  The classical and quantum mechanical correspondence for constant mass
settings is used, along with some point canonical transformation, to find the
position-dependent mass (PDM) classical and quantum Hamiltonians. The
comparison between the resulting quantum PDM-Hamiltonian and the von Roos
PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are
strictly determined. Eliminating, in effect, the ordering ambiguity associated
with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in
the construction and identification of the PDM-momentum operator. The same
recipe is followed to identify the form of the minimal coupling of
electromagnetic interactions for the classical and quantum PDM-Hamiltonians. It
turned out that whilst the minimal coupling may very well inherit the usual
form in classical mechanics, it admits a necessarily different and vital form
in quantum mechanics. Under our point transformation settings, only one of the
two commonly used vector potentialsis found eligible and is considered for our
Illustrative examples.
