Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

Details Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

2004-02-09

arxiv.org/abs/math-ph/0402019v1

Inverse Problems vol 22 (2006) 89-114

Physics

Mathematical Physics

Scientific paper

10.1088/0266-5611/22/1/006

The Schroedinger 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

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