Pauli equation and the method of supersymmetric factorization

TL;DR

This paper explores various methods of factorizing 2x2 matrix Pauli operators in two dimensions, linking their spectra to scalar Schrödinger operators, and discusses electromagnetic field classes with illustrative examples.

Contribution

It introduces new factorization techniques for 2D Pauli operators, extending SUSY QM methods to include covariant derivatives and electromagnetic fields.

Findings

Factorization relates Pauli spectra to scalar Schrödinger spectra.

Extended SUSY QM quasifactorization includes electromagnetic fields.

Examples illustrate the applicability of the methods.

Abstract

We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to one-dimensional Darboux transformations. We consider both the case when such factorization is reduced to the ordinary 2-dimensional SUSY QM quasifactorization and a more general case which involves covariant derivatives. The admissible classes of electromagnetic fields are described and some illustrative examples are given.