Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method

We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene-Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers l. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H-2, and LiH. We have also obtained the relativistic bound state solution of the Klein-Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrdinger system.