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

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.