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Display information for equation id:math.1693.28 on revision:1693

* Page found: Spin- Operatoren und Zustände (eq math.1693.28)

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Spin- Operatoren und Zustände Eq: math.1693.28

Hash: db207824adb0e3a35e27b94703265e5e

TeX (original user input):

\begin{align}

& \left( {{{\hat{\bar{\sigma }}}}_{1}}+i{{{\hat{\bar{\sigma }}}}_{2}} \right)\left| \downarrow  \right\rangle =\left( {{{\hat{\bar{\sigma }}}}_{1}}+{{{\hat{\bar{\sigma }}}}_{1}} \right)\left| \downarrow  \right\rangle =2\left| \uparrow  \right\rangle  \\

& \left( {{{\hat{\bar{\sigma }}}}_{1}}-i{{{\hat{\bar{\sigma }}}}_{2}} \right)\left| \uparrow  \right\rangle =\left( {{{\hat{\bar{\sigma }}}}_{1}}+{{{\hat{\bar{\sigma }}}}_{1}} \right)\left| \uparrow  \right\rangle =2\left| \downarrow  \right\rangle  \\

& \Rightarrow {{{\hat{\bar{\sigma }}}}_{1}}\left| \downarrow  \right\rangle =\left| \uparrow  \right\rangle  \\

& {{{\hat{\bar{\sigma }}}}_{1}}\left| \uparrow  \right\rangle =\left| \downarrow  \right\rangle  \\

\end{align}

TeX (checked):

{\begin{aligned}&\left({{\hat {\bar {\sigma }}}_{1}}+i{{\hat {\bar {\sigma }}}_{2}}\right)\left|\downarrow \right\rangle =\left({{\hat {\bar {\sigma }}}_{1}}+{{\hat {\bar {\sigma }}}_{1}}\right)\left|\downarrow \right\rangle =2\left|\uparrow \right\rangle \\&\left({{\hat {\bar {\sigma }}}_{1}}-i{{\hat {\bar {\sigma }}}_{2}}\right)\left|\uparrow \right\rangle =\left({{\hat {\bar {\sigma }}}_{1}}+{{\hat {\bar {\sigma }}}_{1}}\right)\left|\uparrow \right\rangle =2\left|\downarrow \right\rangle \\&\Rightarrow {{\hat {\bar {\sigma }}}_{1}}\left|\downarrow \right\rangle =\left|\uparrow \right\rangle \\&{{\hat {\bar {\sigma }}}_{1}}\left|\uparrow \right\rangle =\left|\downarrow \right\rangle \\\end{aligned}}

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\begin{aligned} ({\hat{\bar{σ}}}_{1} + i {\hat{\bar{σ}}}_{2}) | ↓ ⟩ = ({\hat{\bar{σ}}}_{1} + {\hat{\bar{σ}}}_{1}) | ↓ ⟩ = 2 | ↑ ⟩ \\ ({\hat{\bar{σ}}}_{1} - i {\hat{\bar{σ}}}_{2}) | ↑ ⟩ = ({\hat{\bar{σ}}}_{1} + {\hat{\bar{σ}}}_{1}) | ↑ ⟩ = 2 | ↓ ⟩ \\ \Rightarrow {\hat{\bar{σ}}}_{1} | ↓ ⟩ = | ↑ ⟩ \\ {\hat{\bar{σ}}}_{1} | ↑ ⟩ = | ↓ ⟩ \end{aligned}

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Identifiers

${\hat{\bar{σ}}}_{1}$

$i$

${\hat{\bar{σ}}}_{2}$

${\hat{\bar{σ}}}_{1}$

${\hat{\bar{σ}}}_{1}$

${\hat{\bar{σ}}}_{1}$

$i$

${\hat{\bar{σ}}}_{2}$

${\hat{\bar{σ}}}_{1}$

${\hat{\bar{σ}}}_{1}$

${\hat{\bar{σ}}}_{1}$

${\hat{\bar{σ}}}_{1}$

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