In this thesis after introducing noncommutative space-time, first we give a brief review on two approach of noncommutative standard model(NCSM). In the first approach the gauge group is restricted to U ( n ) and the symmetry group of the standard model is achieved by reduction of to by an appropriate symmetry breaking. In the second one the noncommutative standard model based on gauge group and Seiberg-Witten maps for the field contents of the theory. we study hydrogen atom spectrum and show that for the case space-time ( ) noncommutativity the hydrogen atom has a noncommutative correction at the tree level of the order of ince parameter of noncommutativity,, is constant, there is a preferred direction in space-time which leads to the lorentz symmetry violation, very strong bounds are set on it, so that in low energies, Lorentz symmetry is an accurate symmetry of nature. Therefore, we study the lorentz conserving NCSM based on . In this model we show that the hydrogen atom spectrum has a noncommutative correction at the tree level of the order of . Finally, we generalize the obtained results to the muonic hydrogen atom( ).We show that in the LCNC there is a shift of the order of in . The obtained result is comparable with difference between the theoretical and the experimental value for lamb shift . Keywords: Noncommutative space-time, Standard model, Hydrogen atom, Lamb shift, NoncomNoncommutative parameter
