The Relativistic Bound and Scattering States of the Eckart Potential With a Proper New Approximate Scheme for the Centrifugal Term

The approximately analytical bound and scattering state solutions of the arbitrary l wave Klein–Gordon equation for mixed Eckart potentials are obtained through a proper new approximation to the centrifugal term. The normalized analytical radial wave functions of the l wave Klein–Gordon equation with the mixed Eckart potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Two special cases — for the s wave and for l = 0 and β = 0 — are also studied, briefly.