Inverse Spectral-Scattering Problems on the Half-Line with the Knowledge of the Potential on a Finite Interval

Abstract

The inverse spectral and scattering problems for the radial Schrodinger equation on the half-line \({[0,\infty)}\) are considered for a real-valued, integrable potential having a finite first moment. It is shown that the potential is uniquely determined in terms of the mixed spectral or scattering data which consist of the partial knowledge of the potential given on the finite interval \({[0,\varepsilon]}\) for some \({\varepsilon > 0}\) and either the amplitude or phase (being equivalent to scattering function) of the Jost function, without bound state data.