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

•An erroneous handling in the literature of the Dirac hydrogen atom with minimal length is pointed out.•A modified perturbation technique, free of divergences, is proposed.•Correction to the ground state energy of the Dirac hydrogen atom with minimal length is calculated. 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.