Abstarct: The nuclear physics models have important roles in studying the structure of nuclear models, which includes the Liquid-Drop model, Shell model and Quark Model. This thesis is about Shell model for deriving the hyperfine interaction. First, we study the Shell model in non-relativistic quantum mechanics so we solve the Schrödinger equation in the presence of Woods-Saxon potential then the energy spectrum derived for different Isotopes of Mg. In addition, we consider the effect of this potential on the Shell Model by using the Spin-Orbit interaction which is a perturbation exxpression. Furthermore, we solve the Schrödinger equation for Woods-Saxon and Spin-Orbit potential for stable and unstable nucleus with numerical method. Hence, we do not use any approximation then we compare the analytical and numerical solutions. In addition, the wavefunction reported as hypergeometry function. Then we solve the Dirac equation for single nucleon in Spin symmetry and Pseudospin symmetry in the presence of physical radial and angular potentials. In addition, we derive the spectrum energy and the components of Dirac spinors. Moreover, by solving the Dirac equation in the presence of tensor potential, the energy spectrum and degeneracy between bound states have been deduced. In the end, we discuss about potential parameters in non-relativistic and relativistic cases, we investigate an important problem in non-relativistic quantum mechanics, we derive the energy spectrum in Coulomb potential for two-center problem, and the parameters have been considered.