Ozfidan, Aysel2025-03-172025-03-1720250031-89491402-4896https://doi.org/10.1088/1402-4896/ada5cchttps://hdl.handle.net/20.500.13099/1838The present work analyzes a physical system with a quantum pseudo-harmonic oscillator in three-dimensional constant curvature spaces within the framework of non-relativistic theory. We present expressions for the energy equation and radial wavefunctions that depend on the curvature parameter kappa, using the functional analysis approach and the asymptotic iteration method. Additionally, we calculate the energy eigenvalues for diatomic molecules N2, H2, and ScH as a function of the constant curvature kappa. Using the Hellmann-Feynmann theorem, we derive expressions for the curvature-dependent expectation values of r-2 and p2, which we detail for the diatomic molecule system in this work. Furthermore, we perform a comparative analysis of the results for non-Euclidean space (spherical and hyperbolic spaces with constant curvature) and Euclidean space.eninfo:eu-repo/semantics/closedAccesscurved spacesdiatomic moleculesexpectation valuesArticle10.1088/1402-4896/ada5cc1002Q2WOS:0013981318000012-s2.0-85215381697Q1