A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials

doi:10.1007/s10915-009-9326-9

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	A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials
	Wen, Xin
	2010-02-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	42 期号:2 页码:318-344
摘要	We develop a fourth order numerical method for the computation of multivalued physical observables (density, momentum, etc.) in the semiclassical limit of the one-dimensional linear Schrodinger equation in the case of discontinuous potentials. We adopt the level set framework developed in (Jin et al. in J. Comput. Phys. 210:497-518, 2005) which allows one to compute the multivalued physical observables via solving the classical Liouville equation with bounded initial data and approximating delta function integrals. We achieve high order accuracy for our method by studying two issues. The first is to highly accurately compute the solution and its derivatives of the Liouville equation with bounded initial data and discontinuous potentials. The second is to design high order numerical methods to evaluate one-dimensional delta function integrals with discontinuous kernel functions. Numerical examples are presented to verify that our method achieves the fourth order L (1)-norm accuracy for computing multivalued physical observables of the one-dimensional linear Schrodinger equation with general discontinuous potentials.
关键词	Semiclassical limit Schrodinger equation Liouville equation Discontinuous potential
DOI	10.1007/s10915-009-9326-9
语种	英语
资助项目	Chinese Academy of Sciences[K3502012S8] ; NSFC[10601062]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000273452600007
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10784
专题	中国科学院数学与系统科学研究院
通讯作者	Wen, Xin
作者单位	Chinese Acad Sci, LSEC, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wen, Xin. A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials[J]. JOURNAL OF SCIENTIFIC COMPUTING,2010,42(2):318-344.
APA	Wen, Xin.(2010).A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials.JOURNAL OF SCIENTIFIC COMPUTING,42(2),318-344.
MLA	Wen, Xin."A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials".JOURNAL OF SCIENTIFIC COMPUTING 42.2(2010):318-344.