  In the present paper we examine in a systematic way the most relevant
orderings of pure kinetic Hamiltonians for five different position-dependent
mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic,
exponential and parabolic. As a result of the non-commutativity between
momentum and position operators, a diversity of effective potentials is
generated. We analyze the whole set and find unexpected coincidences as well as
discrepancies among them. We obtain analytically the full-spectrum of energies
and solutions in the twenty-five cases considered. It is shown how the simple
ordinary constant-mass solutions are transformed into a variety of complex
combinations of transcendental functions and arguments. We find that particles
with a non-uniform mass density can present discrete energy spectra as well as
continuous ones which can be bounded or not. These results are consistent with
the fact that although the external potential is zero, PDM eigenfunctions are
not actual free states but a sort of effective waves in a solid-state sample.
This is precisely the origin of the position-dependent mass. In all the events
we obtain exact complete spectral expressions. Our methodological procedure
thus puts a wide diversity of Hamiltonian seeds on an equal footing in order to
be compared. This allows choosing the better arrangement to model a specific
solid or heterostructure once the spectrum of a given material is
experimentally available. Finally, we perform a one-dimensional model
calculation of a double heterostructure with a parabolic PDM particle in the
interface region. Our study is also indicated for applications inside material
structures with the addition of external potentials.
