Friedel's law

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Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions.

Given a real function f(x), its Fourier transform

F(k)=\int^{+\infty}_{-\infty}f(x)e^{i k \cdot x }dx

has the following properties.

  • F(k)=F^*(-k) \,

where F * is the complex conjugate of F.

Centrosymmetric points (k, − k) are called Friedel's pairs.

The squared amplitude ( | F | 2) is centrosymmetric:

  • |F(k)|^2=|F(-k)|^2 \,

The phase φ of F is antisymmetric:

  • \phi(k) = -\phi(-k) \,.

Friedel's law is used in X-ray diffraction, crystallography and scattering from real potential within the Born approximation.

[edit] Source

G. Friedel, Comptes Rendus, Acad. Sci. (Paris) 157, 1533-1536 (1913).

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