Geodesic Flow on the n-Dimensional Ellipsoid as a Liouville Integrable System

TL;DR

This paper demonstrates that the motion on an n-dimensional ellipsoid is a completely integrable system, with classical and quantum separability, contributing to the understanding of higher-dimensional integrable Hamiltonian systems.

Contribution

It introduces a new class of n-dimensional integrable Hamiltonians defined by arbitrary invertible functions, extending classical integrability results.

Findings

Complete integrability with n involutive integrals

Classical and quantum separability achieved

Introduces a new class of integrable Hamiltonians

Abstract

We show that the motion on the n-dimensional ellipsoid is complete integrable by exhibiting n integrals in involution. The system is separable at classical and quantum level, the separation of classical variables being realized by the inverse of the momentum map. This system is a generic one in a new class of n-dimensional complete integrable Hamiltonians defined by an arbitrary function f(q,p) invertible with respect to momentum p and rational in the coordinate q.