I can't derive it properly even though it should be easy: From Newtons 2nd law: m dv/dt = -eE => v(t) = -meEt + v(0) (the latter will average out when taking average) Now the Drude assumption: An electron will on average travel a time τ before being scattered and starting its motion in the direction of E all over. Thus this means, I think, that on average an electron will travel with a velocity equal to <v> = -meEτ/2 And one can then multiply by electron density to get the Drude formula. Problem is the conductivity should not have the factor ½. Am I not right in thinking that the electron on average will travel at the velocit given above.
yes, this is an error is the drude formula. I found it many years back too. Apparently it's well known. Ctrl-F error on the wiki article http://en.wikipedia.org/wiki/Drude_model