From: Frank Zirkelbach <f.zirkelbach@fkf.mpg.de>
Date: Mon, 25 Feb 2013 14:28:20 +0000 (+0100)
Subject: more on SO
X-Git-Url: https://hackdaworld.org/gitweb/?a=commitdiff_plain;h=056165f01af9aa49e9e247c9c9ba43cfc52309be;p=lectures%2Flatex.git

more on SO
---

diff --git a/physics_compact/solid.tex b/physics_compact/solid.tex
index ca00412..6eee6c2 100644
--- a/physics_compact/solid.tex
+++ b/physics_compact/solid.tex
@@ -249,6 +249,20 @@ V_{l,l-\frac{1}{2}}(\vec{r}) & \text{for } j=l-\frac{1}{2}
 as expected and --- in fact --- obtained from equation~\eqref{eq:solid:so_bs1}.
 \end{proof}
 
+In order to include the spin-orbit interaction into the scalar-relativistic formalism of a normconserving, non-local pseudopotential, scalar-relativistic in contrast to fully relativistic pseudopotential wavefunctions are needed as a basis for the projectors of the spin-orbit potential.
+The transformation
+\begin{equation}
+L\cdot S=L_xS_x+L_yS_y+L_zS_z
+\end{equation}
+using the ladder operators
+\begin{equation}
+L_\pm=L_x\pm iL_y
+\end{equation}
+reads
+\begin{equation}
+\ldots
+\end{equation}
+ 
 
 \subsubsection{Excursus: Real space representation within an iterative treatment}