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We consider the problem of removal of ordering ambiguity in positiondependent mass quantum systems characterized by a generalized positiondependent mass Hamiltonian which generalizes a number of Hermitian as well asnon-Hermitian ordered forms of the Hamiltonian. We implement point canonicaltransformation method to map one-dimensional time-independent positiondependent mass Schr$\"{o}$dinger equation endowed with potentials onto constantmass counterparts which are considered to be exactly solvable. We observe thata class of mass functions and the corresponding potentials give rise tosolutions that do not depend on any particular ordering, leading to the removalof ambiguity in it. In this case, it is imperative that the ordering isHermitian. For non-Hermitian ordering we show that the class of systems canalso be exactly solvable and are also shown to be iso-spectral using suitablesimilarity transformations. We also discuss the normalization of theeigenfunctions obtained from both Hermitian and non-Hermitian orderings. Weillustrate the technique with the quadratic Li$\'{e}$nard type nonlinearoscillators, which admit position dependent mass Hamiltonians.

journal of mathematical physics

Removal of ordering ambiguity for a class of position dependent mass  quantum systems with an application to the quadratic Li\'enard type nonlinear  oscillators