  In this paper we analyze a recent application of perturbation theory by the
moment method to a family of two-dimensional anharmonic oscillators. By means
of straightforward unitary transformations we show that two of the models
studied by the authors are separable. Other is unbounded from below and
therefore cannot be successfully treated by perturbation theory unless a
complex harmonic frequency is introduced in the renormalization process. We
calculate the lowest resonance by means of complex-coordinate rotation and
compare its real part with the eigenvalue estimated by the authors. A pair of
the remaining oscillators are equivalent as they can be transformed into one
another by unitary transformations.
