Analytical and Computational Study of Bound States in Quantum Systems with Topological Defects under the Morse-Hulthén Interaction Potential

Approximate solutions of the Schrödinger equation (SE) for the Morse-Hulthén potential (MHP) in cosmic string spacetime were obtained using the Nikiforov–Uvarov (NU) method together with an improved approximation scheme for the centrifugal term. Closed-form expressions for the energy spectra and normalized wave functions were derived. The Hellmann-Feynman theorem (HFT) was used to determine the expectation values of the inverse-squared distance, the kinetic energy and the momentum squared. Numerical investigations were carried out for H2, HCl and LiH diatomic molecules under the influence of the cosmic string topological parameter   and the potential strength V0. The results showed that the topological defect has a significant effect on the rotational–vibrational spectrum of the molecular system through the angular deficit parameter, thereby breaking the usual angular degeneracy of the states. Furthermore, it was observed that an increase in the potential strength deepens the bound states, whereas increasing the quantum numbers reduces the binding energy of the system. The present results reduce to the ordinary flat space in the limit →1 . Moreover, the obtained solutions recover the standard Morse and Hulthén potentials as special cases and are consistent with previous studies on exponential-type potentials and quantum systems in curved spacetime geometries reported in the literature. Therefore, the study provides useful insight into the effects of spacetime topology on molecular quantum systems and contributes to the applications of quantum mechanics in curved spacetime and molecular spectroscopy.