**Bloch's theorem** In the nearly-free electron approximation, interactions between electrons are completely ignored. This approximation allows use of Bloch's Theorem which states that electrons in a periodic potential have wavefunctions and energies which are periodic in wavevector up to a constant phase shift between neighboring reciprocal lattice vectors.

Bloch's theorem:

The eigenfunctions for electrons that move in a periodic potential can be written in the following form:

ψ

_{nk}(

**r**) = e

^{ik.r}u

_{nk}(

**r**)

The corresponding energy eigenvalues are: Є

_{n}(

**k**)= Є

_{n}(

**k** +

**K**)

**K** lattice vector

**k** wave vector

n index

Because the energies associated with the index n vary continuously with wavevector k we speak of an energy band with band index n.

Because the eigenvalues for given n are periodic in k, all distinct values of Є

_{n}(

**k**) occur for k-values within the first Brillouin zone of the reciprocal lattice.

A Bloch wave or Bloch state is the wavefunction of an electron placed in a periodic potential.

The opposite extreme to the nearly-free electron approximation assumes the electrons in the crystal behave much like an assembly of constituent atoms: the tight binding model

__See also:__ Wave vector

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1247825987 Tight binding

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1275249597 __Reference:__ Bloch wave

http://en.wikipedia.org/wiki/Bloch_wave