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Dynamik des statistischen Operators
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==Bewegungsgleichung der Dichtematrixelemente== * was kann man mit :<math>{{\rho }_{nn}}=,\left\langle n \right|\rho \left| n \right\rangle </math> (kann ich damit etwas) anfangen? * in Quantenmechanik: <math>{{p}_{n}}=\left\langle {{\Psi }_{i0}} | n \right\rangle \left\langle n | {{\Psi }_{i0}} \right\rangle </math> ist Wahrscheinlichkeit bei Messung das System im Zustand <math>\left| n \right\rangle </math> zu finden, wenn <math>\left| {{\Psi }_{i0}} \right\rangle </math> vorliegt * in der Statistik: <math>\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}</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>).
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