Spurious localized highest-frequency modes in Schrodinger-type equations solved by finite-difference methods

被引：1

作者：

Lakoba, T. I. ^{[1
]}

机构：

[1] Univ Vermont, Dept Math & Stat, Burlington, VT 05401 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2013年 / 245卷

关键词：

Finite-difference methods; Eigenvalue problems; High-frequency modes;

D O I：

10.1016/j.cam.2012.12.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

High-frequency solutions of one or several Schrodinger-type equations are well known to differ very little from the plane wave solutions exp[+/- ikx]. That is, the potential terms impact the envelope of a high-frequency plane wave to only a small extent. However, when such equations are solved by a finite-difference method, the highest-frequency solutions may, under certain conditions, turn out to be localized. This may puzzle the researcher and suggest that the code may have an error. However, this is not an error but a numerical artifact, and in this note we explain it. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：117 / 120

页数：4

共 5 条

[1] Count of eigenvalues in the generalized eigenvalue problem
Chugunova, Marina
Pelinovsky, Dmitry
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (05)
[2] RENORMALIZED NUMEROV METHOD APPLIED TO CALCULATING BOUND-STATES OF COUPLED-CHANNEL SCHROEDINGER EQUATION
JOHNSON, BR
[J]. JOURNAL OF CHEMICAL PHYSICS, 1978, 69 (10) : 4678 - 4688
[3] Phase integral approximation for coupled ordinary differential equations of the Schrodinger type
Skorupski, Andrzej A.
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (05)
[4] Exact solution of coupled Schrodinger equations in a stationary n-state exponential model
Teubner, Max
[J]. PHYSICAL REVIEW A, 2006, 74 (01):
[5] Numerical simulation methods for rough surface scattering
Warnick, Karl F.
Chew, Weng Cho
[J]. Waves Random Media, 2001, 11 (01):

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