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A model of the Calogero type in the D-dimensional space

Abstract : In a previous paper, we have proposed a new integrable Hamiltonian describing two interacting particles in a harmonic mean field in D = 1 dimensional space. Here, we generalize this Hamiltonian to the D ≥ 2 dimensional space. We show that the system is exactly solvable for a certain domain of the interaction constant, and that the size of this domain increases with D. We also show this D-dimensional Hamiltonian to be supersymmetric and shape invariant, very much as in the D = 1 case.
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http://hal.in2p3.fr/in2p3-00164749
Contributor : Suzanne Robert <>
Submitted on : Monday, July 23, 2007 - 4:09:11 PM
Last modification on : Wednesday, September 16, 2020 - 4:08:17 PM

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A. Bachkhaznadji, M. Lassaut, R.J. Lombard. A model of the Calogero type in the D-dimensional space. Journal of Physics A General Physics (1968-1972), Institute of Physics (IOP), 2007, 40, pp.8791-8802. ⟨10.1088/1751-8113/40/30/012⟩. ⟨in2p3-00164749⟩

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