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Advances in Mathematical Physics
Volume 2016, Article ID 6031523, 8 pages
Research Article

Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem

Department of Mathematics, National Chung Cheng University, 168 University Rd., Min-Hsiung, Chia-Yi County 621, Taiwan

Received 31 August 2016; Accepted 19 October 2016

Academic Editor: Ricardo Weder

Copyright © 2016 Lung-Hui Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. In some micro/nanostructures, it is impractical to measure the phase information of the scattered wave field emitted from the source. We study the asymptotic behavior of the scattering amplitudes/intensity from the linearization theory of the scattered wave fields. The inverse uniqueness of the scattered waves is reduced to the inverse uniqueness of the analytic function. We deduce the uniqueness of the Schrödinger potential via the identity theorems in complex analysis.