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Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations

par Quesne, Christiane
Référence Journal of Physics A: Mathematical and Theoretical, 41, 24, 244022
Publication Publié, 2008-06

Article révisé par les pairs

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Résumé :

A harmonic oscillator Hamiltonian augmented by a non-Hermitian PT -symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a supersymmetric context. Some quasi-Hermitian supersymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a su(1,1/1) ∼ osp (2/2, ℝ)superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed. © 2008 IOP Publishing Ltd.