Inverse scattering for the magnetic Schrodinger operator

被引：21

作者：

Paivarinta, Lassi ^{[1
]}

Salo, Mikko ^{[1
]}

Uhlmann, Gunther ^{[2
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 07期

基金：

芬兰科学院;

关键词：

Inverse scattering; Schrodinger operator; Complex geometrical optics; Semiclassical pseudodifferential calculus; SHORT-RANGE POTENTIALS; BOUNDARY-VALUE PROBLEM; FIXED-ENERGY; RECOVERING ASYMPTOTICS; GLOBAL UNIQUENESS; EQUATION; FIELD;

D O I：

10.1016/j.jfa.2010.06.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that fixed energy scattering measurements for the magnetic Schrodinger operator uniquely determine the magnetic field and electric potential in dimensions n >= 3. The magnetic potential, its first derivatives, and the electric potential are assumed to be exponentially decaying. This improves an earlier result of Eskin and Ralston (1995) [5] which considered potentials with many derivatives. The proof is close to arguments in inverse boundary problems, and is based on constructing complex geometrical optics solutions to the Schrodinger equation via a pseudodifferential conjugation argument. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1771 / 1798

页数：28

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