Scattering and wave operators for one-dimensional Schrodinger operators with slowly decaying nonsmooth potentials

被引：28

作者：

Christ, M ^{[1
]}

Kiselev, A

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2002年 / 12卷 / 06期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s00039-002-1174-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove existence of modified wave operators for one-dimensional Schrodinger equations with potential in L-P(R), p < 2. If in addition the potential is conditionally integrable, then the usual Moller wave operators exist. We also prove asymptotic completeness of these wave operators for some classes of random potentials, and for almost every boundary condition for any given potential.

引用

页码：1174 / 1234

页数：61

共 45 条

[1]

[Anonymous], THEOR MATH PHYS

[2]

[Anonymous], [No title captured]

[3]

[Anonymous], 1986, TEORET MAT FIZ

[4]

[Anonymous], 1984, CONT SOVIET MATH

[5]

ARONSZAJN N, 1957, J ANAL MATH, V15, P321

[6] ON THE ABSOLUTE CONTINUITY OF SCHRODINGER OPERATORS WITH SPHERICALLY SYMMETRIC, LONG-RANGE POTENTIALS .2. [J].

BENARTZI, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1980, 38 (01) :51-60

[7]

BENARTZI M, 1980, J DIFFER EQUATIONS, V38, P41, DOI 10.1016/0022-0396(80)90023-6

[8] SPECTRAL AND SCATTERING THEORY FOR THE ADIABATIC OSCILLATOR AND RELATED POTENTIALS [J].

BENARTZI, M ;

DEVINATZ, A .

JOURNAL OF MATHEMATICAL PHYSICS, 1979, 20 (04) :594-607

[9]

Birman M. Sh., 1987, SPECTRAL THEORY SELF

[10] WKB and spectral analysis of one-dimensional Schrodinger operators with slowly varying potentials [J].

Christ, M ;

Kiselev, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 218 (02) :245-262

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