Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators

Abstract

We investigate the eigenvalues of perturbed spherical Schrödinger operators under the assumption that the perturbation $q(x)$ satisfies $xq(x)\in L^1(0,1)$. We show that the square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues up to an decaying error depending on the behavior of $q(x)$ near $x=0$. Furthermore, we provide sets of spectral data which uniquely determine $q(x)$.

14 pages

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