Analytical solutions of the N-dimensional Schrödinger equation with modified screened Kratzer plus inversely quadratic Yukawa potential and thermodynamic properties of selected diatomic molecules

Abstract

In this study, we presented approximate analytical solutions to the N-dimensional Schrödinger equation with the screened modified Kratzer plus inversely quadratic Yukawa potential (SMKIQYP) by adopting the Nikiforov-Uvarov method and using the Greene-Aldrich approximation scheme for the inverse square term. The obtained energy eigenvalues were used to investigate four diatomic molecules: Hydrogen (H2), Iodine (I2), Nitrogen monoxide (NO), and Carbon monoxide (CO). The numerical results of the energy spectrum for the NO and CO molecules based on some of the deduced potentials such as modified Kratzer and screened modified Kratzer potentials were also determined. Then, using the obtained partition function, we calculated the thermodynamic properties such as the mean energy, specific heat, entropy, and free energy of the aforementioned diatomic molecules. The partition function of the H2, CO, and I2 diatomic molecules was computed for various temperatures. The results show that the partition function of the three diatomic molecules increased with increasing temperature. To validate our results, the numerical results of the energy spectrum for a few recovered potentials were compared with the results available in the literature, and we observed that our results are in excellent agreement.