The study of H₂ and N₂ diatomic molecules in arbitrary dimensions with collective potential model

The analytical bound state solution of the Schrödinger equation with the collective potential model (Hulthén plus screened Kratzer potential) is solved using the Nikiforov-Uvarov-Functional Analysis (NUFA) method. We obtain the energy equation and the wave function with the Greene-Aldrich approximation scheme to the centrifugal term in closed form. The numerical energy eigenvalues and expectation values using Hellmann–Feynman theorem for Hydrogen and Nitrogen diatomic molecules were computed for various quantum states. We also computed the bound state energy of Hulthén potential and our results are consistent with the reports in the literature. The special case energy equations obtained from the NUFA method were the same when compared to other analytical methods, and this validate a high level of mathematical precision of our method. Key Words: Energy spectra; expectation values; Nikiforov-Uvarov functional analysis method; Hulthén-screened Kratzer potential; diatomic molecules. (author)