  The relevance in Physics of non-Hermitian operators with real eigenvalues is
being widely recognized not only in quantum mechanics but also in other areas,
such as quantum optics, quantum fluid dynamics and quantum field theory.
%stochastic processesand so on. In this note, a quantum system described by a
non-Hermitian Hamiltonian, which is constituted by two types of interacting
bosons, is investigated. The real eigenvalues of the Hamiltonian are explicitly
determined, as well as complete biorthogonal sets of eigenfunctions of the
Hamiltonian and its adjoint. The diagonal representation of $H$ is obtained
using pseudo-bosonic operators.
