SU(2) Symmetry and Degeneracy From SUSY QM of a Neutron in the Magnetic Field of a Linear Current

TL;DR

This paper demonstrates how supersymmetric quantum mechanics can be used to construct su(2) symmetry operators for a neutron in a magnetic field, explaining spectral degeneracies.

Contribution

It introduces a method to derive su(2) symmetry from SUSY ladder operators in a specific quantum system, revealing underlying degeneracies.

Findings

Constructed su(2) algebra from SUSY ladder operators

Explained degeneracy of energy levels in the system

Linked symmetry operators to physical angular momentum component

Abstract

From SUSY ladder operators in momentum space of a neutron in the magnetic field of a linear current, we construct $2\times 2$ matrix operators that together with the z-component of the angular momentum satisfy the su(2) Lie algebra. We use this fact to explain the degeneracy of the energy spectrum.