# The kinetic energy of the electrons outside the FBZ

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1. Nov 15, 2016

### HenryWhu

1. The problem statement, all variables and given/known data
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 $$E_{k}=\frac{\hbar^2k^2}{2m}$$.

2. Relevant equations
For electrons in the FBZ and out of the FBZ, they have different $$E_{k}$$ but same $$E$$
why?

3. The attempt at a solution
it is because they have different potential energy?

2. Nov 18, 2016