Abstarct: Over time, various models have been presented to investigate the even and odd isotopes, each of which has specific complications, each model justifies certain isotopes and cannot be used to investigate All the cores were limited to one model. One of the successful models for light and even nuclei is the cluster model. The cluster model is baxsed on a combination of nucleons that interact with each other in addition to maintaining their position. Investigating multibody systems is a very difficult task due to having high degrees of freedom, and by using the cluster model, multiparticle systems can be converted into two or three particle systems. In this thesis, we have investigated the stable isotopes of neon using the cluster model. One of the studied isotopes is 20Ne, which has 20 nucleons and 60 degrees of freedom, which we convert into a two-body system (core + cluster) 16O+α, respectively, the next stable isotope of 21Ne is 17O We have considered +α and 22Ne as 18O+α, since 20Ne is a light and stable isotope, it has been studied by many researchers. Therefore, at the beginning, we review the previous researches. isotopes in a two-body system in the form of core and cluster, considering the system as relativistic (Klein-Gordon) and non-relativistic (Schrödinger) by using the solution of quadratic differential equations for hypergeometric wave functions, such as the NU method (Nikiforov- Yuvarov) and choosing the appropriate potential, and then using the numerical method, we have calculated the energy levels and wave function for stable isotopes of neon (20Ne, 21Ne, 22Ne) and compared with experimental data. Therefore, the results obtained for the basic state are more consistent with the experimental data.