What is the dispersion relation for a free electron?

[Jayse_83]

Hi, please could someone explain the term dispersion relation to me, particularly for the case of a free electron?

Thanks

Jayse

 

[Meir Achuz]

In wave theory, a dispersion relation is the relation between the wave number and the angular frequency: $$k(\omega)$$. There are also integral relations in S matrix theory that are an integral representation of this. For a free electron, the dispersion relation you refer to must be relating p to E since each is just $$\hbar$$ times k and $$\omega$$. In SR, this is $$p=\sqrt{E^2-m^2}$$. It could be used in the electron wave function, so that the group velocity would be
dE/dp=p/E (all with c=1).