Topological Effects with Inverse Quadratic Yukawa Plus Inverse Square Potential on Eigenvalue Solutions

We study the nonrelativistic Schrödinger wave equation under the influence of a quantum flux field with an interaction potential in the background of a pointlike global monopole (PGM). In fact, we consider an inverse quadratic Yukawa plus inverse square potential and derive the radial equation employing the Greene–Aldrich approximation scheme in the centrifugal term. We determine the approximate eigenvalue solution using the parametric Nikiforov–Uvarov method and analyze the result. Afterwards, we derive the radial wave equation using the same potential employing a power series expansion method in the exponential potential and solve it analytically. We show that the energy eigenvalues are shifted by the topological defects of a pointlike global monopole as compared to the flat space result. In addition, we see that the energy eigenvalues depend on the quantum flux field that shows an analogue to the Aharonov–Bohm effect.