We have studied theoretically the low-field electron transport in a,fr
ee-standing quantum well where the deformation potential scattering of
electrons by acoustic phonons is the major mechanism of the electron
relaxation. The quantisation of acoustic phonons, their multisubband s
pectrum, and the exact form of the dilatational acoustic modes are tak
en into account. We have numerically solved the kinetic equation for e
lectrons in the low electric field limit. At low lattice temperature t
he obtained electron distribution function has several peaks associate
d with scattering by different dilatational phonons. The electron mobi
lity has temperature dependence similar to that described by the Bloch
-Gruneisen formula, however pre have obtained T-3 dependence of mobili
ty in the low temperature legion.