  Transmission probabilities of the scattering problem with a position
dependent mass are studied. After sketching the basis of the theory, within the
context of the Schr\"{o}dinger equation for spatially varying effective mass,
the simplest problem, namely, tranmission through a square well potential with
a position dependent mass barrier is studied and its novel properties are
obtained. The solutions presented here may be adventageous in the design of
semiconductor devices.
