On properties of solutions of the Cauchy problem for the Schrödinger equation degenerate on the half-line

被引：0

作者：

Sakbaev V.Zh. ^{[1
]}

机构：

[1] Moscow Physico-Technical Institute,

来源：

Journal of Mathematical Sciences | 2005年 / 129卷 / 1期

基金：

俄罗斯基础研究基金会;

关键词：

Cauchy Problem; Elliptic Operator; Characteristic Form; Schrodinger Equation; Equation Degenerate;

D O I：

10.1007/s10958-005-0305-x

中图分类号：

学科分类号：

摘要：

We consider the Schrodinger equation on the half-line describing a particle with mass depending on its location. We study the Cauchy problem for the Schrodinger equation with degenerate operator whose characteristic form vanishes on the half-line. A sequence of regularizing Cauchy problems with uniformly elliptic operators is considered, and the convergence of the sequence of solutions of nondegenerate problems to the solution of the degenerate problem is examined. © 2005 Springer Science+Business Media, Inc.

引用

页码：3657 / 3669

页数：12

共 11 条

[1]

Berezin F.A., Shubin M.I., Schrödinger Equation [in Russian], (1983)

[2]

Fichera G., On a unified theory of boundary-value problems for elliptic-parabolic equations of second order, Boundary Problems in Differential Equations, pp. 97-120, (1960)

[3]

Gitman D.M., Tyutin I.D., Canonical Quantization of Fields with Connection [in Russian], (1986)

[4]

Lusternik L.A., Sobolev V.I., A Course of Functional Analysis [In Russian], (1982)

[5]

Mikhlin S.G., Linear Partial Differential Equations [in Russian], (1965)

[6]

Naimark M.A., Normed Rings [in Russian], (1968)

[7]

Pavlotsky I.P., Strianese M., Irreversibility in classical mechanics as a consequence of the Poincaré group, Int. J. Mod. Phys. B, 10, 21, pp. 2675-2685, (1996)

[8]

Reed M., Simon B., Methods of Modern Mathematical Physics. Vol. 1. Functional Analysis, 1, (1980)

[9]

Sakbaev V.Zh., On the statement of the Cauchy problem for the Schrödinger equation degenerate in subspace, Comput. Math. Math. Phys., 42, 11, pp. 1718-1729, (2002)

[10]

Sz-Nagy B., Foias C., Harmonic Analysis of Operators on Hubert Spaces, (1970)

← 1 2 →