The velocity‐field characteristics of hot electrons moving one dimensionally in the lowest subband of a polar semiconductor quantum‐well wire are obtained on a drifted Maxwellian model and also by the Monte Carlo technique. No negative differential resistance is obtained in contradiction to a previous prediction. The size effects at low temperatures are found to be more significant in the drifted Maxwellian model. Our calculations show that the one‐dimensional (1‐D) mobility for large transverse widths may be higher than the 3‐D mobility.