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Display information for equation id:math.2249.1 on revision:2249
* Page found: Dynamik des statistischen Operators (eq math.2249.1)
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\begin{align}
& \rho \left( t \right)=\sum\limits_{i}{{{w}_{i}}\left| {{\Psi }_{i}} \right\rangle \left\langle {{\Psi }_{i}} \right|} \\
& \text{S}\text{.GL:}i\hbar {{\partial }_{t}}\left| {{\Psi }_{i}} \right\rangle =H\left| {{\Psi }_{i}} \right\rangle \quad |\sum\limits_{i}{{{w}_{i}}\left\langle {{\Psi }_{i}} \right|} \\
& \text{h}\text{.c}:-i\hbar {{\partial }_{t}}\left\langle {{\Psi }_{i}} \right|=\left\langle {{\Psi }_{i}} \right|H\quad |\sum\limits_{i}{{{w}_{i}}\left\langle {{\Psi }_{i}} \right|} \\
& \Rightarrow i\hbar {{\partial }_{t}}\sum\limits_{i}{{{w}_{i}}\left\langle {{\Psi }_{i}} \right|}\left| {{\Psi }_{i}} \right\rangle =\sum\limits_{i}{{{w}_{i}}\left( H\left| {{\Psi }_{i}} \right\rangle \left\langle {{\Psi }_{i}} \right|-\left| {{\Psi }_{i}} \right\rangle \left\langle {{\Psi }_{i}} \right|H \right)} \\
\end{align}
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data-mjx-texclass="OPEN">⟨</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>S</mtext></mrow><mrow data-mjx-texclass="ORD"><mtext>.GL:</mtext></mrow><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mi>H</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mspace width="1em"></mspace><mo>|</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mrow 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data-mjx-texclass="CLOSE">|</mo></mrow><mi>H</mi><mspace width="1em"></mspace><mo>|</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>w</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>H</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo 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