Perturbation hydrogen-atom spectrum in deformed space with minimal length

Abstract

We studied energy spectrum for the hydrogen atom with deformed Heisenberg algebra leading to the minimal length. We developed the correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the three-dimensional case the corrections to $s$ levels of the hydrogen atom caused by the minimal length. Comparing our results with the experimental data from precision hydrogen spectroscopy an upper bound for the minimal length is obtained.