a2 c)

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)}