The relaxation‐time approximation is used in the numerical simulation of the Wigner distribution function to incorporate scattering. The effects within the constant relaxation‐time approximation are (a) a decrease in the peak‐to‐valley ratio of the current‐voltage curve; (b) a reduction in the oscillations of the Wigner distribution function, especially at resonance bias; (c) a suppression of the decay time of current oscillations after a sudden bias shift, indicating a smaller switching time than for no scattering; (d) a degradation in the resonant tunneling trajectories towards the characteristics of nonresonant trajectories; (e) a decrease in the spatial range of the quantum influences near resonance; and (f) ballistic transport sets in [i.e., the mean free path of the electrons is greater than the barrier region (110 A˚)] for temperatures less than 74 K.