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Display information for equation id:math.2155.22 on revision:2155

* Page found: Mikroskopisches Modell der Polarisierbarkeit (eq math.2155.22)

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Mikroskopisches Modell der Polarisierbarkeit Eq: math.2156.22

Hash: d1e29c188a11e312ecd8f78569ef57bc

TeX (original user input):

\begin{align}
& \bar{p}=\int_{V}^{{}}{{}}{{d}^{3}}r\acute{\ }{{\rho }_{e}}(r\acute{\ })\bar{r}\acute{\ }+Ze\int_{V}^{{}}{{}}{{d}^{3}}r\acute{\ }\delta (\bar{r}-\bar{r}\acute{\ }) \\
& Ze\int_{V}^{{}}{{}}{{d}^{3}}r\acute{\ }\delta (\bar{r}-\bar{r}\acute{\ })=Ze\bar{r} \\
& \int_{V}^{{}}{{}}{{d}^{3}}r\acute{\ }{{\rho }_{e}}(r\acute{\ })\bar{r}\acute{\ }=-\frac{Ze}{\frac{4\pi }{3}{{R}^{3}}}\int_{V}^{{}}{{}}{{d}^{3}}r\acute{\ }\bar{r}\acute{\ } \\
& \int_{V}^{{}}{{}}{{d}^{3}}r\acute{\ }\bar{r}\acute{\ }=0 \\
\end{align}

TeX (checked):

{\begin{aligned}&{\bar {p}}=\int _{V}^{}{}{{d}^{3}}r{\acute {\ }}{{\rho }_{e}}(r{\acute {\ }}){\bar {r}}{\acute {\ }}+Ze\int _{V}^{}{}{{d}^{3}}r{\acute {\ }}\delta ({\bar {r}}-{\bar {r}}{\acute {\ }})\\&Ze\int _{V}^{}{}{{d}^{3}}r{\acute {\ }}\delta ({\bar {r}}-{\bar {r}}{\acute {\ }})=Ze{\bar {r}}\\&\int _{V}^{}{}{{d}^{3}}r{\acute {\ }}{{\rho }_{e}}(r{\acute {\ }}){\bar {r}}{\acute {\ }}=-{\frac {Ze}{{\frac {4\pi }{3}}{{R}^{3}}}}\int _{V}^{}{}{{d}^{3}}r{\acute {\ }}{\bar {r}}{\acute {\ }}\\&\int _{V}^{}{}{{d}^{3}}r{\acute {\ }}{\bar {r}}{\acute {\ }}=0\\\end{aligned}}

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\begin{matrix} \bar{p} = \int_{V}^{} d^{3} r \overset{´}{} ρ_{e} (r \overset{´}{}) \bar{r} \overset{´}{} + Z e \int_{V}^{} d^{3} r \overset{´}{} δ (\bar{r} - \bar{r} \overset{´}{}) \\ Z e \int_{V}^{} d^{3} r \overset{´}{} δ (\bar{r} - \bar{r} \overset{´}{}) = Z e \bar{r} \\ \int_{V}^{} d^{3} r \overset{´}{} ρ_{e} (r \overset{´}{}) \bar{r} \overset{´}{} = - \frac{Z e}{\frac{4 π}{3} R^{3}} \int_{V}^{} d^{3} r \overset{´}{} \bar{r} \overset{´}{} \\ \int_{V}^{} d^{3} r \overset{´}{} \bar{r} \overset{´}{} = 0 \end{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>p</mi><mo>¯</mo></mover><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">+</mo><mi>Z</mi><mi>e</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>δ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>Z</mi><mi>e</mi><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>δ</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">−</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>Z</mi><mi>e</mi><mover><mi>r</mi><mo>¯</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><msub><mi>ρ</mi><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>Z</mi><mi>e</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$\bar{p}$

$V$

$r$

$\overset{´}{}$

$ρ_{e}$

$r$

$\overset{´}{}$

$\bar{r}$

$\overset{´}{}$

$Z$

$e$

$V$

$r$

$\overset{´}{}$

$δ$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$Z$

$e$

$V$

$r$

$\overset{´}{}$

$δ$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$Z$

$e$

$\bar{r}$

$V$

$r$

$\overset{´}{}$

$ρ_{e}$

$r$

$\overset{´}{}$

$\bar{r}$

$\overset{´}{}$

$Z$

$e$

$π$

$R$

$V$

$r$

$\overset{´}{}$

$\bar{r}$

$\overset{´}{}$

$V$

$r$

$\overset{´}{}$

$\bar{r}$

$\overset{´}{}$

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