The kinetic energy of the electrons outside the FBZ

[HenryWhu]

Homework Statement

In solid state physics,we know all the states of free electrons can be expressed by the First Brillouin Zone. We know the $$E(k+K)=E(k)$$ where K is reciprocal lattice vector. We also know that the kinetic energy of the electron is $$E_{k}=\frac{\hbar^2k^2}{2m}$$. [/B]

Homework Equations

For electrons in the FBZ and out of the FBZ, they have different $$E_{k}$$ but same $$E$$
why?[/B]

The Attempt at a Solution

it is because they have different potential energy?[/B]

 

[DrDu]

How about the band index?