On the spectrum and eigenfunctions of the equivariant general boundary value problem outside the ball for the Schr\"odinger operator with Coulomb potential

Abstract

We consider the Schr\"odinger equation for hydrogen-like atom with Coulomb potential and non-point ball nucleus. The eigenvalues and eigenfunctions of the operator given by an arbitrary rotation-invariant boundary value problem on the spherical boundary of the nucleus are found and as it is proved to be the eigenvalues are independent on selection of any such boundary value problem and they are the same as for point nucleus.