Solutions of Pauli-Dirac Equation in terms of Laguerre Polynomials within Perturbative Scheme

Abstract

We search for first- and second-order corrections to the energy levels of the Pauli-Dirac equation within the Rayleigh-Schr\"odinger theory. We use some identities satisfied by the associated Laguerre polynomials to reach this aim. We give a list presenting analytical forms of some integrals including two associated Laguerre polynomials, or their derivatives.