From 108a03785745dd617ff5356ff747bcf8d9e9d57c Mon Sep 17 00:00:00 2001
From: Daniel Bahrdt <d.bahrdt@gmx.de>
Date: Mon, 30 Jun 2008 15:18:36 +0200
Subject: [PATCH] a2 c)

---
 ueb1.tex | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/ueb1.tex b/ueb1.tex
index 8df4854..46ae8c7 100644
--- a/ueb1.tex
+++ b/ueb1.tex
@@ -6,6 +6,20 @@
 
 \section{Aufgabe 2: Pauli Matrizen}
 \subsection*{a)}
+
+	\begin{math}
+	\textbf{\sigma} 	= (\sigma_x, \sigma_y, \sigma_z) \\
+	\textbf{\a},\textbf{\b} \in \setR
+	\end{math}
+	
+	\begin{align}
+	
+	(\textbf{a \cdot \sigma})(\textbf{b \cdot \sigma})	&= \one (\textbf{a \cdot b} + \i \textbf{\sigma} \cdot (\textbf{\a} \times \textbf{b}) \\
+	\sum a_\alpha b_\beta \sigma_\alpha \sigma_\beta	&=  \\
+	\sum a_\alpha b_\beta ( \krondelta{\alpha \beta} \one	+ \i \levicivita{\alpha,\beta,\gamma} \sigma_\gamma )	&= \\
+	\sum a_\alpha b_\beta \krondelta{\alpha \beta} \cdot \one + \i a_\alpha b_\beta \levicivita{\alpha,\beta,\gamma} \sigma_\gamma &= \\
+	\one (\textbf{a \cdot b} + \i \sigma \cdot (a \times b)
+	\end{align}
 \subsection*{b)}
 \subsection*{c)}
 \subsection*{d)}