Quantum systems related to root systems and radial parts of Laplace operators

TL;DR

This paper explores the connection between quantum systems linked to root structures and the radial components of Laplace operators on symmetric spaces, demonstrating their complete integrability.

Contribution

It establishes a relationship between root system quantum models and radial Laplace operators, proving the integrability of certain quantum systems.

Findings

Established the relation between quantum systems and radial Laplace operators.

Proved the complete integrability of some quantum systems.

Connected root systems with symmetric space analysis.

Abstract

The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.