Inverse eigenvalue problems for perturbed spherical Schr?dinger operators

摘要

We investigate the eigenvalues of perturbed spherical Schr?dinger operators under the assumption that the perturbation q{x) satisfies xq(x) ε L~1(0, 1). We show that the square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues up to a decaying error depending on the behavior of q(x) near x = 0. Furthermore, we provide sets of spectral data which uniquely determine q (x).