Bound-state Solutions of Klein-Gordon and Schrodinger Equations for Arbitrary l-state with Linear Combination of Hulthen and Kratzer Potentials

We present approximate solutions of the both the modified Klein-Gordon (MKGE) and modified Schrodinger equation (MSE) containing the modified Hulthen and modified Kratzer potential using the procedure of Bopp's shift method and perturbation theory in addition to the Greene-Aldrich approximation method of handling centrifugal barriers. This study is conducted in the relativistic and nonrelativistic non-commutative 3-dimensional real space (RNC: 3D-RS) and (NRNC: 3D-RS) symmetries, respectively. The Hulthen-Kratzer potential model is extended to include new radial terms. Furthermore, this potential model is proposed to study some selected diatomic molecules, namely N-2, I-2, CO, NO and HCl. The ordinary Bopp's shift method and perturbation theory are surveyed to get generalized excited states energy as a function of the shift energy and the energy E-nl of the HKP model. Furthermore, the obtained perturbative solutions of the discrete spectrum were dependent on Gamma function, the discreet atomic quantum numbers (j, l, s, m) and the potential parameters (V-0,alpha,r(e), D-e) , and the NC-parameters, which are generated with the effect of (space-space) noncommutative properties. We have also applied our results on diatomic-molecules with spin-0 and spin-1, and have shown that the modified Klein-Gordon equation MKG under the MHKP model becomes similar to the Duffin-Kemmer equation.