Editing Ornstein-Zernike relation
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particle labels. | particle labels. | ||
The Ornstein-Zernike relation can be derived by performing a functional differentiation | The Ornstein-Zernike relation can be derived by performing a functional differentiation | ||
of the | of the grand canonical distribution function (HM check this). | ||
==Ornstein-Zernike relation in Fourier space== | ==Ornstein-Zernike relation in Fourier space== | ||
The Ornstein-Zernike equation may be written in [[Fourier analysis |Fourier space]] as (<ref>[http://dx.doi.org/10.1063/1.470724 Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]</ref> Eq. 5): | The Ornstein-Zernike equation may be written in [[Fourier analysis |Fourier space]] as (<ref>[http://dx.doi.org/10.1063/1.470724 Der-Ming Duh and A. D. J. Haymet "Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function", Journal of Chemical Physics '''103''' pp. 2625-2633 (1995)]</ref> Eq. 5): | ||
:<math>\hat{\gamma} = (\mathbf | :<math>\hat{\gamma} = ({\mathbf I} - \rho {\mathbf \hat{c}})^{-1} {\mathbf \hat{c}} \rho {\mathbf \hat{c}}</math> | ||
The carets denote the three-dimensional Fourier transformed quantities which reduce explicitly | The carets denote the three-dimensional Fourier transformed quantities which reduce explicitly | ||
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:<math>\gamma (r) = \frac{1}{2 \pi^2 r} \int_0^\infty k~\sin (kr) \hat{\gamma}( | :<math>\gamma (r) = \frac{1}{2 \pi^2 r} \int_0^\infty k~\sin (kr) \hat{\gamma}(r) dk</math> | ||
Note: | Note: | ||
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'''Related reading''' | '''Related reading''' | ||
*Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition) ISBN 0-12-370535-5 § 3.5 | *Jean-Pierre Hansen and I.R. McDonald "Theory of Simple Liquids", Academic Press (2006) (Third Edition) ISBN 0-12-370535-5 § 3.5 | ||
[[Category: Integral equations]] | [[Category: Integral equations]] |