Effects of a global monopole on quantum systems with the exponential potential

We study the Schrödinger wave equation with an exponential potential in the context of a point-like global monopole. This exponential potential is composed of a generalized $q$-deformed Hulthen potential and a Yukawa-type potential. We incorporate the Greene–Aldrich approximation scheme to handle the centrifugal and other terms and obtain an approximate eigenvalue solutions in terms of special functions. We show that the eigenvalue solution is influenced by the topological defect with this exponential potential, and therefore breaks the degeneracy of the spectrum compared to the flat-space case. We then use this eigenvalue solution to analyze a few superposed potential models, and discuss the results.