Tuncay Aktosun and Ricardo Weder 2006 Inverse Problems 22 89 doi:10.1088/0266-5611/22/1/006
Inverse spectral-scattering problem with two sets of discrete spectra for the radial Schrödinger equation
Tuncay Aktosun1 and Ricardo Weder2
Show affiliationsThe 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.
- PACS
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02.30.Hq Ordinary differential equations
03.65.Ge Solutions of wave equations: bound states
02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
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47E05 Ordinary differential operators (See also 34Bxx, 34Lxx)
81U40 Inverse scattering problems
34B24 Sturm-Liouville theory (See also 34Lxx)
34L40 Particular operators (Dirac, one-dimensional Schrödinger, etc.)
- Subjects
- Dates
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Issue 1 (February 2006)
Received 6 August 2005, in final form 23 November 2005
Published 22 December 2005
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Inverse spectral-scattering problem with two sets of discrete spectra for the radial Schrödinger equation
Tuncay Aktosun and Ricardo Weder 2006 Inverse Problems 22 89
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