Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential propagators for the Schr\"odinger 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-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.

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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: nlin