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We present an important contribution to the non-commutative approach to the hydrogen atom to deal with lamb shift corrections. This can be done by studying the Klein-Gordon and Dirac equations in a non-commutative space-time up to first-order of the non-commutativity parameter using the Seiberg-Witten maps. We thus find the non-commutative modification of the energy levels and by comparing with the the current experimental results on the Lamb shift of the 2P level to extract a bound on the parameter of non-commutativity, we show that the fundamental length ($\sqrt{\Theta}$) is compatible with the value of the electroweak length scale ($l$). Phenomenologically, this effectively confirms the presence of gravity at this level.

Noncommutative Space-Time of the Relativistic Equations with a Coulomb Potential Using Seiberg-Witten Map