Editing Density-functional theory
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Helmholtz energy of an ideal system: | Helmholtz energy of an ideal system: | ||
<math>F_{id}=kT\int dr \rho(r) [\log \rho(r) -1 -U(r)],</math> | |||
where <math>U(r)</math> is an external potential. It is an easy exercise | where <math>U(r)</math> is an external potential. It is an easy exercise | ||
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of [[1-dimensional hard rods]]: | of [[1-dimensional hard rods]]: | ||
<math>F_{ex}=-kT\int dz \rho(z) \log [1-t(z)],</math> | |||
where <math>t(z)=\int_{z-\sigma}^z dy \rho(y)</math>, | where <math>t(z)=\int_{z-\sigma}^z dy \rho(y)</math>, |