Inverse spectral-scattering problem for the half-line Schrödinger equation

Tuncay Aktosun Mississippi State University, USA

For the Schrödinger equation on the half line with selfadjoint boundary conditions at the origin, the inverse problem of recovery of the potential and the boundary conditions is analyzed. When the scattering data consist of the absolute value of the Jost function for one boundary condition, the discrete eigenvalues for that boundary condition, and a subset of discrete eigenvalues for a second boundary condition, it is indicated whether the corresponding data set yields the unique recovery, or else what additional information is needed for the uniqueness. This is joint work with Ricardo Weder.