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 $\widehat{x}$ and ${\widehat{p}}_{\gamma }$. Such a formalism naturally leads to a Schrödinger-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 are demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.

• Received 30 September 2011

DOI:https://doi.org/10.1103/PhysRevA.84.050102