Born-Green equation: Difference between revisions

Revision as of 14:52, 10 July 2007

kT{\frac {\partial \ln {\rm {g}}(r_{12})}{\partial {\mathbf {r} }_{1}}}={\frac {-\partial U(r_{12})}{\partial {\mathbf {r} }_{1}}}-\rho \int \left[{\frac {\partial U(r_{13})}{\partial {\mathbf {r} }_{1}}}\right]{\rm {g}}(r_{13}){\rm {g}}(r_{23})~{\rm {d}}{\mathbf {r} }_{3}

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-:<math>kT \frac{\partial \ln g(r_{12})}{\partial r_1}=
+:<math>kT \frac{\partial \ln {\rm g}(r_{12})}{\partial {\mathbf r}_1}=
-\frac{-\partial U(r_{12})}{\partial r_1}-  \rho \int \left[ \frac{\partial U(r_{13})}{\partial r_1} \right] g(r_{13})g(r_{23})  ~ d r_3</math>
+\frac{-\partial U(r_{12})}{\partial {\mathbf r}_1}-  \rho \int \left[ \frac{\partial U(r_{13})}{\partial {\mathbf r}_1} \right] {\rm g}(r_{13}){\rm g}(r_{23})  ~ {\rm d}{\mathbf r}_3</math>
 ==References==
 #[http://links.jstor.org/sici?sici=0080-4630%2819461231%29188%3A1012%3C10%3AAGKTOL%3E2.0.CO%3B2-9 M. Born and Herbert Sydney Green "A General Kinetic Theory of Liquids I: The Molecular Distribution Functions", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences '''188''' pp. 10-18 (1946)]
 [[category:statistical mechanics]]