Dynamical Supersymmetry of a Vortex System with $1/r^{2}$ Potential

TL;DR

This paper explores the dynamical supersymmetry in a vortex system with a $1/r^{2}$ potential, deriving the spectrum and wave functions, and extending the symmetry to include an external harmonic potential.

Contribution

It demonstrates the presence of $Osp(1,1)$ supersymmetry in the system and extends this symmetry to cases with an added harmonic potential.

Findings

Spectrum and wave functions derived using supersymmetry.

Supersymmetry persists with an external harmonic potential.

Provides a framework for analyzing vortex systems with supersymmetry.

Abstract

The Pauli Hamiltonian for a spin $\frac{1}{2}$ charged particle interacting with a point magnetic vortex and $1/r^{2}$ potential exhibits a dynamical supersymmetry $Osp(1,1)$ on the plane except at the origin. Using this symmetry, the spectrum and the wave functions have been obtained. And, the dynamical supersymmetry could be imported to the case when an external harmonic potential is added.