  We describe a method for numerically incorporating electron--electron
scattering in quantum wells for small deviations of the distribution function
from equilibrium, within the framework of the Boltzmann equation. For a given
temperature $T$ and density $n$, a symmetric matrix needs to be evaluated only
once, and henceforth it can be used to describe electron--electron scattering
in any Boltzmann equation linear-response calculation for that particular $T$
and $n$. Using this method, we calculate the distribution function and mobility
for electrons in a quantum-well, including full finite-temperature dynamic
screening effects. We find that at some parameters which we investigated,
electron--electron scattering reduces mobility by approximately 40\%.
