### hbox overflow

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1 changed files with 8 additions and 7 deletions

#### 15 ueb5.tex View File

 @ -1,5 +1,5 @@ %\includegraphics{excs/qm1_blatt05_SS08.pdf} %\pagebreak \includegraphics{excs/qm1_blatt05_SS08.pdf} \pagebreak   \chapter{Quantenmechanik I - Übungsblatt 5} \section{Aufgabe 11: Spin-1-Teilchen im konstanten Magnetfeld} @ -22,9 +22,11 @@  &= \abs{\frac{1}{2} \inlinematrix{1 \\ \sqrt{2} \\ 1} \cdot \inlinematrix{\frac{1}{2} \cdot e^{\i \gamma \mtrx{B} t} \\  \frac{\sqrt{2}}{2} \\ \frac{1}{2} \cdot e^{-\i \gamma \mtrx{B} t}}}^2 \\  &= \frac{1}{4} \sbk{1 + e^{\i \gamma \mtrx{B}} + e^{-\i \gamma \mtrx{B} t}}^2 \\  &= \frac{1}{4} \sbk{1 + \cosb{\gamma \mtrx{B} t}}^2 \\  &\Rightarrow  \probb{\Sigma_x \cequiv +1}{\psi(t)} &= \frac{1}{2} \sin^2\sbk{\gamma \mtrx{B} t} %da stimmt wat net  &= \frac{1}{4} \sbk{1 + \cosb{\gamma \mtrx{B} t}}^2 \end{align} $\Rightarrow$ \begin{align}  \probb{\Sigma_x \cequiv +1}{\psi(t)} &= \frac{1}{2} \sin^2\sbk{\gamma \mtrx{B} t} \\ %da stimmt wat net  \probb{\Sigma_y \cequiv +1}{\psi(t)} &= \frac{1}{4} \sbk{1 - \cosb{\gamma \mtrx{B} t}}^2 \end{align}   @ -92,7 +94,7 @@ R \ket{\Phi} = \underbrace{e^{\i \frac{2 \pi s}{6}}}_{\text{Eigenwerte}} \ket{\   \subsection*{c)} \begin{align}  \ket{\chi_s} &= \frac{1}{\sqrt{6}} \sum_{n=0}^5 e^{\i n \delta_s} \ket{\Phi_n}  \ket{\chi_s} &= \frac{1}{\sqrt{6}} \sum_{n=0}^5 e^{\i n \delta_s} \ket{\Phi_n} \\  \detb{\mtrx{R} - \sbk{\lambda_s \one}} &\Rightarrow \\  e^{\i \delta_s} x_1 &= -x2 \\  e^{\i \delta_s} x2 &= -x3 \\ @ -109,7 +111,6 @@ Die Eigenvektoren lauten dann:  &= E_0 - 2 A \cosb{\delta_s} \\  &= E_s \end{align}   Die Gesamtenergie beträgt dann: \equationblock{E_ges = 6 E_0 - 8 A} E_{Kekule} = 3 \sbk{E_{Ethen}} = 6 E_0 - 6 A\$ (Pauli-Prinzip)