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

被引：20

作者：

Bader, Philipp ^{[1
]}

Iserles, Arieh ^{[2
]}

Kropielnicka, Karolina ^{[3
]}

Singh, Pranav ^{[2
]}

机构：

[1] La Trobe Univ, Dept Math, Kingsbury Dr, Melbourne, Vic 3086, Australia

[2] Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

[3] Univ Gdansk, Inst Math, 57 Stwosz St, PL-90952 Gdansk, Poland

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2016年 / 472卷 / 2193期

基金：

澳大利亚研究理事会;

关键词：

numerical analysis; Schrodinger equation; exponential splitting; QUANTUM CONTROL; APPROXIMATION;

D O I：

10.1098/rspa.2015.0733

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We build efficient and unitary (hence stable) methods for the solution of the linear time-dependent Schrodinger 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.

引用

页数：18

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