  When a non-hermitian hamiltonian has a certain symmetry, such as the PT
pseudo-hermiticity, it is still possible that the hamiltonian has a real
spectrum. In this note, by adding an imaginary potential proportional to
ip_1p_2 to the hamiltonian of an anisotropic planar oscillator, we construct a
PT pseudo-hermitian hamiltonian and obtain its real spectrum. In addition, we
find that the reality of the energy spectrum remains when the model is extended
to the canonical noncommutative space.
