EXPLICIT SOLUTION OF 3-D PHASELESS INVERSE SCATTERING PROBLEM FOR THE SCHRODINGER EQUATION: THE PLANE WAVE CASE

被引：17

作者：

Klibanov, M. V. ^{[1
]}

Romanov, V. G. ^{[2
]}

机构：

[1] Univ North Carolina Charlotte, Dept Math & Stat, Charlotte, NC 28223 USA

[2] Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS | 2015年 / 3卷 / 01期

关键词：

phaseless inverse scattering; incident plane wave; Schrodinger equation; reconstruction formula; Radon transform;

D O I：

10.32523/2306-6172-2015-3-1-48-63

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The inverse scattering problem of the reconstruction of the unknown potential in the 3-d Schrodinger equation is considered. Unlike the conventional case of an inverse scattering problem, here only the modulus of the complex valued scattered wave field is assumed to be known outside of the scatterer. The phase is unknown. This problem arises in inverse quantum scattering. Unlike the previous work of the authors [8], where the case of the point source was studied, here the incident plane wave is considered. An explicit solution via the inverse Radon transform is obtained.

引用

页码：48 / 63

页数：16

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