Some Properties of the Calogero-Sutherland Model with Reflections
Abstract
We prove that the Calogero-Sutherland Model with reflections (the BCN model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wave-functions for certain particular cases (associated to the root systems of the classical Lie groups BN, CN and DN) is also discussed.
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