Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media

doi:10.1016/j.amc.2010.10.002

	Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media
	Cao, Li-qun1 ; Luo, Jian-lan 2; Wang, Chong-yu 3
	2010-12-15
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	217 期号:8 页码:3955-3973
摘要	In solid state physics, the most widely used techniques to calculate the electronic levels in nanostructures are the effective masses approximation (EMA) and its extension the multiband k.p method (see [9]). They have been particularly successful in the case of heterostructures (see, e. g. [4,9,11]). This paper discusses the multiscale analysis of the Schrodinger equation with rapidly oscillating coefficients. The new contributions obtained in this paper are the determination of the convergence rate for the approximate solutions, the definition of boundary layer solutions, and higher-order correctors. Consequently, a multiscale finite element method and some numerical results are presented. As one of the main results of this paper, we give a reasonable interpretation why the effective mass approximation is very accurate for calculating the band structures in semiconductor in the vicinity of C point, from the viewpoint of mathematics. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.
关键词	Homogenization Multiscale asymptotic expansion Schrodinger equation The effective mass approximation Multiscale finite element method
DOI	10.1016/j.amc.2010.10.002
语种	英语
资助项目	National Natural Science Foundation of China[60971121] ; National Natural Science Foundation of China[90916027] ; National Basic Research Program of China (973 Program)[2010CB832702] ; National Basic Research Program of China (973 Program)[2011CB606002]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000284600700029
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10328
专题	计算数学与科学工程计算研究所
通讯作者	Cao, Li-qun
作者单位	1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Beijing Univ Aeronaut & Astronaut, Sch Phys & Nucl Energy Engn, Beijing 100191, Peoples R China 3.Tsinghua Univ, Dept Phys, Beijing 100191, Peoples R China
推荐引用方式 GB/T 7714	Cao, Li-qun,Luo, Jian-lan,Wang, Chong-yu. Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media[J]. APPLIED MATHEMATICS AND COMPUTATION,2010,217(8):3955-3973.
APA	Cao, Li-qun,Luo, Jian-lan,&Wang, Chong-yu.(2010).Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media.APPLIED MATHEMATICS AND COMPUTATION,217(8),3955-3973.
MLA	Cao, Li-qun,et al."Multiscale analysis and numerical algorithm for the Schrodinger equations in heterogeneous media".APPLIED MATHEMATICS AND COMPUTATION 217.8(2010):3955-3973.