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Arbitrary $\ell$-state solutions of the Klein-Gordon equation with the Manning-Rosen plus a Class of Yukawa potentials

Focusing on an improved approximation scheme, we present how to treat the centrifugal and the Coulombic behavior terms and then to obtain the bound state solutions of the Klein-Gordon (KG) equation with the Manning-Rosen plus a Class of Yukawa potentials. By means of the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods, we present the energy spectrum for any $\ell$-state and the corresponding radial wave functions in terms of the hypergeometric functions. From both methods we obtain the same results. Several special cases for the potentials which are useful for other physical systems are also discussed. These are consistent with those results in previous works. We obtain that the energy level $E$ is sensitive to the potential parameter $δ$ at fixed values of other parameters and increases when $δ$ runs from $0.05$ to $0.3$. Furthermore, $E$ is sensitive to the quantum numbers $\ell$ and $n_r$ for a given $δ$, as expected.