Spherical Calogero model with oscillator/Coulomb potential: quantum case

Abstract

We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and its restriction to (Coxeter reflection) symmetric wave functions. By the same method we also find the symmetry generators and compute their algebras.

7 pages, no figures

References in corpus (4)

• Physics and Mathematics of Calogero particles
• Calogero models and nonlocal conformal transformations
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• Spherical Calogero model with oscillator/Coulomb potential: classical case

Cited by in corpus (11)

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• Spherical Calogero model with oscillator/Coulomb potential: classical case
• Hidden symmetries of the Higgs oscillator and the conformal algebra
• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• 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
• Dynamical symmetries of the Calogero-Coulomb model
• Superintegrable deformations of oscillator and Coulomb systems