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The energy levels of the Schr\"odinger equation under the Eckart-Hellmannpotential (EHP) energy function are studied by the Nikiforov-Uvarov-FunctionalAnalysis (NUFA) method. We obtained the analytic solution of the energy spectraand the wave function in closed form with the help of Greene-Aldrichapproximation. The numerical bound states energy for various screeningparameters at different quantum states and vibrational energies of EHP forCuLi, TiH, VH, and TiC diatomic molecules were computed. Four particular casesof this potential were achieved. To test the accuracy of our results, wecomputed the bound states energy eigenvalues of Hellmann potential which are inexcellent agreement with the report of other researchers.

Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional Analysis (NUFA) method