Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential

Philipp Bader, Arieh Iserles, Karolina Kropielnicka, Pranav Singh

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16 Citations (Scopus)

Abstract

We build efficient and unitary (hence stable) methods for the solution of the linear time-dependent Schrödinger equation with explicitly time-dependent potentials in a semiclassical regime. The Magnus-Zassenhaus schemes presented here are based on a combination of the Zassenhaus decomposition (Bader et al. 2014 Found. Comput. Math. 14, 689-720. (doi:10.1007/s10208-013-9182-8)) with the Magnus expansion of the time-dependent Hamiltonian. We conclude with numerical experiments.

Original languageEnglish
Article number20160733
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume472
Issue number2193
DOIs
Publication statusPublished - 1 Sep 2016

Keywords

  • Exponential splitting
  • Numerical analysis
  • Schrödinger equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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