  Using the approach the modified Euler-Lagrange field equation together with
the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative
Dirac equation with a Coulomb potential is derived. We then find the
noncommutative modification the energy levels and the possible new transitions.
In the nonrelativistic limit a general form of the hamiltonian of the hydrogen
atom is obtained, and we show that the noncommmutativity plays the role of spin
and magnetic field which gives the hyper fine structure.
