The '''Emptyempty Latticelattice Approximationapproximation''' is a theoretical [[electronic band structure]] model in which the '''potential''' is defined not more precisely than '''periodic''' and '''weak'''. The Emptyempty Latticelattice Approximationapproximation describes a number of properties of energy dispersion relations of non-interacting [[Free electron model|'''free electrons''']] that move through a '''[[crystal structure|crystal lattice]]'''. The energy of the electrons in the "empty lattice" is the same as the energy of free electrons. The model is useful because it clearly illustrates a number of the sometimes very complex features of energy dispersion relations in solids which are fundamental to all electronic band structures.
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:<math>U_{\bold{G}} = \frac{4 \pi Z e}{q^2 + \bold{G}^2}</math>
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 Emptyempty Latticelattice Approximationapproximation is obtained.
