Form of the quantum kinetic-energy operator with spatially varying effective mass

Through a nonrelativistic limit of the Dirac Hamiltonian and considering the spatial dependence of the particle mass in the Foldy-Wouthuysen transformation, it is shown that the quantum kinetic-energy operator with spatially varying effective mass has the form 1/4{(p) over cap[1/root m(r)](p) over cap[1/root m(r)] + [1/root m(r)](p) over cap[1/root m(r)](p) over cap}. However, the transmission properties of an electron through a GaAs/AlxGa1-xAs heterojunction calculated both with this form and the BenDaniel and Duke operator (p) over cap[m(r)](-1)(p) over cap/2, the most used kinetic-energy operator, differ at most by 1% if the existence of interface regions as thin as two GaAs lattice units is taken into account.