Relativistic spectrum of hydrogen atom in the space-time non-commutativity

We study space-time non-commutativity applied to the hydrogen atom 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.