Determination of closed expressions for the perturbation theory corrections to the wave functions of bound states by means of a Sturm function expansion

By summation of expansions with respect to a complete system of eigenfunctions of a Sturm–Liouville type operatorwith only a discrete spectrum, closed expressions are obtained for the first- and second-order perturbation corrections to the wave function of an arbitrary bound state of an electron in a Coulomb field in the presence of a centrally symmetric perturbing potential.