Exponential propagators for the Schrödinger equation with a time-dependent potential

We consider the numerical integration of the Schr\"odinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-depen...

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Veröffentlicht in:arXiv.org 2018-04
Hauptverfasser: Bader, Philipp, Blanes, Sergio, Kopylov, Nikita
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Sprache:eng
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Zusammenfassung:We consider the numerical integration of the Schr\"odinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-dependent Hamiltonians. We propose new CF propagators that are tailored for Hamiltonians of said structure, showing a considerably improved performance. We obtain new fourth- and sixth-order CF propagators as well as a novel sixth-order propagator that incorporates a double commutator that only depends on coordinates, so this term can be considered as cost-free. The algorithms require the computation of the action of exponentials on a vector similarly to the well known exponential midpoint propagator, and this is carried out using the Lanczos method. We illustrate the performance of the new methods on several numerical examples.
ISSN:2331-8422
DOI:10.48550/arxiv.1804.07103