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Display information for equation id:math.1641.16 on revision:1641

* Page found: Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild (eq math.1641.16)

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\begin{align}
& \frac{d}{dt}F(\bar{q},\bar{p},t)=\frac{\partial }{\partial t}F(\bar{q},\bar{p},t)+\sum\limits_{i=1}^{3}{\left( \frac{\partial F(\bar{q},\bar{p},t)}{\partial {{q}_{i}}}{{{\dot{q}}}_{i}}+\frac{\partial F(\bar{q},\bar{p},t)}{\partial {{p}_{i}}}{{{\dot{p}}}_{i}} \right)} \\
& \frac{d}{dt}F(\bar{q},\bar{p},t)=\frac{\partial }{\partial t}F(\bar{q},\bar{p},t)+\sum\limits_{i=1}^{3}{\left( \frac{\partial F(\bar{q},\bar{p},t)}{\partial {{q}_{i}}}\frac{\partial H}{\partial {{p}_{i}}}-\frac{\partial F(\bar{q},\bar{p},t)}{\partial {{p}_{i}}}\frac{\partial H}{\partial {{q}_{i}}} \right)}=\frac{\partial }{\partial t}F(\bar{q},\bar{p},t)+\left\{ H,F \right\} \\
\end{align}

TeX (checked): 

{\begin{aligned}&{\frac {d}{dt}}F({\bar {q}},{\bar {p}},t)={\frac {\partial }{\partial t}}F({\bar {q}},{\bar {p}},t)+\sum \limits _{i=1}^{3}{\left({\frac {\partial F({\bar {q}},{\bar {p}},t)}{\partial {{q}_{i}}}}{{\dot {q}}_{i}}+{\frac {\partial F({\bar {q}},{\bar {p}},t)}{\partial {{p}_{i}}}}{{\dot {p}}_{i}}\right)}\\&{\frac {d}{dt}}F({\bar {q}},{\bar {p}},t)={\frac {\partial }{\partial t}}F({\bar {q}},{\bar {p}},t)+\sum \limits _{i=1}^{3}{\left({\frac {\partial F({\bar {q}},{\bar {p}},t)}{\partial {{q}_{i}}}}{\frac {\partial H}{\partial {{p}_{i}}}}-{\frac {\partial F({\bar {q}},{\bar {p}},t)}{\partial {{p}_{i}}}}{\frac {\partial H}{\partial {{q}_{i}}}}\right)}={\frac {\partial }{\partial t}}F({\bar {q}},{\bar {p}},t)+\left\{H,F\right\}\\\end{aligned}}

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MathML (64.015 KB / 5.935 KB) :

d d ⁢ t ⁢ F ⁢ ( q ¯ , p ¯ , t ) = ∂ ∂ ⁡ t ⁢ F ⁢ ( q ¯ , p ¯ , t ) + ∑ i = 1 3 ( ∂ ⁡ F ⁢ ( q ¯ , p ¯ , t ) ∂ ⁡ q i ⁢ q ˙ i + ∂ ⁡ F ⁢ ( q ¯ , p ¯ , t ) ∂ ⁡ p i ⁢ p ˙ i ) d d ⁢ t ⁢ F ⁢ ( q ¯ , p ¯ , t ) = ∂ ∂ ⁡ t ⁢ F ⁢ ( q ¯ , p ¯ , t ) + ∑ i = 1 3 ( ∂ ⁡ F ⁢ ( q ¯ , p ¯ , t ) ∂ ⁡ q i ⁢ ∂ ⁡ H ∂ ⁡ p i - ∂ ⁡ F ⁢ ( q ¯ , p ¯ , t ) ∂ ⁡ p i ⁢ ∂ ⁡ H ∂ ⁡ q i ) = ∂ ∂ ⁡ t ⁢ F ⁢ ( q ¯ , p ¯ , t ) + { H , F } missing-subexpression 𝑑 𝑑 𝑡 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 𝑡 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 superscript subscript 𝑖 1 3 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 subscript 𝑞 𝑖 subscript ˙ 𝑞 𝑖 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 subscript 𝑝 𝑖 subscript ˙ 𝑝 𝑖 missing-subexpression 𝑑 𝑑 𝑡 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 𝑡 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 superscript subscript 𝑖 1 3 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 subscript 𝑞 𝑖 𝐻 subscript 𝑝 𝑖 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 subscript 𝑝 𝑖 𝐻 subscript 𝑞 𝑖 𝑡 𝐹 ¯ 𝑞 ¯ 𝑝 𝑡 𝐻 𝐹 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\frac{d}{dt}F(\bar{q% },\bar{p},t)=\frac{\partial}{\partial t}F(\bar{q},\bar{p},t)+\sum\limits_{i=1}% ^{3}{\left(\frac{\partial F(\bar{q},\bar{p},t)}{\partial{{q}_{i}}}{{{\dot{q}}}% _{i}}+\frac{\partial F(\bar{q},\bar{p},t)}{\partial{{p}_{i}}}{{{\dot{p}}}_{i}}% \right)}\\ &\displaystyle\frac{d}{dt}F(\bar{q},\bar{p},t)=\frac{\partial}{\partial t}F(% \bar{q},\bar{p},t)+\sum\limits_{i=1}^{3}{\left(\frac{\partial F(\bar{q},\bar{p% },t)}{\partial{{q}_{i}}}\frac{\partial H}{\partial{{p}_{i}}}-\frac{\partial F(% \bar{q},\bar{p},t)}{\partial{{p}_{i}}}\frac{\partial H}{\partial{{q}_{i}}}% \right)}=\frac{\partial}{\partial t}F(\bar{q},\bar{p},t)+\left\{H,F\right\}\\ \end{aligned}}}

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ddtF(q¯,p¯,t)=∂∂tF(q¯,p¯,t)+∑i=13(∂F(q¯,p¯,t)∂qiq˙i+∂F(q¯,p¯,t)∂pip˙i)ddtF(q¯,p¯,t)=∂∂tF(q¯,p¯,t)+∑i=13(∂F(q¯,p¯,t)∂qi∂H∂pi−∂F(q¯,p¯,t)∂pi∂H∂qi)=∂∂tF(q¯,p¯,t)+{H,F}

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