SUSY approach to Pauli Hamiltonians with an axial symmetry

TL;DR

This paper applies supersymmetric quantum mechanics to analyze a two-dimensional Pauli Hamiltonian with axial symmetry, revealing its spectral properties, symmetries, and algebraic structure through shape-invariance and intertwining operators.

Contribution

It introduces a SUSY-based framework for analyzing Pauli Hamiltonians with axial symmetry, connecting intertwining operators to second order symmetries and constructing the dynamical algebra.

Findings

Spectrum analyzed via shape-invariance.

Intertwining operators linked to second order symmetries.

Full set of ladder operators constructed.

Abstract

A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix Hamiltonian is analyzed from the point of view of supersymmetric quantum mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and also to the Hamiltonian hierarchies generated by intertwining operators. The spectrum is studied by means of the associated matrix shape-invariance. The relation between the intertwining operators and the second order symmetries is established and the full set of ladder operators that complete the dynamical algebra is constructed.