Integrability and supersymmetry of Schroedinger-Pauli equations for neutral particles

TL;DR

This paper classifies integrable 2D quantum systems for neutral spin-1/2 particles with dipole moments, revealing new solvable models, explicit solutions, and their symmetry structures, expanding understanding of quantum integrability and supersymmetry.

Contribution

It provides a classification of integrable 2D Schroedinger-Pauli systems with spin and dipole moments, introducing new exactly solvable models and analyzing their symmetry algebras.

Findings

Three explicit solutions of the classified systems

Identification of symmetry and superalgebras involved

Restriction to systems with linear matrix integrals of motion

Abstract

Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear physical content. Solutions for three of them are given in explicit form. The related symmetry algebras and superalgebras are discussed. The presented classification is restricted to two-dimensional systems which admit matrix integrals of motion linear in momenta.