An inverse problem for the Schrödinger equation with a radial potential (Q685813)

The author studies the inverse spectral problem for the time independent Schrödinger operator with a radial potential on the unit ball in \(\mathbb{R}^ 3\), where homogeneous Dirichlet boundary conditions are imposed. As the main question it is asked whether the potential under consideration can be uniquely determined given the spectra associated to the pair of Sturm-Liouville operators. It is shown that the intersection of the isospectral sets concerning the first two harmonics of the Schrödinger equation is locally compact under the assumptions stated in the paper.