Approximate energy spectra of diatomic molecules (LiH, HCl, VH, I2) case of the Hulthén plus screened Kratzer potential

In this research, we used the Nikiforov Uvarov functional analysis method to solve the Schrödinger equation with the Hulthén plus screened Kratzer potential using the Greene Aldrich approximation to remove the centrifugal barrier. We determine the bound state energies and corresponding wave functions. We applied our results to several diatomic molecules (LiH, HCl, VH, and I2) to analyze their energy spectra. Our technique produced accurate results, which were validated by comparing our eigenvalue data with numerical data obtained by other researchers. Given the precision of this analytical method, we recommend its application in solving problems in non-relativistic and relativistic systems, particularly those involving exponential potentials.