This Demonstration shows the sampling of the

-points in the first Brillouin zone (BZ) of a virtually infinite linear crystal as a function of the number of sites in the unit cell. By choosing a periodic chain with

sites one can sample

-points in the reciprocal space of the first BZ, whose spacing is inversely proportional to

and the lattice parameter

. Then

, where

* *is the allowed quantum number for the chain (

or equivalently,

). There is also cyclic periodicity in

. The

-points thus obtained are mapped onto the analytical form of the tight-binding electronic dispersion relation

for the chain. Diagonalizing the associated Bloch Hamiltonian gives the electronic energy eigenvalues

. These are calculated and plotted as a function of the tight-binding hopping parameter

and the on-site energy parameter

expressed in electron volts.