30 lines
1002 B
TeX
30 lines
1002 B
TeX
%\includegraphics{excs/qm1_blatt01_SS08.pdf}
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%\pagebreak
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\chapter{Quantenmechanik I - Übungsblatt 1}
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\section{Aufgabe 1: Stern-Gerlach Experimente}
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\section{Aufgabe 2: Pauli Matrizen}
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\subsection*{a)}
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\begin{math}
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\textbf{\sigma} = (\sigma_x, \sigma_y, \sigma_z) \\
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\textbf{\a},\textbf{\b} \in \setR
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\end{math}
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\begin{align}
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(\textbf{a \cdot \sigma})(\textbf{b \cdot \sigma}) &= \one (\textbf{a \cdot b} + \i \textbf{\sigma} \cdot (\textbf{\a} \times \textbf{b}) \\
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\sum a_\alpha b_\beta \sigma_\alpha \sigma_\beta &= \\
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\sum a_\alpha b_\beta ( \krondelta{\alpha \beta} \one + \i \levicivita{\alpha,\beta,\gamma} \sigma_\gamma ) &= \\
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\sum a_\alpha b_\beta \krondelta{\alpha \beta} \cdot \one + \i a_\alpha b_\beta \levicivita{\alpha,\beta,\gamma} \sigma_\gamma &= \\
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\one (\textbf{a \cdot b} + \i \sigma \cdot (a \times b)
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\end{align}
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\subsection*{b)}
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\subsection*{c)}
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\subsection*{d)}
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\section{Aufgabe 3: Operator-Identitäten}
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\subsection*{a)}
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\subsection*{b)}
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\subsection*{c)} |