Hellmann potential and topological effects on non-relativistic particles confined by Aharonov–Bohm flux field

In this analysis, we investigate the quantum motions of a non-relativistic particle confined by the Aharonov–Bohm flux field with Hellmann potential (Coulomb plus Yukawa potential) in a topological defect space-time produced by a point-like defect. We employ a suitable approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation and determine the eigenvalue solution using the parametric Nikiforov–Uvarov method. Afterwards, we study the quantum system with an attractive Coulomb potential and obtained the eigenvalue solution using the same NU-method. These eigenvalue solutions are analysed and see the effects of topological defects produced by a point-like defect and the AB-flux field with these potentials. We also see that in addition to the topological effects, the energy levels shift more by the magnetic flux field, which gives us an analogue of the Aharonov–Bohm effect for the bound state. Finally, we plot a few graphs of the energy levels and the radial wave function with different parameters, such as the topological defect, the magnetic flux field, and the screening parameter, and discuss the results.