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Display information for equation id:math.1938.21 on revision:1938
* Page found: Räumliche Translationsinvarianz (eq math.1938.21)
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Hash: 1ed71b600a737e353fb70dc18201b0b0
TeX (original user input):
{{Q}_{1}}=0\Rightarrow \frac{\partial }{\partial {{q}_{1}}}V({{\bar{r}}_{1}}+{{q}_{1}}{{\bar{e}}_{x}},...,{{\bar{r}}_{N}}+{{q}_{1}}{{\bar{e}}_{x}})=\sum\limits_{i}{{{\nabla }_{ri}}}V\frac{\partial }{\partial {{q}_{1}}}\left( {{q}_{1}}{{{\bar{e}}}_{x}} \right)={{\bar{e}}_{x}}\sum\limits_{i}{{{\nabla }_{ri}}}V=-{{\bar{e}}_{x}}\sum\limits_{i}{{{{\bar{X}}}_{i}}=0}
TeX (checked):
{{Q}_{1}}=0\Rightarrow {\frac {\partial }{\partial {{q}_{1}}}}V({{\bar {r}}_{1}}+{{q}_{1}}{{\bar {e}}_{x}},...,{{\bar {r}}_{N}}+{{q}_{1}}{{\bar {e}}_{x}})=\sum \limits _{i}{{\nabla }_{ri}}V{\frac {\partial }{\partial {{q}_{1}}}}\left({{q}_{1}}{{\bar {e}}_{x}}\right)={{\bar {e}}_{x}}\sum \limits _{i}{{\nabla }_{ri}}V=-{{\bar {e}}_{x}}\sum \limits _{i}{{{\bar {X}}_{i}}=0}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mstyle><mo>=</mo><mn>0</mn><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><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow><mi>V</mi><mo stretchy="false">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>e</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo>+</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>e</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>r</mi><mi>i</mi></mrow></mrow></msub><mi>V</mi><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><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>e</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>e</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></munder><msub><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>r</mi><mi>i</mi></mrow></mrow></msub><mi>V</mi><mo>=</mo><mo>−</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>e</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>x</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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>X</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></mrow></math>
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