Integrable and superintegrable systems with spin

TL;DR

This paper investigates a two-particle quantum system with spin in a plane, revealing conditions for superintegrability with spin-orbit interaction and solving the Pauli equation in this context.

Contribution

It identifies an 8-dimensional Lie algebra of first-order integrals for a spin system and solves the Pauli equation under superintegrability conditions.

Findings

System admits an 8-dimensional Lie algebra of integrals

Pauli equation solved explicitly in superintegrable case

Reduced to ODEs with a single first-order integral

Abstract

A system of two particles with spin s=0 and s=1/2 respectively, moving in a plane is considered. It is shown that such a system with a nontrivial spin-orbit interaction can allow an 8 dimensional Lie algebra of first-order integrals of motion. The Pauli equation is solved in this superintegrable case and reduced to a system of ordinary differential equations when only one first-order integral exists.