Reciprocal lattice vector
= Reciprocal lattice vector
{title2=$\mathbf G\cdot\mathbf R\in2\pi\mathbb Z$}
A reciprocal lattice vector $\mathbf G$ has the displayed property for every direct <lattice vector> $\mathbf R$. Thus $e^{i\mathbf G\cdot\mathbf R}=1$. Fourier components of a lattice-periodic potential carry these wavevectors and couple plane-wave electronic states whose momenta differ by $\hbar\mathbf G$. This is the origin of the Bragg-plane mixing in a <nearly-free electron model>.