The non-Hermitian Hartree approximation and the variational principle with quasi-Hermitian operators are compared in two different boson models. In a very simple schematic model the two methods provide comparable results. For the non-Hermitian boson Hamiltonian obtained applying the Dyson boson expansion to a two-level pairing model the results obtained are different. The first approach, although it does not provide an upper bound for the ground state energy, is not limited by the appearance of spurious states that break the quasi-Hermiticity of the Hamiltonian.

• Received 22 June 1994

DOI:https://doi.org/10.1103/PhysRevC.50.1932