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Display information for equation id:math.1618.22 on revision:1618

* Page found: Zustandsvektoren im Hilbertraum (eq math.1618.22)

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Zustandsvektoren im Hilbertraum Eq: math.1619.22

Hash: 4153d5e6ce51fd5a05fa7f7e16a04c37

TeX (original user input):

\begin{align}

& \bar{a}=\sum\limits_{j}{{}}{{a}_{j}}\left| {{{\bar{e}}}_{j}} \right\rangle =\sum\limits_{j}{\left\langle  {{{\bar{e}}}_{j}} | {\bar{a}} \right\rangle }\left| {{{\bar{e}}}_{j}} \right\rangle =\sum\limits_{j}{\left| {{{\bar{e}}}_{j}} \right\rangle \left\langle  {{{\bar{e}}}_{j}}  |  {\bar{a}} \right\rangle } \\

& \bar{a}=\sum\limits_{j}{{}}{{a}_{j}}\acute{\ }\left| {{{\bar{e}}}_{j}}\acute{\ } \right\rangle =\sum\limits_{j}{\left\langle  {{{\bar{e}}}_{j}}\acute{\ } | {\bar{a}} \right\rangle }\left| {{{\bar{e}}}_{j}}\acute{\ } \right\rangle =\sum\limits_{j}{\left| {{{\bar{e}}}_{j}}\acute{\ } \right\rangle \left\langle  {{{\bar{e}}}_{j}}\acute{\ }  |  {\bar{a}} \right\rangle } \\

\end{align}

TeX (checked):

{\begin{aligned}&{\bar {a}}=\sum \limits _{j}{}{{a}_{j}}\left|{{\bar {e}}_{j}}\right\rangle =\sum \limits _{j}{\left\langle {{\bar {e}}_{j}}|{\bar {a}}\right\rangle }\left|{{\bar {e}}_{j}}\right\rangle =\sum \limits _{j}{\left|{{\bar {e}}_{j}}\right\rangle \left\langle {{\bar {e}}_{j}}|{\bar {a}}\right\rangle }\\&{\bar {a}}=\sum \limits _{j}{}{{a}_{j}}{\acute {\ }}\left|{{\bar {e}}_{j}}{\acute {\ }}\right\rangle =\sum \limits _{j}{\left\langle {{\bar {e}}_{j}}{\acute {\ }}|{\bar {a}}\right\rangle }\left|{{\bar {e}}_{j}}{\acute {\ }}\right\rangle =\sum \limits _{j}{\left|{{\bar {e}}_{j}}{\acute {\ }}\right\rangle \left\langle {{\bar {e}}_{j}}{\acute {\ }}|{\bar {a}}\right\rangle }\\\end{aligned}}

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\begin{matrix} \bar{a} = \sum_{j} a_{j} | {\bar{e}}_{j} ⟩ = \sum_{j} ⟨ {\bar{e}}_{j} | \bar{a} ⟩ | {\bar{e}}_{j} ⟩ = \sum_{j} | {\bar{e}}_{j} ⟩ ⟨ {\bar{e}}_{j} | \bar{a} ⟩ \\ \bar{a} = \sum_{j} a_{j} \overset{´}{} | {\bar{e}}_{j} \overset{´}{} ⟩ = \sum_{j} ⟨ {\bar{e}}_{j} \overset{´}{} | \bar{a} ⟩ | {\bar{e}}_{j} \overset{´}{} ⟩ = \sum_{j} | {\bar{e}}_{j} \overset{´}{} ⟩ ⟨ {\bar{e}}_{j} \overset{´}{} | \bar{a} ⟩ \end{matrix}

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Identifiers

$\bar{a}$

$j$

$a_{j}$

${\bar{e}}_{j}$

$j$

${\bar{e}}_{j}$

$\bar{a}$

${\bar{e}}_{j}$

$j$

${\bar{e}}_{j}$

${\bar{e}}_{j}$

$\bar{a}$

$\bar{a}$

$j$

$a_{j}$

$\overset{´}{}$

${\bar{e}}_{j}$

$\overset{´}{}$

$j$

${\bar{e}}_{j}$

$\overset{´}{}$

$\bar{a}$

${\bar{e}}_{j}$

$\overset{´}{}$

$j$

${\bar{e}}_{j}$

$\overset{´}{}$

${\bar{e}}_{j}$

$\overset{´}{}$

$\bar{a}$

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