Bound state solutions and thermal properties of the N-dimensional Schrödinger equation with Varshni plus Woods-Saxon potential via Nikiforov-Uvarov method

We have solved the Schrödinger equation for Varshni plus Woods-Saxon potential in N-dimensions within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier term. We obtained the numerical bound state energies for both physical parameters and some diatomic molecules for various values of screening parameter which characterizes the strength of the potential. We obtained the energy eigen equation in a closed and compact form and applied it to study partition function and other thermodynamic properties as applied to four selected diatomic molecules namely: Nitrogen (N₂), Carbon (II) Oxide (CO), Nitrogen Oxide (NO) and Hydrogen (H₂) molecules, respectively using experimentally determined spectroscopic parameter. The numerical energy eigenvalues obtained both for physical parameters and for selected diatomic molecules at various dimensions (N= 2, 4 and 6) reveals that constant degeneracies occurs for S and P quantum state. The result also shows that 1S-quantum state has the highest bound state energies which are experimentally verified because of its proximity to the nucleus of an atom. To ascertain the accuracy of our work, the thermodynamic spectral diagram produces an excellent curves as compared to work of an existence literature. This research has application in the field of molecular spectroscopy.