We used a tool of conventional Nikiforov‐Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen‐Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann‐Feynman Theorem (HFT) to compute expectation values 〈r⁻²〉, 〈r⁻¹〉, 〈T〉, and 〈p²〉 for four different diatomic molecules: hydrogen molecule (H₂), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule. The resulting energy equation reduces to three well‐known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.