# American Institute of Mathematical Sciences

February  2015, 9(1): 239-255. doi: 10.3934/ipi.2015.9.239

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

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

Received  March 2013 Revised  July 2014 Published  January 2015

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.
Citation: Guangsheng Wei, Hong-Kun Xu. On the missing bound state data of inverse spectral-scattering problems on the half-line. Inverse Problems & Imaging, 2015, 9 (1) : 239-255. doi: 10.3934/ipi.2015.9.239
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