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

Position-dependent mass harmonic oscillator: classical-quantum mechanical correspondence and ordering-ambiguity