Operator ordering in effective-mass theory

We study the problem of operator ordering in the effective-mass Hamiltonian with kinetic energy operator 1/4(m^α{pm}^{{{β}}}pm^γ+m^γ{pm}^{{{β}}}pm^α), for a position-dependent effective mass m. Here {α}+{β}+{γ}=-1. We use merely the inherent criterion that the eigenvalues of the Hamiltonian should correspond to finite and uniquely determined energies. Through exact model calculations we show first that divergences occur unless {α}={γ}, and second that {α}={γ}=0, {β}=-1 is the only universal set of operator ordering parameters which gives unique results.