Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
  In this work we show that relativistic contributions to the ground state energy of the hydrogen atom arising from the presence of a minimal length introduced by a Lorentz-covariant algebra are more relevant than non-relativistic ones, and because of this the non-relativistic approach is not suitable. In addition, comparing our result with experimental data we can roughly estimate the upper bound for the minimal length value of the order $10^{-20}m$. 
R. O. Francisco, T. L. Antonacci Oakes, J. C. Fabris and J. A.   Nogueira
hep-th