From: hackbard <hackbard@hackdaworld.org>
Date: Thu, 15 Sep 2011 10:29:15 +0000 (+0200)
Subject: average
X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=0d3acfac2b23ed5b37c86a77118a7f467f48c0e8;p=lectures%2Flatex.git

average
---

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index bd2453e..249614a 100644
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -566,7 +566,7 @@ Writing down the derivative of the total energy $E$ with respect to the position
 indeed reveals a contribution to the change in total energy due to the change of the wave functions $\Phi_j$.
 However, provided that the $\Phi_j$ are eigenstates of $H$, it is easy to show that the last two terms cancel each other and in the special case of $H=T+V$ the force is given by
 \begin{equation}
-\vec{F}_i=-\sum_j \Phi_j^*\Phi_j\frac{\partial V}{\partial \vec{R}_i}
+\vec{F}_i=-\sum_j \langle \Phi_j | \Phi_j\frac{\partial V}{\partial \vec{R}_i} \rangle
 \text{ .}
 \end{equation}
 This is called the Hellmann-Feynman theorem \cite{feynman39}, which enables the calculation of forces, called the Hellmann-Feynman forces, acting on the nuclei for a given configuration, without the need for evaluating computationally costly energy maps.