Spherical Calogero model with oscillator/Coulomb potential: quantum case

TL;DR

This paper investigates the quantum Calogero model on an N-dimensional sphere with oscillator or Coulomb potentials, using Dunkl deformation to derive Hamiltonians, symmetry generators, and their algebraic structures.

Contribution

It introduces a Dunkl deformation approach to quantum Calogero models on spheres, deriving Hamiltonians and symmetry algebras for oscillator and Coulomb potentials.

Findings

Hamiltonians obtained via Dunkl deformation

Symmetry generators identified and algebra computed

Models extended to N-dimensional spherical geometry

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.