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N = 2 supersymmetric extension of the Tremblay-Turbiner-Winternitz Hamiltonians on a plane

par Quesne, Christiane
Référence Journal of Physics A: Mathematical and Theoretical, 43, 30, 305202
Publication Publié, 2010

Article révisé par les pairs

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Résumé :

The family of Tremblay-Turbiner-Winternitz Hamiltonians Hk on a plane, corresponding to any positive real value of k, is shown to admit an supersymmetric extension of the same kind as that introduced by Freedman and Mende for the Calogero problem and based on an superalgebra. The irreducible representations of the latter are characterized by the quantum number specifying the eigenvalues of the first integral of motion Xk of Hk. Bases for them are explicitly constructed. The ground state of each supersymmetrized Hamiltonian is shown to belong to an atypical lowest-weight state irreducible representation. © 2010 IOP Publishing Ltd.