Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems

TL;DR

This paper introduces integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems, deriving their constants of motion and demonstrating how their Schrödinger equations decouple, revealing effects on energy degeneracy.

Contribution

It constructs new integrable models using Dunkl operators and analyzes their quantum properties, extending classical Coulomb systems.

Findings

Constants of motion derived via Dunkl operators

Schrödinger equations decouple in specific coordinates

Calogero term affects energy degeneracy

Abstract

We propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schr\"odinger equations decouple in parabolic and elliptic coordinates into the set of three differential equations like for the Coulomb-Stark and two-center Coulomb problems. The Calogero term preserves the energy levels, but changes their degrees of degeneracy.