Bloch function - Solid state physics

big man

1. The problem statement, all variables and given/known data
What are Bloch functions? Explain briefly how these function are used in the quantum mechanical modelling of crystals.

2. Relevant equations
[tex]\psi _k (r)=u_k(r)exp(ik.r)[/tex]


3. 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.