科研之友
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摘要
The family of Tremblay-Turbiner-Winternitz Hamiltonians H(k) on a plane, corresponding to any positive real value of k, is shown to admit an N = 2 supersymmetric extension of the same kind as that introduced by Freedman and Mende for the Calogero problem and based on an osp(2/2, R) similar to su(1, 1/1) superalgebra. The irreducible representations of the latter are characterized by the quantum number specifying the eigenvalues of the first integral of motion X(k) of H(k). 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.
- 出版日期2010-7-30
