  We study space-time non-commutativity applied to the hydrogen atom via the
Seiberg-Witten map and its phenomenological effects. We find that it modifies
the Coulomb potential in the Hamiltonian and add an r-3 part. By calculating
the energies from Dirac equation using perturbation theory, we study the
modifications to the hydrogen spectrum. We find that it removes the degeneracy
with respect to the total angular momentum quantum number and acts like a Lamb
shift. Comparing the results with experimental values from spectroscopy, we get
a new bound for the space-time non-commutative parameter. N.B: In precedent
works (arXiv:0907.1904, arXiv:1003.5732 and arXiv:1006.4590), we have used the
Bopp Shift formulation of non-commutativity but here use it \`a la
Seiberg-Witten in the Relativistic case.
