# Spherical Calogero model with oscillator/Coulomb potential: quantum case

@article{Correa2016SphericalCM, title={Spherical Calogero model with oscillator/Coulomb potential: quantum case}, author={Francisco Correa and Tigran Hakobyan and Olaf Lechtenfeld and Armen Nersessian}, journal={Physical Review D}, year={2016}, volume={93}, pages={125009} }

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.

## 15 Citations

Spherical Calogero model with oscillator/Coulomb potential: Classical case

- Physics
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We construct the Hamiltonians and symmetry generators of Calogero-oscillator and Calogero-Coulomb models on the N-dimensional sphere within the matrix-model reduction approach. Our method also…

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Generalizations of oscillator and Coulomb models are discussed via introduction of holomorphic coordinates. Complex Euclidean analogue of the Smorodinsky-Winternitz system is introduced and studied.…

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We give a solution to the long-standing problem of constructing the generators of hidden symmetries of the quantum Higgs oscillator, a particle on a d-sphere moving in a central potential varying as…

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We propose new superintegrable mechanical system on the complex projective space $\mathbb{CP}^N$ involving a potential term together with coupling to a constant magnetic fields. This system can be…

Mapping superintegrable quantum mechanics to resonant spacetimes

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We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our…

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The symmetry of the generalized Polychronakos-Frahm chain is obtained from the Dunkl-operator deformation of the unitary algebra, which describes the symmetry of the generalized Calogero model.

A ug 2 01 9 On symmetries of the generalized Calogero model and Polychronakos-Frahm chain

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Integrable chains with inverse-square interactions were first introduced by Haldane and Shastry for equidistantly localized spins on a cycle [1, 2]. The Haldane-Shastry model extends the…

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We construct the Hamiltonians and symmetry generators of Calogero-oscillator and Calogero-Coulomb models on the N-dimensional sphere within the matrix-model reduction approach. Our method also…

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