On the ground state of the Dirac hydrogen atom under a minimal-length assumption

Abstract

We point out an erroneous handling in the literature regarding corrections to the ground state energy of the Dirac hydrogen atom related to the presence of a minimal length. The latter is a non-zero minimal uncertainty in position implied by a modified version of the Heisenberg uncertainty relation known as the Generalized Uncertainty Principle. We show that Brau’s perturbation method, used therein, should lead to problematic divergent terms. We propose then a modified perturbation technique, free of divergences, which allows to calculate the desired energy shift.