Energy bands diagram in semiconductors

[mendes]

We usually plot the energy versus k, the wave vector, in the so-called "energy band diagram" for semiconductors. I am trying to understand the significance of "k" in this case. k is the wave vector, which means come kind of reciprocal of the space wavelength of the wave. But this definition does not make me understand the utility of plotting the energy versus k ! Does k mean something else also ?

 

[genneth]

\hbar k is the momentum, modulo crystal momentum.

In free space, symmetry under translations mean that momentum is a good quantum number (i.e. it makes sense to label energy eigenstates with it). In a lattice, you can only translate by lattice vectors; mathematically, you have something like momentum, but is periodic instead.