FAST TRACK COMMUNICATION: A nonHermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
Abstract
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 nonHermitian \cal PT symmetric part, is reexamined 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 nonHermitian (not necessarily \cal PT symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 July 2007
 DOI:
 10.1088/17518113/40/30/F07
 arXiv:
 arXiv:0705.2868
 Bibcode:
 2007JPhA...40..745Q
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 11 pages, no figure