Non-relativistic quantum particles interacting with pseudoharmonic-type potential under flux field in a topological defect geometry

In this work, we investigate the quantum motions of non-relativistic particles interacting with a potential in the presence of the Aharonov-Bohm (AB) flux field within a topological defect geometry, for example, space-time with a distortion of a vertical line into a vertical spiral. We begin by deriving the radial Schr\"odinger wave equation, incorporating an anharmonic oscillator potential, which is a superposition of a harmonic oscillator and an inverse square potential, along with a constant term. The eigenvalue solution is obtained through the confluent Heun equation focusing on the ground state energy level and the radial wave function for the radial mode $n=1$ as an example and analyze the results. Subsequently, we use these results in molecular potential models, considering pseudoharmonic and shifted pseudoharmonic potentials. The derived eigenvalue solutions provide insights into the behavior of particles within these potentials. Expanding our exploration, we study the quantum system featuring only an inverse square potential in the presence of the quantum flux field in the same geometry background. Employing the same procedure, we determine the ground state energy level and the radial wave function. Notably, our findings reveal that the eigenvalue solutions are significantly influenced by the topological defect characterized by the parameter $\beta$, and the quantum flux field $\Phi_{AB}$. This influence manifests as a shift in the energy spectrum, drawing parallels to the gravitational analog of the Aharonov-Bohm effect.