  The exact solvability and impressive pedagogical implementation of the
harmonic oscillator creation and annihilation operators make it a problem of
great physical relevance and the most fundamental one in quantum mechanics. So
would be the position dependent mass oscillator for the position dependent mass
quantum mechanics. We, hereby, construct the position dependent mass creation
and annihilation operators for the position dependent mass oscillator via two
different approaches. First, via von Roos position dependent mass Hamiltonian
and show that the commutation relation between the position dependent mass
creation and annihilation operators not only offers a unique position dependent
mass Hamiltonian but also suggests a position dependent mass deformation in the
coordinate system. Next, we use a position dependent mass point canonical
transformation of the textbook constant mass harmonic oscillator analog and
obtain yet another set of position dependent mass creation and annihilation
operators, hence an apparently new position dependent mass Hamiltonian is
obtained. The new position dependent mass Hamiltonian turned out to be not only
correlated but also represents an alternative and most simplistic user-friendly
position dependent mass Hamiltonian that has never been reported before.
