Optimization of explicit symplectic schemes for time-dependent Schrodinger equations

doi:10.1016/j.camwa.2004.09.015

	Optimization of explicit symplectic schemes for time-dependent Schrodinger equations
	Liu, XY ; Ding, PZ ; Hong, JL; Wang, LJ
	2005-08-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	50 期号:3-4 页码:637-644
摘要	In this paper, in order to conserve the discrete squared norm of the wave function, we propose a condition for optimizing the n-stage and n-order explicit symplectic schemes, which are applied to solving finite-dimensional canonical equations obtained by discretizing the time-dependent Schrodinger equations. It is showed that the 'half unitary' (i.e., symmetric) conditions proposed by Gray and Manolopoulos can automatically satisfy the optimal condition proposed in this paper for even n but not for odd n. In particular, two-order or four-order optimized explicit symplectic schemes are obtained. Calculations and comparisons with three kinds of explicit symplectic schemes are presented for a model in quantum systems. (c) 2005 Elsevier Ltd. All rights reserved.
关键词	symplectic scheme wave function Schrodinger equation
DOI	10.1016/j.camwa.2004.09.015
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000231915100027
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1610
专题	计算数学与科学工程计算研究所
通讯作者	Liu, XY
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.NE Normal Univ, Dept Math, Changchun 130024, Peoples R China 3.Jilin Univ, Inst Atom & Mol Phys, Changchun 130012, Peoples R China 4.Chinese Acad Sci, Grad Sch, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liu, XY,Ding, PZ,Hong, JL,et al. Optimization of explicit symplectic schemes for time-dependent Schrodinger equations[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2005,50(3-4):637-644.
APA	Liu, XY,Ding, PZ,Hong, JL,&Wang, LJ.(2005).Optimization of explicit symplectic schemes for time-dependent Schrodinger equations.COMPUTERS & MATHEMATICS WITH APPLICATIONS,50(3-4),637-644.
MLA	Liu, XY,et al."Optimization of explicit symplectic schemes for time-dependent Schrodinger equations".COMPUTERS & MATHEMATICS WITH APPLICATIONS 50.3-4(2005):637-644.