Effects of Conical Geometry on Approximate Solutions Under Modified Pöschl-Teller Potential and Shannon Entropy

In this study, we investigate the behavior of non-relativistic quantum particles interacting with a modified Pöschl-Teller potential in the backdrop of a topological defect created by global monopoles. We derive the radial equation of the Schrödinger wave equation through a wave function ansatz and obtain an approximate \(\ell \ne 0\)-state eigenvalue solution by employing the Nikiforov-Uvarov method. Our analysis demonstrates that the presence of a global monopole affects both the energy eigenvalue and the wave functions of non-relativistic quantum particles, deviating from the behavior observed in flat space with this potential. Furthermore, we calculate the Shannon entropy for this quantum system and evaluate how the existence of the topological defect and potential influences it.