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

We consider the numerical integration of the Schrödinger 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 Ha...

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Veröffentlicht in:The Journal of chemical physics 2018-06, Vol.148 (24), p.244109-244109
Hauptverfasser: Bader, Philipp, Blanes, Sergio, Kopylov, Nikita
Format: Artikel
Sprache:eng
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Zusammenfassung:We consider the numerical integration of the Schrödinger 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 the 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 similar 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:0021-9606
1089-7690
DOI:10.1063/1.5036838