Free electron gas model or classical theory

1. Jun 15, 2011

logearav

1. The problem statement, all variables and given/known data

In Drude - Lorentz' FREE ELECTRON GAS MODEL , it has been said " since the conduction electrons move in a uniform electrostatic field of ion cores, their potential energy remains constant and is normally taken as zero, i.e., the existence of ion cores is ignored." I don't understand this point i.e
1) how we say uniform electrostatic field
2) why movement in uniform electrostatic field makes potential energy as constant

2. Relevant equations

3. The attempt at a solution

2. Jun 15, 2011

chrisbaird

In reality, the existence of the ion cores is not completely ignored. What we do is use an effective mass for the electron in all of the equations instead of the real mass of the electron to account for the fact that the electrons are really bound to a potential created by the ion cores. The beauty is that once we use the effective mass, we can effectively ignore the ions because we have already accounted for them and treat the electrons as free.

1) a conduction electron in a solid is so delocalized that the electrostatic potential of the ions looks essentially uniform and constant for low energy electrons. If you heat up the solid enough are drive a current strong enough, this approximation will break down.

2) Let's be careful with words here. In the effective mass approximation, the potential due to the ions looks constant to a conduction electron, so their field is zero. (The field is the negative gradient of the potential and the derivative of a constant is zero.)