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

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 Schrödinger 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.

18 pages

References in corpus (7)

• Physics and Mathematics of Calogero particles
• On Dunkl angular momenta algebra
• The quantum angular Calogero-Moser model
• Action-angle variables for dihedral systems on the circle
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Runge-Lenz vector in Calogero-Coulomb problem
• The structure of invariants in conformal mechanics

Cited by in corpus (8)

• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Lobachevsky geometry in TTW and PW systems
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Coupling and particle number intertwiners in the Calogero model
• Superintegrable deformations of oscillator and Coulomb systems