Spectrum of the Metric Operator of a Simple -Symmetric Model

Ebru Ergün

David Krejčiřı́k

In a previous paper [1] we introduced a very simple -symmetric non-Hermitian Hamiltonian with a real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this paper we propose an alternative formula for the metric operator, which we believe is more elegant and whose construction—based on a backward use of the spectral theorem for self-adjoint operators—provides new insights into the nature of the model.

Rajkumar Roychoudhury, P Roy

Ebru Ergün, M. Sağlam

David Krejčiřı́k, Hynek Bíla, Miloslav Znojil

We introduce a very simple, exactly solvable PT-symmetric non-Hermitian model with real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.

Petr Siegl

We explore some aspects of -symmetric Hamiltonians with two point interactions. We determine classes of point interactions for which the Hamiltonians are supersymmetric. We prove that these Hamiltonians are quasi-Hermitian and find a very simple formula for the metric operator Θ and its square root ϱ as well. Further, we present the quasi-Hermitian Hamiltonian (with one-point interaction) with a continuous spectrum.