On the missing bound state dataof inverse spectral-scattering problems on the half-line

Guangsheng Wei; Hong-Kun Xu

doi:10.3934/ipi.2015.9.239

Article Contents

2015, Volume 9, Issue 1: 239-255. Doi: 10.3934/ipi.2015.9.239

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On the missing bound state data of inverse spectral-scattering problems on the half-line

Guangsheng Wei^1, and
Hong-Kun Xu^2,

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaaxi 710062
2.
Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018

Received: February 28, 2013

Revised: June 30, 2014

Published: January 2015

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Abstract

The inverse spectral-scattering problems for the radial Schrödinger equation on the half-line are considered with a real-valued integrable potential with a finite moment. It is shown that if the potential is sufficiently smooth in a neighborhood of the origin and its derivatives are known, then it is uniquely determined on the half-line in terms of the amplitude or scattering phase of the Jost function without bound state data, that is, the bound state data is missing.

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Mathematics Subject Classification: Primary: 34A55; Secondary: 34L40, 34L20.

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