As far as I understand: In the Drude model we take the electron to be moving in a random direction after each collision (*), such that the mean velocity is simply the average of -eEt/m, which is just -eEτ/m, where τ is the relaxation time. But Im very confused about this basic assumption (*), if the electron has a velocity in the direction of the field and suffers collision with another electron, it does not seem likely that the direction of the velocity of the 2 electrons after collision will be completely random.
I wrote some details on this last winter for a class; see #7 in this thread: https://www.physicsforums.com/showthread.php?t=712978
That was quite helpful. Now I don't suppose you could help me interpreting another l) states that the equation for the displacement of a Fermi sphere is (all h's are hbars): h(d/dt + 1/τ)δk = F Now Newtons law for a completely free electron is: hdk/dt = F Why have they put in a δk, and how is the equation to be interpreted? Does it represent the motion of the Fermi sphere in steady state?