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Physics Letters A

Comment on “PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian” by Omar Mustafa [Phys. Lett. A 384 (2020) 126265]

Biswanath Rath

Published Jan 22, 2021• 2 citations
Publisher
DOI
10.1016/j.physleta.2021.127174

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Comment on “The harmonic oscillator propagator” by Barry R. Holstein [Am. J. Phys. 66 (7), 583–589 (1998)]

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American Journal of Physics•Jul 1, 1999•4 citations
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.