The next logical step be to include the scattering in the path integral transmission coefficient derived, as scattering is an important part of the RTD operation. This would give a better model and further calculation of the I-V characteristics can help to compare with the available experimental data.
In summary, it has been quantitatively confirmed that the negative resistance originates from the multiple reflections (resonant behaviour) of the electrons, as opposed to sequential tunneling through the barriers. Though we are unable to conclude this satisfactorily from the WKB approximation approach, this is seen clearly through the path integral approach.