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

TL;DR

This paper derives first- and second-order energy corrections for the Pauli-Dirac equation using Laguerre polynomial identities within a perturbative framework, providing analytical integral forms.

Contribution

It introduces a method to compute perturbative corrections to the Pauli-Dirac equation using Laguerre polynomial identities, enhancing analytical approaches.

Findings

Analytical expressions for energy corrections up to second order.

Explicit integral formulas involving Laguerre polynomials.

Application of perturbation theory to relativistic quantum equations.

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.