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arXiv · 0710.2453

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

C. Quesne
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Abstract

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. Quasi-Hermitian supersymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a ${\rm su}(1,1/1) \sim {\rm osp}(2/2, \R)$ superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.

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C. Quesne. 2008-06-03. Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations. https://doi.org/10.1088/1751-8113/41/24/244022

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