Abstract: In this study, the equation needed for the formal treatment of the scattering problems in the light of the Dyson’s equation, which is a reduced form of the more complex Lippmann-Schwinger equation written in terms of the total Green function has been developed. This was achieved by the combination of the boundary conditions and scattering potentials and the combination of non-overlapping scattering potentials within the context of the scattering theory to obtain the transition matrix, which is the most important parameter in scattering problems due to its direct relation with the scattering cross section.