Quantum Lie systems and integrability conditions

TL;DR

This paper develops a geometric framework for integrability in Quantum Mechanics by combining Lie systems theory and integrability conditions, leading to new integrable models and unifying existing results.

Contribution

It introduces a geometric theory of quantum integrability using Lie systems and provides new integrable quantum models while unifying previous findings.

Findings

Development of a geometric integrability framework for Quantum Mechanics

Construction of new non-trivial integrable quantum models

Recovery of known results within a unified geometric approach

Abstract

The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper we use both developments to obtain a geometric theory of integrability in Quantum Mechanics and we use it to provide a series of non-trivial integrable quantum mechanical models and to recover some known results from our unifying point of view.