Bloch function - Solid state physics

[big man]

Homework Statement

What are Bloch functions? Explain briefly how these function are used in the quantum mechanical modelling of crystals.

Homework Equations

$$\psi _k (r)=u_k(r)exp(ik.r)$$

The Attempt at a Solution

Now I know that a bloch function is a one-electron wavefunction that is given by the above equation. But I don't really know how to explain how it is used for the quantum mechanical modelling of crystals.

Kittel gives this information on a bloch function:
Bloch functions can be assembled into wave packets to represent electrons that propagate freely trhough the potential field of the ion cores.

To me this description answers it and hell the equation gives the relationship between the electron wavefunction with the periodicity of the crystal lattice so I would have thought that, that is quantum mechanic modelling in itself. Is there something else I should be putting down or have I just interpreted this incorrectly.

Any help is greatly appreciated.

 

[TeethWhitener]

$u_r$ and $e^{ikr}$ are both periodic by Bloch’s theorem, so we can use a plane wave basis set to approximate the actual wavefunction of the system. By calculating at a number of crystal moments, we can work out the electronic band structure of the material, which we can use to get a long list of properties of the solid.