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Display information for equation id:math.1693.44 on revision:1693

* Page found: Spin- Operatoren und Zustände (eq math.1693.44)

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Spin- Operatoren und Zustände Eq: math.1693.44

Hash: a55c1b64d425aa40899c15404e3c2874

TeX (original user input):

\begin{align}

& {{{\hat{\bar{\sigma }}}}_{1}}{{{\hat{\bar{\sigma }}}}_{2}}=\left( \begin{matrix}

0 & 1  \\

1 & 0  \\

\end{matrix} \right)\left( \begin{matrix}

0 & -i  \\

i & 0  \\

\end{matrix} \right)=\left( \begin{matrix}

-i & 0  \\

0 & i  \\

\end{matrix} \right)=i{{{\hat{\bar{\sigma }}}}_{3}} \\

& {{{\hat{\bar{\sigma }}}}_{2}}{{{\hat{\bar{\sigma }}}}_{1}}=\left( \begin{matrix}

0 & -i  \\

i & 0  \\

\end{matrix} \right)\left( \begin{matrix}

0 & 1  \\

1 & 0  \\

\end{matrix} \right)=-i{{{\hat{\bar{\sigma }}}}_{3}} \\

& \Rightarrow \left[ {{{\hat{\bar{\sigma }}}}_{1,}}{{{\hat{\bar{\sigma }}}}_{2}} \right]=2i{{{\hat{\bar{\sigma }}}}_{3}} \\

\end{align}

TeX (checked):

{\begin{aligned}&{{\hat {\bar {\sigma }}}_{1}}{{\hat {\bar {\sigma }}}_{2}}=\left({\begin{matrix}0&1\\1&0\\\end{matrix}}\right)\left({\begin{matrix}0&-i\\i&0\\\end{matrix}}\right)=\left({\begin{matrix}-i&0\\0&i\\\end{matrix}}\right)=i{{\hat {\bar {\sigma }}}_{3}}\\&{{\hat {\bar {\sigma }}}_{2}}{{\hat {\bar {\sigma }}}_{1}}=\left({\begin{matrix}0&-i\\i&0\\\end{matrix}}\right)\left({\begin{matrix}0&1\\1&0\\\end{matrix}}\right)=-i{{\hat {\bar {\sigma }}}_{3}}\\&\Rightarrow \left[{{\hat {\bar {\sigma }}}_{1,}}{{\hat {\bar {\sigma }}}_{2}}\right]=2i{{\hat {\bar {\sigma }}}_{3}}\\\end{aligned}}

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MathML (4.877 KB / 492 B) :

\begin{aligned} {\hat{\bar{σ}}}_{1} {\hat{\bar{σ}}}_{2} = (\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}) (\begin{matrix} 0 & - i \\ i & 0 \end{matrix}) = (\begin{matrix} - i & 0 \\ 0 & i \end{matrix}) = i {\hat{\bar{σ}}}_{3} \\ {\hat{\bar{σ}}}_{2} {\hat{\bar{σ}}}_{1} = (\begin{matrix} 0 & - i \\ i & 0 \end{matrix}) (\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}) = - i {\hat{\bar{σ}}}_{3} \\ \Rightarrow [{\hat{\bar{σ}}}_{1,} {\hat{\bar{σ}}}_{2}] = 2 i {\hat{\bar{σ}}}_{3} \end{aligned}

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Identifiers

${\hat{\bar{σ}}}_{1}$

${\hat{\bar{σ}}}_{2}$

$i$

$i$

$i$

$i$

$i$

${\hat{\bar{σ}}}_{3}$

${\hat{\bar{σ}}}_{2}$

${\hat{\bar{σ}}}_{1}$

$i$

$i$

$i$

${\hat{\bar{σ}}}_{3}$

${\hat{\bar{σ}}}_{1,}$

${\hat{\bar{σ}}}_{2}$

$i$

${\hat{\bar{σ}}}_{3}$

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