THE INITIAL BOUNDARY-VALUE PROBLEM FOR THE SCHRODINGER-EQUATION

被引：6

作者：

ABRAHAMSSON, L ^{[1
]}

KREISS, HO ^{[1
]}

机构：

[1] UNIV CALIF LOS ANGELES,DEPT MATH,LOS ANGELES,CA 90024

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 1990年 / 13卷 / 05期

关键词：

D O I：

10.1002/mma.1670130503

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the stability properties of the one‐dimensional Schrödinger equation with boundary conditions that involve the derivative in the direction of propagation (or time). We show that this type of boundary condition might cause a strong growth of the amplitude of the solution. Such a model is not useful for numerical computations. One example is the parabolic wave equation in underwater acoustics for wave propagation in a downsloping duct with the normal derivative condition ∂u/∂n =0 at the bottom. Copyright © 1990 John Wiley & Sons, Ltd

引用

页码：385 / 390

页数：6

共 5 条

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ABRAHAMSSON, L ;

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1990, 87 (06) :2438-2441

[2] STABILITY ANALYSIS OF DIFFERENCE-SCHEMES FOR VARIABLE-COEFFICIENT SCHRODINGER TYPE EQUATIONS [J].

CHAN, TF ;

SHEN, L .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (02) :336-349

[3]

Gajewski H, 1979, INT J MATH MATH SCI, V2, P503, DOI DOI 10.1155/S0161171279000405

[4] SCHRODINGER-EQUATION WITH TIME-DEPENDENT BOUNDARY-CONDITIONS [J].

MUNIER, A ;

BURGAN, JR ;

FEIX, M ;

FIJALKOW, E .

JOURNAL OF MATHEMATICAL PHYSICS, 1981, 22 (06) :1219-1223

[5]

TAPPERT FD, 1977, WAVE PROPAGATION UND

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