  In this report we study the quantum transport of charge carriers for low
dimensional systems with spin-orbit coupling by means of Heisenberg's
inequalities. To develop our analysis, an accurate \emph{gendanken} experiment
was carefully put together, mainly based on the spin-field effect transistor
phenomenology and taking into account several wide accepted approaches on
quantum mechanical limited determinism. While verifying the applicability of
time-energy uncertainty relation (TEUR) during electronic wavepacket's
evolution through a semiconductor quantum wire, some qualitative information
related the dynamic behavior of the system is found. The problem is also
approached in the framework of the stationary phase method to guarantee robust
coherence for wavepacket's evolution, which lately implies certain restrictions
on the incident energy values for the envisioned cases. Tailoring different
input parameters such as: incoming particles spin polarization, barrier
thickness and Rashba's spin-orbit interaction (R-SOI) strength, we have
observed appealing effects while the packet evolves through a quasi-1D
heterostructure. Hopefully some of them could be of help in spintronics device
designing. We have obtained most of the numerical simulation results, within
the so-called conservation zone. However, for certain barrier thicknesses, some
values drop into the forbidden area regarding the clear theoretical limit
imposed by the TEUR. As an expected bonus throughout our theoretical validation
of the TEUR, spin splitting due to finite values of R-SOI was nicely noticed.
