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arxiv: math-ph/0402019 · v1 · submitted 2004-02-09 · 🧮 math-ph · math.MP· math.SP

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

classification 🧮 math-ph math.MPmath.SP
keywords boundaryconditiondiscretecontinuouseigenvaluesequationpotentialschroedinger
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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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