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

Philipp Bader | Zendy; Arieh Iserles | Zendy; Karolina Kropielnicka | Zendy; Pranav Singh | Zendy

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

Author(s) -

Philipp Bader,

Arieh Iserles,

Karolina Kropielnicka,

Pranav Singh

Publication year - 2016

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2015.0733

Subject(s) - semiclassical physics , hamiltonian (control theory) , unitary state , schrödinger equation , mathematical physics , mathematics , quantum mechanics , physics , mathematical analysis , quantum , mathematical optimization , law , political science

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 (Baderet al. 2014Found. 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.

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