The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrödinger Equations
Year: 2010
Communications in Mathematical Research , Vol. 26 (2010), Iss. 4 : pp. 321–336
Abstract
This paper is concerned with the inverse scattering problems for Schrödinger equations with compactly supported potentials. For purpose of reconstructing the support of the potential, we derive a factorization of the scattering amplitude operator $A$ and prove that the ranges of $(A^∗A) ^{1/4}$ and $G$ which maps more general incident fields than plane waves into the scattering amplitude coincide. As an application we characterize the support of the potential using only the spectral data of the operator $A$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-CMR-19130
Communications in Mathematical Research , Vol. 26 (2010), Iss. 4 : pp. 321–336
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: factorization method inverse scattering Schrödinger equation interior transmission problem.