Thermodynamic Properties and Solutions of the D-dimensional Schrödinger Equation with the Modified Möbius Square plus Modified Schiöberg Potential

The approximate bound-state energy spectrum of the Modified Möbius Square plus Modified Schioberg Potential (MMSMSP) within the d-dimensional Schrödinger equation was analytically studied using the Nikiforov-Uvarov Functional Analysis (NUFA) method. The associated normalized wave functions were obtained via the hypergeometric differential equation approach. Energy eigenvalues were analyzed for selected spatial dimensions by varying the potential depth and other model parameters. Furthermore, closed-form analytical expressions for the thermal properties of the MMSMSP were derived, and their temperature dependence was examined across the chosen dimensions. The results obtained show good agreement with previously reported studies and can be apply in atomic and molecular physics