Finding of the metric operator for a quasi-hermitian model

We consider on an appropriate sobolev space a non-hermitian hamiltonian h α,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 h α,β hermitian. in some particular cases,we calculate the hermitian counterpart of h α,β. © 2013 ebru ergun.