Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential-Reference-Cited by-同舟云学术

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

Published:2016-09 Issue:2193 Volume:472 Page:20150733
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Bader Philipp¹,Iserles Arieh²,Kropielnicka Karolina³^ORCID,Singh Pranav²

Affiliation:

1. Department of Mathematics, La Trobe University, Kingsbury Drive, Melbourne, 3086 Victoria, Australia

2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

3. Institute of Mathematics, University of Gdańsk, 57 Stwosz Street, 90-952 Gdańsk, Poland

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2015.0733

Reference23 articles.

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