Joseph, Gabriel WirdzeliiTargema, Terkaa VictorOyewumi, Kayode JohnOmugbe, EkwevugbeAjulo, Kayode RichardGabriel, OchocheZoe, Heeseung2025-09-252025-09-2520250026-89761362-3028https://doi.org/10.1080/00268976.2025.2547935Omugbe, Ekwevugbe/0000-0003-1510-4235; /0000-0002-7917-1317In this paper, we examine the effects of point-like and cosmic string topological defects on non-relativistic particles confined within external potentials using analytical methods. The external potentials under consideration include the Hellmann-Kratzer potential, the standard Kratzer potential, the energy-dependent Kratzer potential, and the modified Kratzer potential. The modified Kratzer potential is employed to illustrate the impact of topological defects on diatomic molecules, demonstrating that these defects impose significant constraints on the molecules. In all defect types, the depth of the effective potential increases with increasing curvature. In these regions, molecules become trapped and experience a substantial reduction in energy in the case of point-like defects. Conversely, when particles propagate in a cosmic string background, their energy increases. When the constraints imposed by the topological defects on these molecules are removed, the results obtained in this study align well with existing literature. Thus, we establish beyond reasonable doubt the effects of topological defects on non-relativistic particles and, consequently, on diatomic molecules, which arise from the geometry of these defects. Additionally, we have employed analytical methods to obtain the solutions without introducing any modification to the centrifugal term. The approach is straightforward, highly efficient, and effective.eninfo:eu-repo/semantics/closedAccessNon-Relativistic ParticlesExternal PotentialsAnalytical MethodsDiatomic MoleculesTopological DefectsArticle2-s2.0-10501375195310.1080/00268976.2025.2547935