To illustrate the capabilities of the above approach, the resonant states of a finite superlattice structure under bias were evaluated and are illustrated in Fig. 1.
Figure 1: The resonant states of a finite superlattice with electric field
superimposed. The states are plotted as horizontal lines at the real energy
of the resonance, and the lines are drawn for those x at
which 
exceeds its average value. This gives a visual indication
of the density of states.
The electric field has removed the degeneracy of the states in the individual quantum wells, leaving the resonant states generally localized. But the the remains of the miniband structure are still discernible.
As another example, which is simple enough to document more thoroughly, the resonant states of a double-barrier structure are illustrated in Fig. 2. Both the energy-band diagram and the wavefunctions of the resonances are shown.
Figure 2: Resonant states of a double-barrier structure. The states are located
on the energy-band diagram (a). The wavefunctions of the (b) first, (c) second,
and (d) third resonant states are shown. Notice the outgoing traveling waves
in each case.
To check the credibility of
the imaginary parts of the eigenvalues, the lowest resonant state was
evaluated for a series of double-barrier structures with equal well width
but varying
barrier widths. One expects the lifetime, and thus 
, to vary
exponentially with barrier width.
Figure 3: Variation of imaginary energy 
of the lowest resonance of
a double-barrier structure with barrier width. One expects, and observes,
an exponential dependence.
As shown in Fig. 3, such an exponential variation is obtained over many decades.