Abstract
We consider the spherical reduction of the rational Calogero model (of type A n-1, without the center of mass) as a maximally superintegrable quantum system. It describes a particle on the (n = 2)-sphere in a very special potential. A detailed analysis is provided of the simplest non-separable case, n = 4, whose potential blows up at the edges of a spherical tetrahexahedron, tesselating the two-sphere into 24 identical right isosceles spherical triangles in which the particle is trapped. We construct a complete set of independent conserved charges and of Hamiltonian intertwiners and elucidate their algebra. The key structure is the ring of polynomials in Dunkl-deformed angular momenta, in particular the subspaces invariant and antiinvariant under all Weyl reflections, respectively.
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Correa, F., Lechtenfeld, O. The tetrahexahedric Calogero model. Phys. Part. Nuclei Lett. 14, 304–311 (2017). https://doi.org/10.1134/S1547477117020066
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DOI: https://doi.org/10.1134/S1547477117020066