Runge-Lenz vector in Calogero-Coulomb problem

Abstract

We construct the Runge-Lenz vector and symmetry algebra of rational Calogero-Coulomb problem, formulated in terms of Dunkl operators. We find that they are proper deformations of their Coulomb counterpart. Together with similar correspondence between the Calogero-oscillator and oscillator models, this observation permits to claim that most of properties of Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of momenta by Dunkl momenta operators.

6 pages, published version

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• N=4 superconformal Calogero models
• N=4 supersymmetric 3-particles Calogero model
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Cited by in corpus (12)

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• Fourth order Superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials
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• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• Lobachevsky geometry in TTW and PW systems
• Dunkl symplectic algebra in generalized Calogero models
• On symmetries of generalized Calogero model and Polychronakos-Frahm chain
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Superintegrable deformations of oscillator and Coulomb systems
• Dynamical symmetries of the Calogero-Coulomb model