**ABSTRACT**

In this work, we present the analytical and numerical study of the bound state energy eigenvalues using the Nikiforov-Uvarov method. The Hulthen plus Yukawa potentials were combined to solve the approximate bound state solutions of the radial part of the Schrödinger wave equation. The NU method is used to solve hypergeometric-type second-order differential equations having special orthogonal functions. We presented graphically the behavior of the Hulthen and the Yukawa potentials at different screening parameters, and potential strength, . The investigation of how the energy eigenvalues respond or behave when plotted against the screening parameter and the potential depth was done. And from our results, it was observed in table 1 that as the quantum state or quantum number increased, the energy eigenvalues became more bounded. That means that the energy eigenvalues increased as the quantum number increased. Also, that the energy eigenvalues decreased when the values of the screening parameter are increased. For Table 1 and 2, we noticed the degeneracies of the energy levels in quantum numbers n = 2, 3, 4 and 5 for dimensions, D = 3 and 5. Also, as the values of the potential depth were increased, the energy eigenvalues reduced. The results are consistent with existing literatures referenced in the work.

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