On the missing bound state data of inverse spectral-scattering problems on the half-line
Guangsheng Wei Hong-Kun Xu
Inverse Problems & Imaging 2015, 9(1): 239-255 doi: 10.3934/ipi.2015.9.239
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.
keywords: inverse problem Jost function Marchenko equation. Gel'fand-Levitan integral equation Bargmann-Jost-Kohn class scattering data

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