Abstarct: Study of multi-particle systems has received much attention in recent years, researchers and scholars in the field of Nuclear Sciences because of it in this master of science thesis we try to describe two and three particle system with Laplace Transform Approach (LTA). This new approach is suitable for a case study of two and three particle systems in the presence of different potential. This thesis begins with an introduction of elementary particles and then describes the core of the binding energy has been with the introduction of nuclear potential Yukawa, by applying the Laplace transform descxription of the core are provided. Then, using the Laplace transform approach for two-particle systems have been studied for a number of known potential. Finally, a system of three particles in the presence of the Coulomb potential and the interaction potential spin - orbit Rashba is studied.