On the Hellmann–Feynman theorem and the corrections to the energy in the Rayleigh–Schrödinger perturbation theory

In this work we present an alternative method, based on the Hellmann–Feynman theorem, to generate energy corrections within the standard Rayleigh–Schrödinger perturbation theory. As a result, compact expressions for the corrections to the energy at different orders are obtained. We also review a method that allows us to calculate the corrections to the wave function needed in the energy calculations. Finally, our results are compared with those obtained by other authors by a different technique.