  Recently R. N. Costa Filho et al. (PRA 84, 050102(R) (2011)) have introduced
a position dependent infinitesimal translation operator which corresponds to a
position dependent linear momentum and consequently to a position dependent
effective mass quantum particle. Although there is no doubt in novelty of the
idea and the formalism, we believe that some aspects of the quantum mechanics
could be complemented in their original work. Here in this letter first we
address those points and then an alternative will be introduced. Finally we
apply the formalism for a quantum particle under a null potential confined in a
square well and the results will be compared with those in the paper mentioned
above.
