  We study space-time noncommutativity applied to the hydrogen atom and its
phenomenological effects. We find that it modifies the potential part of the
Hamiltonian in such a way we get the Kratzer potential instead of the Coulomb
one and this is similar to add a dipole potential or to consider the extended
charged nature of the proton in the nucleus. By calculating the energies from
the Schr\"odinger equation analytically and computing the fine structure
corrections using perturbation theory, we study the modifications of the
hydrogen spectrum. We find that it removes the degeneracy with respect to both
the orbital quantum number l and the total angular momentum quantum number j;
it acts here like a Lamb shift. Comparing the results with the experimental
values from spectroscopy, we get a new bound for the space-time non-commutative
parameter. We do the same perturbative calculation for the relativistic case
and compute the corrections of the Dirac energies; we find that in this case
too, the corrections are similar to a Lamb shift and they remove the degeneracy
with respect to j ; we get an other bound for the parameter of
non-commutativity.
