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Volume 26, Issue 4
The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrödinger Equations

Yuan Li & Fuming Ma

Commun. Math. Res., 26 (2010), pp. 321-336.

Published online: 2021-05

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  • 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 $A$.

  • Keywords

factorization method, inverse scattering, Schrödinger equation, interior transmission problem.

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COPYRIGHT: © Global Science Press

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@Article{CMR-26-321, author = {Li , Yuan and Ma , Fuming}, title = {The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrödinger Equations}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {4}, pages = {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 $A$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19130.html} }
TY - JOUR T1 - The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrödinger Equations AU - Li , Yuan AU - Ma , Fuming JO - Communications in Mathematical Research VL - 4 SP - 321 EP - 336 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19130.html KW - factorization method, inverse scattering, Schrödinger equation, interior transmission problem. AB -

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 $A$.

Li , Yuan and Ma , Fuming. (2021). The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrödinger Equations. Communications in Mathematical Research . 26 (4). 321-336. doi:
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