Does it make sense to speak about the speed of electrons in a current-carrying wire (non perfect conductor)? If so, what is their speed?
Here are my thoughts:
On the Internet (Wikipedia, physicsforums, here on PSE, etc., and many other websites), one can read that the electrons move randomly at high velocities but that their average velocity, called drift velocity, is $\vec 0$ when no current is applied and very small (a few cm/s at most) when a current is applied. However, as Ron Maimon wrote, this assumption is based on Drude's model of a conductor, which is known to be incorrect in many ways. In that model, electrons are like particles of a classical ideal gas, with a well defined position and speed at all times. However, it has been many decades since that model was been supplanted by QM models that invoke a wave function to describe the electrons in the material. I don't know which models exactly (tight binding for instance?).
Ron Maimon wrote:
the electronic wave functions are spread out in a metal. The correct notion of electron velocity is the Fermi velocity, which is enormous typically, because the wavelength is about 1 atomic radius. While it isn't the same as the speed of electricity going down the wire (which is the speed of the field perturbations, some significant fraction of the speed of light), it is enormously high.
So he speaks about a Fermi velocity, as if a velocity made sense. I've also read (from him and I think Ashcroft and Mermin's book "Solid State Physics") that only electrons near the Fermi energy contribute to the electric conductivity. If that's correct, then I can understand why the Fermi velocity makes some sense, because that's the speed an electron in vacuum would have if it had an energy equal to the Fermi energy. I involved the vacuum because I think that the electron can have a well definite momentum (and hence velocity), unlike in a solid conductor metal. Am I wrong?
So the correct answer would be that in reality, it doesn't even make sense to speak about the speed of electrons in a current carrying metallic wire. If the conductive electrons (the ones responsible for the electric conductivity) were somehow instantly put into a vacuum without changing their energy, they could have a well definite (assuming a measurement is done, I suppose? I.e. a wave function collapse into an eigenstate of the momentum operator.) speed/velocity equal to the Fermi velocity. There is therefore no such thing as a drift velocity, and the common assertion that an AC almost impedes the motion of the electrons is also false. Indeed, I've seen the claim that the electrons move at the drift velocity back and forth and so that the electrons are almost static (see here for instance). This view is completely erroneous. Am I wrong here, too?