The perturbed ladder operator method-analytical determination of the generalised central field energies and wavefunctions

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Abstract
In order to extend the original range of applicability of the ladder operator formalism, a novel method of resolution of perturbed equations is presented. This method, capable of handling any order of the perturbation, allows an easy determination of 'perturbed ladder operators' and hence gives analytical expressions for the perturbed eigenvalues and eigenfunctions in terms of the quantum numbers of the unperturbed factorisable problem. The case of a wave equation with a Coulomb potential (factorisable type F) perturbed by an additive Hamiltonian expanded in a positive power series of r, i.e. V(r)=-(l(l+1)/r2)-(2q/r)+b0+b1r+...+bsrs, is worked out in detail. Application to the screened (static or cosine) Coulombic problem is given as an illustrative example.