Bound state solutions of the Klein–Gordon equation with the improved expression of the Manning–Rosen potential energy model

By employing the improved Greene–Aldrich approximation scheme to deal with the centrifugal term, we solve approximately the Klein–Gordon equation with the improved expression of the Manning–Rosen empirical potential energy model. The bound state energy equation and the unnormalized radial wave functions have been approximately obtained by using the supersymmetric WKB approach and the function analysis method. The relativistic vibrational transition frequencies for the a3Σu+ state of 7Li2 molecule have been computed by using the Manning–Rosen potential model. The relativistic vibrational transition frequencies are in good agreement with the observed data.

► Bound state solutions of the Klein–Gordon equation with the improved expression of the Manning–Rosen potential energy model are explored.
► Relativistic vibrational transition frequencies for the a3Σu+ state of 7Li2 molecule are presented.
► Relativistic vibrational transition frequencies are in good agreement with the observed data.