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Display information for equation id:math.2156.22 on revision:2156

* Page found: Mikroskopisches Modell der Polarisierbarkeit (eq math.2156.22)

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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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MathML (6.354 KB / 570 B) :

\begin{aligned} \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{aligned}

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Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

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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