Editing Dynamik des statistischen Operators
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* in der Statistik: <math>\begin{align} | * in der Statistik: <math>\begin{align} | ||
& {{p}_{n}}=\operatorname{Tr}\left( \rho \left| n \right\rangle \left\langle n \right| \right) \\ | & {{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 | & =\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 \right|\left| j \right\rangle } \\ | ||
& =\sum\limits_{j}{\underbrace{\left\langle j | & =\sum\limits_{j}{\underbrace{\left\langle j \right|\left| j \right\rangle }_{1}\sum\limits_{i}{\left\langle {{\Psi }_{i}} \right|\left| n \right\rangle }\left\langle n \right|{{w}_{i}}\left| {{\Psi }_{i}} \right\rangle } \\ | ||
& =\sum\limits_{i}{{{w}_{i}}\left\langle n | & =\sum\limits_{i}{{{w}_{i}}\left\langle n \right|\left| {{\Psi }_{i}} \right\rangle \left\langle {{\Psi }_{i}} \right|\left| n \right\rangle }=\left\langle n \right|\rho \left| n \right\rangle | ||
\end{align}</math> Der Wert <math>\left\langle n \right|\rho \left| n \right\rangle </math> stellt die Wahrscheinlichkeit dar, System im Zustand <math>\left| n \right\rangle </math> bei einer Messung zu finden. (Observable mit eigensystem <math>\left| n \right\rangle </math>). | \end{align}</math> Der Wert <math>\left\langle n \right|\rho \left| n \right\rangle </math> stellt die Wahrscheinlichkeit dar, System im Zustand <math>\left| n \right\rangle </math> bei einer Messung zu finden. (Observable mit eigensystem <math>\left| n \right\rangle </math>). | ||