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

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

2007-05-21

arxiv.org/abs/0705.2868v2

J.Phys.A40:F745-F751,2007

Physics

Mathematical Physics

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

Scientific paper

10.1088/1751-8113/40/30/F07

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 $\cal PT$-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 $\cal PT$-symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.

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