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

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 $\mathrm{su}(1,1/1)\sim \mathrm{osp}(2/2,\mathbb{R})$ superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.

arXiv comment15 pages, no figure; published version

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• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Pseudo supersymmetric partners for the generalized Swanson model
• Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
• The Quantum Effective Mass Hamilton-Jacobi Problem
• New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework