Perturbed Coulomb potentials in the Klein–Gordon equation via the asymptotic iteration method

The asymptotic iteration method is used to construct the exact energy eigenvalues for a Lorentz vector or a Lorentz scalar, and an equally mixed Lorentz vector and Lorentz scalar Coulombic potentials. Highly accurate and rapidly converging ground-state energies for Lorentz vector Coulomb with a Lorentz vector or a Lorentz scalar linear potential, V(r)=-Λ1/r+krandV(r)=-Λ1/randW(r)=kr, respectively, are obtained.