as an N‐degrees of freedom classical Hamiltonian system. This opens the possibility of using in quantum dynamics numerical integrators originally devised for classical mechanics. When the Hamiltonian matrix is time‐dependent, Gray and Verosky suggest the use of a Magnus approximation before reducing the quantum system to its classical format. We show that Magnus approximations are not necessary and suggest an alternative technique. With the new technique it is possible to obtain simple integrators of arbitrarily high orders of accuracy that can be applied to all matrix Schrödinger problems with a, possibly time‐dependent, real Hamiltonian matrix. The connection between the new approach and high‐order split‐operator methods is studied.