Editing Free electron model (section)

== From the Drude model ==
{{main|Drude model}}
Many physical properties follow directly from the [[Drude model]], as some equations do not depend on the statistical distribution of the particles. Taking the [[Maxwell–Boltzmann distribution#Distribution for the velocity vector|classical velocity distribution]] of an ideal gas or the velocity distribution of a [[Fermi gas]] only changes the results related to the speed of the electrons.<ref name=":0" group="Ashcroft & Mermin">{{Harvnb|Ashcroft|Mermin|1976|pp=49-51}}</ref>

Mainly, the free electron model and the Drude model predict the same DC electrical conductivity ''σ'' for [[Ohm's law]], that is<ref group="Ashcroft & Mermin">{{Harvnb|Ashcroft|Mermin|1976|pp=|p=7}}</ref>
:<math>\mathbf{J} = \sigma \mathbf{E}\quad</math> with <math>\quad\sigma = \frac{ne^2\tau}{m_e},</math>

where <math>\mathbf{J}</math> is the [[current density]], <math>\mathbf{E}</math> is the external electric field, <math>n</math> is the [[electronic density]] (number of electrons/volume), <math>\tau</math> is the [[mean free time]] and <math>e</math> is the [[elementary charge|electron electric charge]].<!-- , and  <math>m_e</math> is the [[electron rest mass|electron mass]]. To include if paragraph above about Bloch's theorem disappears -->

Other quantities that remain the same under the free electron model as under Drude's are the AC susceptibility, the [[plasma oscillation|plasma frequency]],  the [[magnetoresistance]], and the Hall coefficient related to the [[Hall effect]].<ref name=":0" group="Ashcroft & Mermin" />