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and consists of a increasing number of free electron bands <math>E_n(\bold{k})</math> when the energy rises. <math>\bold{G}_n</math> is the [[reciprocal lattice]] vector to which the band <math>E_n(\bold{k})</math> belongs. Electrons with larger wave vectors outside the first [[Brillouin zone]] are mapped back into the first Brillouin zone by a so called [[Umklapp scattering|Umklapp process]].
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;Nearly free electron model▼
In the [[Nearly free electron model|NFE model]] the [[Fourier transform]], <math>U_{\bold{G}}</math>, of the lattice potential, <math>V(\bold{r})</math>, in the NFE Hamiltonian, can be reduced to an infinitesimal value. When the values of the off-diagonal elements <math>U_{\bold{G}}</math> between the reciprocal lattice vectors in the Hamiltonian almost go to zero. As a result the magnitude of the band gap <math>2|U_{\bold{G}}|</math> collapses and the Empty Lattice Approximation is optained.
"Free electrons" that move through the lattice of a solid with wave vectors <math>\bold{k}</math> far outside the first Brillouin zone are still reflected back into the first Brillouin zone. See the [[#External links|external links]] section for sites with examples and figures.
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