Energy spectra of position-dependent masses in double heterostructures

We consider position-dependent effective mass particles in double heterostructures, subject to the action of several potentials. A comparative study of the energy spectra of these particles is carried out, emphasizing the effect of different boundary conditions associated with the kinetic energy operator. Energy spectra that cannot be expressed analytically, have been estimated by means of the corresponding reflection coefficient poles. The heterostructure model adopted assumes a middle region, where the potential and mass are some finite distributions of the position, but outside of it its behavior is constant. Finally, we discuss the gain of a double parabolic quantum well in a laser.