FAST TRACK COMMUNICATION: A non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
The family of metric operators, constructed by Musumbu et al (2007 J. Phys. A: Math. Theor. 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.