Bound and Scattering States Solution of the Relativistic Spinless Particles in View of the Multiparameter Potential

In this paper, we explore the analytical solutions for both bound and scattering states of the Klein–Gordon equation with the multiparameter potential which describes atomic, diatomic and polyatomic molecular structures via the standard method by applying a Pekeris-type approximation to the centrifugal potential. For the bound states, we obtain the energy eigenvalues and the corresponding normalized eigenfunctions in terms of hypergeometric functions. In the scattering states, the phase shift relation is derived. Besides, we investigate the special potentials, which are defined in the literature and derived from to the multiparameter potential. Finally, by using the obtained relations, we give the results both for bound and scattering states numerically and graphically. (author)