  A translation operator is introduced to describe the quantum dynamics of a
position-dependent mass particle in a null or constant potential. From this
operator, we obtain a generalized form of the momentum operator as well as a
unique commutation relation for $\hat x$ and $\hat p_\gamma$. Such a formalism
naturally leads to a Schr\"odinger-like equation that is reminiscent of wave
equations typically used to model electrons with position-dependent (effective)
masses propagating through abrupt interfaces in semiconductor heterostructures.
The distinctive features of our approach is demonstrated through analytical
solutions calculated for particles under null and constant potentials like
infinite wells in one and two dimensions and potential barriers.
