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rm clear. looks better like this, to me. |
→The nearly free electron model: if q is not bold, then G neither |
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where ''Z'' is the [[atomic number]], ''e'' is the elementary unit charge, ''r'' is the distance to the nucleus of the embedded ion and ''q'' is a screening parameter that determines the range of the potential. The [[Fourier transform]], <math>U_{\mathbf{G}}</math>, of the lattice potential, <math>V(\mathbf{r})</math>, is expressed as
:<math>U_{\mathbf{G}} = \frac{4 \pi Z e}{q^2 +
When the values of the off-diagonal elements <math>U_{\mathbf{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_{\mathbf{G}}|</math> collapses and the empty lattice approximation is obtained.
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