Non-Hermitian Hamiltonians of Lie algebraic type

Details Non-Hermitian Hamiltonians of Lie algebraic type Non-Hermitian Hamiltonians of Lie algebraic type

2008-04-29

arxiv.org/abs/0804.4677v3

J. Phys. A: Math. Theor. 42 (2009) 015203

Physics

Quantum Physics

27 pages

Scientific paper

10.1088/1751-8113/42/1/015203

We analyse a class of non-Hermitian Hamiltonians, which can be expressed bilinearly in terms of generators of a sl(2,R)-Lie algebra or their isomorphic su(1,1)-counterparts. The Hamlitonians are prototypes for solvable models of Lie algebraic type. Demanding a real spectrum and the existence of a well defined metric, we systematically investigate the constraints these requirements impose on the coupling constants of the model and the parameters in the metric operator. We compute isospectral Hermitian counterparts for some of the original non-Hermitian Hamiltonian. Alternatively we employ a generalized Bogoliubov transformation, which allows to compute explicitly real energy eigenvalue spectra for these type of Hamiltonians, together with their eigenstates. We compare the two approaches.

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