Bound states in the dynamics of a dipole in the presence of a conical defect

TL;DR

This paper studies the quantum behavior of an electric dipole in a conical spacetime, revealing bound states with a spectrum that requires regularization for physical validity.

Contribution

It provides an exact solution for the Schrödinger equation in a conical defect spacetime and addresses the unphysical spectrum issue by introducing a finite defect radius.

Findings

Bound states exist with a spectrum from minus infinity to zero.

The spectrum's unphysical divergence is resolved by considering a finite defect radius.

Eigenfunctions are explicitly determined for the system.

Abstract

In this work we investigate the quantum dynamics of an electric dipole in a $(2+1)$-dimensional conical spacetime. For specific conditions, the Schr\"odinger equation is solved and bound states are found with the energy spectrum and eigenfunctions determined. We find that the bound states spectrum extends from minus infinity to zero with a point of accumulation at zero. This unphysical result is fixed when a finite radius for the defect is introduced.