Rotational and inverse square potential effects on harmonic oscillator confined by flux field in a space-time with screw dislocation

This research paper delves into the study of a non-relativistic quantum system, considering the interplay of non-inertial effects induced by a rotating frame and confinement by the Aharonov-Bohm (AB) flux field with potential in the backdrop of topological defects, specifically a screw dislocation. We first focus on the harmonic oscillator problem, incorporating an inverse-square repulsive potential. Notably, it becomes evident that the energy eigenvalues and wave functions are intricately influenced by multiple factors: the topological defect parameter $\beta$ (representing the screw dislocation), the presence of a rotating frame engaged in constant angular motion with speed $\Omega$, and the external potential. Then we study the quantum behavior of non-relativistic particles, engaging in interactions governed by an inverse square potential, all while taking into account the effects of the rotating frame. In both scenarios, a significant observation is made: the quantum flux field's existence brings about a shift in the energy spectrum. This phenomenon bears a resemblance to the electromagnetic Aharonov-Bohm effect.