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Display information for equation id:math.2156.16 on revision:2156

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Mikroskopisches Modell der Polarisierbarkeit Eq: math.2156.16

Hash: 8f463d005f149cde38c4e447b75c278d

TeX (original user input):

\begin{align}
&  {{m}_{K}}{{{\ddot{\bar{r}}}}_{k}}={{{\bar{F}}}_{K}}+{{Q}_{K}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=-\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)+{{Q}_{K}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=-\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)+Ze{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right) \\
& Z{{m}_{e}}{{{\ddot{\bar{r}}}}_{e}}=-{{{\bar{F}}}_{K}}+{{Q}_{e}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)+{{Q}_{e}}{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right)=\frac{{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}\left( {{{\bar{r}}}_{k}}-{{{\bar{r}}}_{e}} \right)-Ze{{{\bar{E}}}_{a}}\left( {{{\bar{r}}}_{\acute{\ }k}},t \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&{{m}_{K}}{{\ddot {\bar {r}}}_{k}}={{\bar {F}}_{K}}+{{Q}_{K}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)=-{\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)+{{Q}_{K}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)=-{\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)+Ze{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)\\&Z{{m}_{e}}{{\ddot {\bar {r}}}_{e}}=-{{\bar {F}}_{K}}+{{Q}_{e}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)={\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)+{{Q}_{e}}{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)={\frac {{{Z}^{2}}{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{R}^{3}}}}\left({{\bar {r}}_{k}}-{{\bar {r}}_{e}}\right)-Ze{{\bar {E}}_{a}}\left({{\bar {r}}_{{\acute {\ }}k}},t\right)\\\end{aligned}}

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\begin{aligned} m_{K} {\ddot{\bar{r}}}_{k} = {\bar{F}}_{K} + Q_{K} {\bar{E}}_{a} ({\bar{r}}_{\overset{´}{} k}, t) = - \frac{Z^{2} e^{2}}{4 π ε_{0} R^{3}} ({\bar{r}}_{k} - {\bar{r}}_{e}) + Q_{K} {\bar{E}}_{a} ({\bar{r}}_{\overset{´}{} k}, t) = - \frac{Z^{2} e^{2}}{4 π ε_{0} R^{3}} ({\bar{r}}_{k} - {\bar{r}}_{e}) + Z e {\bar{E}}_{a} ({\bar{r}}_{\overset{´}{} k}, t) \\ Z m_{e} {\ddot{\bar{r}}}_{e} = - {\bar{F}}_{K} + Q_{e} {\bar{E}}_{a} ({\bar{r}}_{\overset{´}{} k}, t) = \frac{Z^{2} e^{2}}{4 π ε_{0} R^{3}} ({\bar{r}}_{k} - {\bar{r}}_{e}) + Q_{e} {\bar{E}}_{a} ({\bar{r}}_{\overset{´}{} k}, t) = \frac{Z^{2} e^{2}}{4 π ε_{0} R^{3}} ({\bar{r}}_{k} - {\bar{r}}_{e}) - Z e {\bar{E}}_{a} ({\bar{r}}_{\overset{´}{} k}, t) \end{aligned}

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Identifiers

$m_{K}$

${\ddot{\bar{r}}}_{k}$

${\bar{F}}_{K}$

$Q_{K}$

${\bar{E}}_{a}$

$\bar{r}$

$\overset{´}{}$

$k$

$t$

$Z$

$e$

$π$

$ε_{0}$

$R$

${\bar{r}}_{k}$

${\bar{r}}_{e}$

$Q_{K}$

${\bar{E}}_{a}$

$\bar{r}$

$\overset{´}{}$

$k$

$t$

$Z$

$e$

$π$

$ε_{0}$

$R$

${\bar{r}}_{k}$

${\bar{r}}_{e}$

$Z$

$e$

${\bar{E}}_{a}$

$\bar{r}$

$\overset{´}{}$

$k$

$t$

$Z$

$m_{e}$

${\ddot{\bar{r}}}_{e}$

${\bar{F}}_{K}$

$Q_{e}$

${\bar{E}}_{a}$

$\bar{r}$

$\overset{´}{}$

$k$

$t$

$Z$

$e$

$π$

$ε_{0}$

$R$

${\bar{r}}_{k}$

${\bar{r}}_{e}$

$Q_{e}$

${\bar{E}}_{a}$

$\bar{r}$

$\overset{´}{}$

$k$

$t$

$Z$

$e$

$π$

$ε_{0}$

$R$

${\bar{r}}_{k}$

${\bar{r}}_{e}$

$Z$

$e$

${\bar{E}}_{a}$

$\bar{r}$

$\overset{´}{}$

$k$

$t$

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