Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations

Abstract

The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily $\mathcal{P}\mathcal{T}$-symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.

11 pages, no figure; changes in title and in paragraphs 3 and 5; final published version

References in corpus (2)

• Moyal products -- a new perspective on quasi-hermitian quantum mechanics
• Quantization and Conformal Properties of a Generalized Calogero Model

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