PX262 - K3 - wavevector space and brillouin zone

the wigner-seitz unit cell for the reciprocal space is called the brillouin zone (BZ)
it is constructed in the same way as in the actual lattice
picking a value of the wavevector, $\vec{k}$ , anywhere in the space occupied by the reciprocal lattice points, appropriate to the electron waves, $A \exp (i \vec{k} \cdot \vec{r})$
in 1D, the reciprocal lattice:

- \frac{π}{a} \leq k \leq \frac{π}{a}