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

2012/08/10 by Omar Mustafa, Mustafa, Omar
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Mechanical and Optical Resonators #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.1208.2109

Abstract

We recycle Cruz et al.'s (Phys. Lett. A 369 (2007) 400) work on the classical\nand quantum position-dependent mass (PDM) oscillators. To elaborate on the\nordering ambiguity, we properly amend some of the results reported in their\nwork and discuss the classical and quantum mechanical correspondence for the\nPDM harmonic oscillators. We use a point canonical transformation and show that\none unique quantum PDM oscillator Hamiltonian (consequently, one unique\nordering-ambiguity parametric set j=l=-1/4 and k=-1/2) is obtained. To show\nthat such a parametric set is not just a manifestation of the quantum PDM\noscillator Hamiltonian, we consider the classical and quantum mechanical\ncorrespondence for quasi-free PDM particles moving under the influence of their\nown PDM force fields.\n

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