Jump to navigation
Jump to search
General
Display information for equation id:math.1649.16 on revision:1649
* Page found: Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild (eq math.1649.16)
(force rerendering)Occurrences on the following pages:
Hash: 5e0e58527dc0465a4753cb09374d0f39
TeX (original user input):
\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}}
LaTeXML (experimental; uses MathML) rendering
MathML (0 B / 8 B) :
SVG image empty. Force Re-Rendering
SVG (0 B / 8 B) :
MathML (experimental; no images) rendering
MathML (7.223 KB / 582 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi>F</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mi>H</mi><mo>,</mo><mi>F</mi><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
Translations to Computer Algebra Systems
Translation to Maple
In Maple:
Translation to Mathematica
In Mathematica:
Similar pages
Calculated based on the variables occurring on the entire Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results