Finding of the Metric Operator for a Quasi-Hermitian Model

Abstract EN

We consider on an appropriate Sobolev space a non-Hermitian Hamiltonian Hα,β depending on the two complex parameters α and β and having real spectrum.

We derive a closed formula for a family of the metric operators, which render the Hamiltonian Hα,β Hermitian.

In some particular cases, we calculate the Hermitian counterpart of Hα,β.