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

TL;DR

This paper investigates how topological defects and quantum flux influence eigenvalue solutions of the Schrödinger equation with inverse quadratic Yukawa and inverse square potentials, revealing shifts and flux-dependent energy levels.

Contribution

It introduces an analytical approach to solve the Schrödinger equation with complex potentials in a topologically non-trivial background, highlighting flux effects on eigenvalues.

Findings

Energy eigenvalues are shifted by topological defects.

Eigenvalues depend on quantum flux, indicating Aharonov-Bohm-like effects.

Analytical solutions are obtained using Nikiforov-Uvarov and power series methods.

Abstract

In this analysis, we study the non-relativistic Schrodinger wave equation under the influence of quantum flux field with interactions potential in the background of a point-like 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 point-like global monopole 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