var meth

[lectures/latex.git] / physics_compact / solid.tex

diff --git a/physics_compact/solid.tex b/physics_compact/solid.tex
index 50df24d..6c25ff1 100644 (file)
--- a/physics_compact/solid.tex
+++ b/physics_compact/solid.tex
@@ -18,7 +18,7 @@
 
 \subsubsection{Hohenberg-Kohn theorem}
 
-Considering a system with a nondegenerate ground state, there is obviously only one ground-state charge density $n_0(\vec{r})$ that correpsonds to a given potential $V(\vec{r})$.
+Considering a system with a nondegenerate ground state, there is obviously only one ground-state charge density $n_0(\vec{r})$ that corresponds to a given potential $V(\vec{r})$.
 In 1964, Hohenberg and Kohn showed the opposite and far less obvious result \cite{hohenberg64}.
 For a nondegenerate ground state, the ground-state charge density uniquely determines the external potential in which the electrons reside.
 The proof presented by Hohenberg and Kohn proceeds by {\em reductio ad absurdum}.
@@ -55,5 +55,5 @@ 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.
+is revealed, which proofs the Hohenberg Kohn theorem.