= Indirect gap in a uniformly split zone-boundary model
{title2=$E_g^{\rm ind}=2V-(E_{\max}^{(0)}-E_{\min}^{(0)})$}
Suppose a model replaces a set of free-electron boundary energies $E^{(0)}$ by lower and upper edges $E^{(0)}-V$ and $E^{(0)}+V$, with $V>0$. If these are the relevant global band edges, the <indirect band gap> is $(E_{\min}^{(0)}+V)-(E_{\max}^{(0)}-V)$, giving the displayed expression. A positive direct gap $2V$ at each crossing need not be enough: a <band insulator> needs $2V>E_{\max}^{(0)}-E_{\min}^{(0)}$. This is a band-edge estimate, not a general three-dimensional nearly-free-electron theorem; multiple Bragg planes at a corner can require a larger coupling matrix.
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