Approximate bound state solutions of the Klein-Gordon equation with the linear combination of Hulthén and Yukawa potentials

Based on a developed scheme we show how to deal with the centrifugal term and the Coulombic behavior part and then to solve the Klein-Gordon (KG) equation for the linear combination of Hulthén and Yukawa potentials. Two cases, i.e., the scalar potential which is equal and unequal to vector potential, are considered for arbitrary l state. With the aid of the Nikiforov-Uvarov (NU) method and the traditional approach, we present the eigenvalues and the corresponding radial wave functions expressed by the Jacobi polynomials or hypergeometric functions and find that the results obtained by them are consistent. For given values of potential parameters V₀,V₀ ^′,S₀,S₀ ^′ and M=1, we notice that the energy levels E are sensitively relevant for the potential parameter δ and the energy levels E increase for δ>0.1 as quantum numbers n_r and l increase. However, for δ∈(0,0.1) the energy levels E do not always increase with the quantum numbers n_r and l. We find that the energy levels E are inversely proportional to quantum numbers n_r and l when δ∈(0,0.05).