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 |
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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. |
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ISSN: | 0021-9606 1089-7690 |
DOI: | 10.1063/1.5036838 |