  The classical Lippmann-Schwinger equation (LS equation) plays an important
role in the scattering theory for the non-relativistic case (Schr\"odinger
equation). In our previous paper arXiv:1801.05370, we consider the relativistic
analogue of the Lippmann-Schwinger equation (RLS equation). We represent the
corresponding equation in the integral form. In the present paper, we use the
corresponding integral equation and investigate the scattering problems for
both stationary and dynamical cases. Our approach allows us to develop an RLS
equation theory which is comparable in its completeness with the theory of the
LS equation. In particular, we consider the eigenfunction expansion associated
with the relativistic Dirac equation. We note that the works on the theory of
the LS equation serve as a model for us.
