  The hydrogen atom is investigated, within a pseudo-complex extension of the
coordinates and momenta, which introduces a minimal length scale (l) and
results into a non-commutative Quantum Mechanics. After resuming the
pseudo-complex extension of Quantum Mechanics, the modified energies of the
hydrogen atom are deduced, producing corrections of the order of the square of
the minimal length scale. Using the Lamb Shift, we obtain an upper boundary for
the minimal length scale l, orders of magnitude more restrictive than former
estimations.
