Relativistic and nonrelativistic treatment of Hulthen–Kratzer potential model in D-dimensions

We present approximate solutions of the Klein–Gordon equation containing an interaction of the Hulthen and modified Kratzer potential using the procedure of Nikiforov–Uvarov and the Greene–Aldrich approximation method of handling centrifugal barriers. In our results, we obtained the bound-state relativistic energy eigenvalues and their corresponding eigenfunctions in terms of the Jacobi polynomials. We then showed that in the nonrelativistic limit, the energy eigenvalues reduces to the one obtained using the Schrodinger equation. Furthermore, to get a better insight into the behaviour of diatomic molecular systems, we investigated the behaviour of some selected diatomic molecules, namely N 2 , I 2 , CO, NO and HCl, when subjected to the potentials under study. This was done by determining the shape of the potential of the molecules when the interatomic distance r equals the equilibrium bond length r e . Also, the energy spectrum was computed for the selected diatomic molecules for various vibrational and rotational quantum numbers. Special cases of the potential and their corresponding energies were deduced and were found to be in agreement with the literature. Finally, we present the variations of the energy eigenvalues with the potential strength, equilibrium bond length, dissociation energy, screening parameter, dimensions, vibrational and rotational quantum numbers, respectively.