Bound state solution of the Klein-Gordon equation for vector and scalar Hellmann plus modified Kratzer potentials

In this study, the analytical solutions of the Klein–Gordon equation for any l states of the scalar and vector Hellmann plus modified Kratzer potential are derived by using an approximation method to the centrifugal potential term. The analytical expressions for eigenvalues and corresponding normalized eigenfunctions of the spin-zero particle have been estimated by using the parametric Nikiforov-Uvarov method. The solution for the radial part of the Klein-Gordon equation is formulated in terms of the generalized Jacobi polynomials. The energy state equation and the wave function for special cases are in good agreement with the previous literature. In addition, we have measured the numerical results of the energy eigenvalues and also the trend of the eigenvalues concerning of different potential parameters have been plotted. Furthermore, it was shown that the energy levels E and quantum numbers n and l are inversely proportional to each other.