Abstarct: There have been many propositions to study the structure of the nucleon including the shell, liquid drop and quark-like models with their own advantages and failures. Here we work on the basis of nonrelativistic quantum mechanics. More precisely speaking, in order to obtain more exact results, the repulsion among the protons is considered and the modified WoodsSaxon potential is applied. After obtaining the energy spectrum and filling up the energy levels by taking into account the Pauli Exclusion Principle, we have succeeded in finding the proper potential coefficient by phenomenological considerations and thereby the average binding energies of different nuclei have been reported. In addition, the energy eigenvalues are given in terms of the Jacobi polynomials and the expectation values are obtained via the Hellmann-Feynman theorem. In chapter 4, Deuteron binding energy has been calculated under the Yukawa potential and the comparison with the existing experimental data is included. In the last chapter, bearing in mind the possible application of position-dependent mass formalism and appealing consequences of relativistic wave equations, we have reported the binding energies of some spin-zero and –one Mesons under the established Hulthén and Kratzer potentials.