Journal of Physics A Mathematical and Theoretical

A two-parameter family of non-Hermitian Hamiltonians with real spectrum

Ebru Ergün

Published Oct 22, 2010• 5 citations

Abstract

We introduce a Hamiltonian H α, β depending on the two complex parameters α and β and develop a through analysis of the spectral properties of this Hamiltonian and its adjoint. We determine the regions in the space of the complex parameters α and β, where H α, β is (i) Hermitian, (ii) non-Hermitian with real spectrum and (iii) non-Hermitian but PT -symmetric. In the case when H α, β is non-Hermitian having real spectrum, we derive a closed formula for a family of the metric operators, depending on two arbitrary real positive parameters, which render the Hamiltonian H α, β Hermitian. In a particular case we calculate the Hermitian counterpart of H α, β .

DOI: 10.1088/1751-8113/43/45/455212

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