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Display information for equation id:math.2250.10 on revision:2250
* Page found: Dynamik des statistischen Operators (eq math.2250.10)
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\begin{align}
& {{p}_{n}}=\operatorname{Tr}\left( \rho \left| n \right\rangle \left\langle n \right| \right) \\
& =\sum\limits_{j}{\left\langle j \right|\sum\limits_{i}{{{w}_{i}}\left| {{\Psi }_{i}} \right\rangle \left\langle {{\Psi }_{i}} \right|}\left| n \right\rangle \left\langle n | j \right\rangle } \\
& =\sum\limits_{j}{\underbrace{\left\langle j | j \right\rangle }_{1}\sum\limits_{i}{\left\langle {{\Psi }_{i}} | n \right\rangle }\left\langle n \right|{{w}_{i}}\left| {{\Psi }_{i}} \right\rangle } \\
& =\sum\limits_{i}{{{w}_{i}}\left\langle n | {{\Psi }_{i}} \right\rangle \left\langle {{\Psi }_{i}} | n \right\rangle }=\left\langle n \right|\rho \left| n \right\rangle
\end{align}
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