Effects of Pöschl-Teller potential on approximate ℓ ≠ 0-states solution in topological defect geometry and Shannon entropy

Abstract

This study is centered on examining the behavior of quantum particles governed by the Schrödinger equation, particularly when subjected to a trigonometric Pöschl-Teller potential within the context of a topological defect environment. We set out to derive the radial wave equation and employ the Nikiforov-Uvarov method to solve it and present the eigenvalue solution of the quantum system. In fact, it is shown that the topological defect alters both the energy eigenvalues and the corresponding wave functions of quantum particles, diverging from the behavior observed in flat space with this potential. Moreover, we compute the Shannon entropy for this quantum system under investigation and assess how the presence of the topological defect and potential influences it.