X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=physics_compact%2Fsolid.tex;h=0d5b1b2d0d6cdee705b7002bbf76a4b0c74f4e73;hp=30e078e936858ff59fea30de1d04dcdb4cb012f9;hb=2006b30651b6a44bd8af1d9f4b1c9a8ac104686a;hpb=a36c755ca1b7c925fbcde7dc24eeb910f773a77c diff --git a/physics_compact/solid.tex b/physics_compact/solid.tex index 30e078e..0d5b1b2 100644 --- a/physics_compact/solid.tex +++ b/physics_compact/solid.tex @@ -2,6 +2,10 @@ \chapter{Atomic structure} +\chapter{Reciprocal lattice} + +Example of primitive cell ... + \chapter{Electronic structure} \section{Noninteracting electrons} @@ -64,7 +68,7 @@ n_0(\vec{r})=\int \Psi_0^*(\vec{r},\vec{r}_2,\vec{r}_3,\ldots,\vec{r}_N) \end{equation} In 1964, Hohenberg and Kohn showed the opposite and far less obvious result \cite{hohenberg64}. -{\begin{theorem} +\begin{theorem}[Hohenberg / Kohn] For a nondegenerate ground state, the ground-state charge density uniquely determines the external potential in which the electrons reside. \end{theorem} @@ -102,6 +106,6 @@ E_1 + E_2 < E_2 + E_1 + \int n(\vec{r}) \left( V_2(\vec{r})-V_1(\vec{r}) \right) d\vec{r} }_{=0} \end{equation} -is revealed, which proofs the Hohenberg Kohn theorem. \qed +is revealed, which proofs the Hohenberg Kohn theorem.% \qed \end{proof}