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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 thepotential and the boundary conditions are uniquely determined by the datacontaining the discrete eigenvalues for a boundary condition at the origin, thecontinuous part of the spectral measure for that boundary condition, and asubset of the discrete eigenvalues for a different boundary condition. Thisresult extends the celebrated two-spectrum uniqueness theorem of Borg andMarchenko to the case where there is also a continuous spectru

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