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Display information for equation id:math.995.25 on revision:995
* Page found: Master Gleichung (eq math.995.25)
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\begin{align}
& {{d}_{t}}\tilde{\rho }={{d}_{t}}\left( U_{0}^{\dagger }\rho {{U}_{0}} \right) \\
& =\mathfrak{i}{{H}_{0}}U_{0}^{\dagger }\rho {{U}_{0}}-iU_{0}^{\dagger }\rho {{H}_{0}}{{U}_{0}}+U_{0}^{\dagger }{{d}_{t}}\left( \rho \right){{U}_{0}} \\
& =\mathfrak{i}\left[ {{H}_{0}},\tilde{\rho } \right]-\mathfrak{i}U_{0}^{\dagger }\left[ H,\rho \right]{{U}_{0}} \\
& =\mathfrak{i}\left[ {{H}_{0}},\tilde{\rho } \right]-\mathfrak{i}U_{0}^{\dagger }\left[ {{H}_{0}}+{{H}_{SB}},\rho \right]{{U}_{0}} \\
& =\mathfrak{i}\left[ {{H}_{0}},\tilde{\rho } \right]-\mathfrak{i}\left[ {{H}_{0}},\tilde{\rho } \right]-\mathfrak{i}U_{0}^{\dagger }\left[ {{H}_{SB}},\rho \right]{{U}_{0}} \\
& =-\mathfrak{i}\left[ {{{\tilde{H}}}_{SB}},\tilde{\rho } \right] \\
\end{align}
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data-mjx-texclass="ORD"><mover><mi>ρ</mi><mo>~</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><msubsup><mi>U</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mo>†</mo></mrow></msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mi>H</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>S</mi><mi>B</mi></mrow></mrow></msub><mo>,</mo><mi>ρ</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mrow data-mjx-texclass="ORD"><mrow 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