Relativistic scattering $s$-states problem for superposition of two potentials «$\delta$-sphere» type

Exact solutions of relativistic two-particle equations for scattering $s$-states are obtained in cases of the $\delta$-function potential and superposition of two $\delta$-function potentials. Scattering amplitudes and phase shifts are calculated on the basis of wave functions found. The analysis of values obtained was carried out. As a result, the unitarity condition and vanishing conditions of scattering amplitudes are proved. It is shown that the non-relativistic limit of relativistic expressions obtained yields results which coincide with corresponding expressions which were found in the process of solving the Schrödinger equation.