A factorization method with application to perturbation theory

A new implementation of perturbation theory is presented for separable problems which is a blend of two previously proposed factorization methods. The resulting technique offers several advantages with respect to the parent methods and yields the perturbation corrections exactly in terms of the quantum numbers of the unperturbed problem through equations in which the unperturbed eigenfunction does not appear explicitly. As an example a perturbed Legendre equation is considered and the application of the approach to other problems of physical interest is discussed.