<p>This study investigates the expectation values and Shannon entropy of selected diatomic molecules—HCl, CO, and LiH—within the framework of the Kratzer plus Generalized Morse Potential. The energy eigenvalues and wave functions are determined using the parametric Nikiforov–Uvarov approach, enabling a detailed analysis of key quantum mechanical properties, including kinetic energy, squared momentum, and inverse square distance expectation values. Furthermore, Shannon entropy is applied to examine wave function localization in both position and momentum spaces, emphasizing the impact of screening parameters on molecular behavior. The findings indicate that an increase in the rotational quantum number results in higher energy spectra and expectation values. The Shannon entropy analysis reinforces the uncertainty principle by demonstrating an inverse relationship between position and momentum entropy. These insights contribute to quantum information measures in molecular systems, with potential applications in spectroscopy, molecular modeling, and quantum chemistry.</p>