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Inverse spectral-scattering problem with two sets of discrete spectra for the radial Schrödinger equation

By Tuncay Aktosun and Ricardo Weder


The Schrödinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectrum

Topics: inverse scattering problem, inverse spectral problem, radial Schrödinger equation, Gel’fand-Levitan method, Marchenko method, Borg-Marchenko theorem
Year: 2004
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