Abstarct: For studying the doubly magic even-even isotops in the cluster and laxyer model, first we should consider the different cluster structures for the doubly magic isotops. These structures change depending on the energy of the used systems that are as α+nucleus, the sum of two smaller nuclei and finally the sum of many alpha particles. The cluster model is used due to its successes for the light nuclei. We want to calculate the energy levels and the wave functions for the light nuclei from the NikiVarov- Uvarov(NU) method that indeed this method is the solution of the second-order differential equation for the super geometric wave functions. First, we have represented the NU method for solving the Schrodinger equation with a local potential and also have explained the calculation way of the wave function and the energy levels in this method briefly. We ignore the internal structure of the alpha cluster. The used potentials have been considered the modified Yukawa potential or the potential similar to the Ali-Bodmer potential. In this thesis, we consider the energy levels and the ordering structure of the alpha particles for the nuclei of 8Be, 16O, 24Mg, 20Ne and 32S that the used model is the cluster model and the used method is the NU method. Therefore, we determined the different structures of nuclei by comparing the calculated results with the experimental data and obtained the good results for these isotops.