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Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd k

par Quesne, Christiane
Référence Journal of Physics A: Mathematical and Theoretical, 43, 8, 082001
Publication Publié, 2010

Article révisé par les pairs

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Résumé :

In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k ≥ 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian , which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion , from which Y2k can be obtained by projection in the D2k identity representation space. © 2010 IOP Publishing Ltd.