Ro-vibrational energies and expectation values of selected diatomic molecules via Varshni plus modified Kratzer potential model

The analytical solutions of the Klein–Gordon equation of diatomic molecules with an approximation to the centrifugal term for the Varshni plus modified Kratzer potential model are obtained approximately within the framework of the Nikiforov–Uvarov (NU) method. The expression for ro-vibrational energy, normalized wave function, and expectation values for the diatomic molecules N_2, CO, NO, I_2 and H_2 have all been obtained. The ro-vibrational energies for the dimer molecules were computed using their separate spectroscopic parameters. Utilizing Hellman–Feynman theorem, the expectation values of the inverse square position ⟨r^ - 2⟩ , kinetic energy ⟨ T ⟩ , square of momentum ⟨P^2⟩ , and their separate numerical values for the selected diatomic molecules were obtained explicitly. Two special cases of the potential are also studied, and their numerical energy eigenvalues obtained are reliable and very consistent with the existing literature.