Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

Details Exactly solvable potentials of Calogero type for q-deformed Coxeter groups Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

2004-05-17

arxiv.org/abs/hep-th/0405147v2

J.Phys. A37 (2004) 10931-10950

Physics

High Energy Physics

High Energy Physics - Theory

22 pages Latex

Scientific paper

10.1088/0305-4470/37/45/012

We establish that by parameterizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite dimensional representation spaces of a Lie algebra. We present explicitly the $G_2^q $-case for which we construct the potentials by means of suitable gauge transformations.

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