X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fbasics.tex;h=249614ae173c0d53adf87671ee8925e332f4dec6;hb=1409915a2449cdf810e0a88c5880b887766b3f28;hp=bd2453ecf5594eb5fc9b4d5df33cbbbe3fced8c0;hpb=768e3639a14034a169ae6e347f0b132c4f0f397d;p=lectures%2Flatex.git

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.