Schrödinger equation under central and extended double ring-shaped potentials in a conical geometry background

In this paper, our objective is to analyze the behavior of quantum particles governed by the Schrödinger equation subjected to radial- and angular-dependent potentials within a topological defect environment. We focus on deriving the radial equation with a pseudoharmonic potential as the radial component and the angular equations with an extended ring-shaped potential as the angular dependent component. The Bethe ansatz method is utilized to determine solutions for the angular equations, while the radial wave equation is addressed through the confluent hypergeometric equation. Our findings demonstrate that the presence of the topological defect influences the eigenvalue solutions of the non-relativistic quantum particles. Furthermore, we observe that the presence of the topological defect breaks the degeneracy of the energy spectra and gets modification in results compared to the flat space.