# Is Free-electron model := Drude Model (of metals) ?

1. Jun 10, 2008

### iLIKEstuff

Is the free-electron model synonymous with Drude model? or is Drude model a special subset of the free-electron model?

I have seen texts that refer to a "free-electron model" and do not mention Drude's name. and i have also seen texts use these two terms interchangeably.

Sorry, i have no specific examples. I'm just looking for a generalization.

Thanks guys.

also as a small side question: whenever a text refers to energy bands, fermi levels, or potential wells, is this necessarily a "quantum approach"? or is this why the Drude model is considered "semi-classical"?

Last edited: Jun 10, 2008
2. Jun 10, 2008

### malawi_glenn

As far as I know, Free electron model is a combination of the quantum behaviour of electrons (Pauli principle) and the classical Drude model.

Thus the difference between Free Electron model and Drude, is that FEM takes into account that electrons are fermions, hence we get a fermi surface in k-space even at temperature of 0K.

Yes those are quantum approaches, since one has wave functions and quantum statistics (Pauli principle).

I dont know exaclty how to explain that the Drude Model is considered to be Semiclassical, but Iam sure that someone else here know it and will explain it to you ;-)

3. Jun 10, 2008

### Physics Monkey

Usually the "free electron approximation" means your model ignores the background potential seen by the electrons. For example, one of the simplest ways to calculate band structure is called the "nearly free electron approximation" in which you simply compute perturbative corrections to the energy levels of the free electron gas due to the nuclear lattice.

Another important approximation is the "independent electron approximation" which means your model neglects electron-electron interactions. The Sommerfeld model of electrons assumes both free and independent electrons and retains only their basic quantum character via the Pauli principle.

The Drude model is completely classical because it contains classical particles obeying Netwon's laws. The Drude model is also a mean field description because it includes scattering only in an average way via the relaxation time. Because of the relation between dissipation and fluctuation, there should be an additional fluctuating force which the Drude model effectively averages over. I'm not sure if you would say the Drude model assumes free electrons because I think Drude originally thought the relaxation time came from the nuclei (it doesn't, of course, because of Bloch's theorem). One should simply imagine some unspecified scatterers (impurities, phonons, etc) leading to an effective relaxation time.

On the other hand, the Sommerfeld model of electrons is a quantum model but of free and independent electrons. One can incorporate a description of transport using, for example, a classical Boltzmann equation. However, when using such an equation one is implicitly assuming a description in terms of wavepackets with reasonably sharp momentum and position which approximately obey Newton's laws. This makes the description semi-classical.

Hope this helps.
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