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Structure Factor

The structure factor $S_\Gamma$ of a discrete set $\Gamma$ is the Fourier Transform of $\delta$-scatterers of equal strengths on all points of $\Gamma$,

S_\Gamma(k)=\int \sum_{x\in\Gamma} \delta(x'-x)e^{-2\pi ikx'}\,dx'=\sum_{x\in\Gamma} e^{-2\pi ikx}.


Baake, M.; Grimm, U.; and Warrington, D. H. ``Some Remarks on the Visible Points of a Lattice.'' J. Phys. A: Math. General 27, 2669-2674, 1994.

© 1996-9 Eric W. Weisstein