  We recycle Cruz et al.'s (Phys. Lett. A 369 (2007) 400) work on the classical
and quantum position-dependent mass (PDM) oscillators. To elaborate on the
ordering ambiguity, we properly amend some of the results reported in their
work and discuss the classical and quantum mechanical correspondence for the
PDM harmonic oscillators. We use a point canonical transformation and show that
one unique quantum PDM oscillator Hamiltonian (consequently, one unique
ordering-ambiguity parametric set j=l=-1/4 and k=-1/2) is obtained. To show
that such a parametric set is not just a manifestation of the quantum PDM
oscillator Hamiltonian, we consider the classical and quantum mechanical
correspondence for quasi-free PDM particles moving under the influence of their
own PDM force fields.
