In this paper we endeavour to determine the energy levels of an atom by virtue ofthe modified Dirac equation.(This arises from the non commutative nature of spacetime whichagain arises from non-Abelian gauge theory, as argued by Iorio and Sykora in 2001)It has beenfound that the energy levels contain an extra term in the expression which accounts for thezitterbewegung effects in the Compton scale. Applying our perspective to the hydrogen atomwe have been able to find the Lamb shift for the 2S 12and 2P 12states. This result substantiatesthat a slight modification of the Dirac equation suffices to explain the phenomenon, wherethe modification of the Dirac equation arises due to the non-commutative nature of spacetime. Besides, several other unexplained phenomena can emerge as a natural consequence ofthis modification.It must be mentioned that in this Quantum Gravity like approach, the usualQuantum Theory and QFT are low energy approximations where the squares of the Comptonwave length are neglected, as shown over the past fifteen years.
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