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Display information for equation id:math.2137.28 on revision:2137

* Page found: Wellenoptik und Beugung (eq math.2137.28)

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Wellenoptik und Beugung Eq: math.2137.28

Hash: 022477f631f403f3aca592c42b27eb25

TeX (original user input):

\begin{align}
& \Phi \left( \bar{r}\acute{\ },t \right)=\frac{1}{4\pi }\int_{\partial V}^{{}}{d{{{\bar{f}}}_{R}}}\left[ \frac{{{e}^{ikR}}}{R}{{\nabla }_{r}}\Phi \left( {\bar{r}} \right)-\Phi \left( {\bar{r}} \right){{\nabla }_{r}}\frac{{{e}^{ikR}}}{R} \right] \\
& {{\nabla }_{r}}\frac{{{e}^{ikR}}}{R}=\frac{{{e}^{ikR}}}{R}\left( ik-\frac{1}{R} \right)\frac{\bar{r}-\bar{r}\acute{\ }}{\left| \bar{r}-\bar{r}\acute{\ } \right|} \\
\end{align}

TeX (checked):

{\begin{aligned}&\Phi \left({\bar {r}}{\acute {\ }},t\right)={\frac {1}{4\pi }}\int _{\partial V}^{}{d{{\bar {f}}_{R}}}\left[{\frac {{e}^{ikR}}{R}}{{\nabla }_{r}}\Phi \left({\bar {r}}\right)-\Phi \left({\bar {r}}\right){{\nabla }_{r}}{\frac {{e}^{ikR}}{R}}\right]\\&{{\nabla }_{r}}{\frac {{e}^{ikR}}{R}}={\frac {{e}^{ikR}}{R}}\left(ik-{\frac {1}{R}}\right){\frac {{\bar {r}}-{\bar {r}}{\acute {\ }}}{\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}\\\end{aligned}}

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\begin{aligned} Φ (\bar{r} \overset{´}{}, t) = \frac{1}{4 π} \int_{\partial V}^{} d {\bar{f}}_{R} [\frac{e^{i k R}}{R} \nabla_{r} Φ (\bar{r}) - Φ (\bar{r}) \nabla_{r} \frac{e^{i k R}}{R}] \\ \nabla_{r} \frac{e^{i k R}}{R} = \frac{e^{i k R}}{R} (i k - \frac{1}{R}) \frac{\bar{r} - \bar{r} \overset{´}{}}{| \bar{r} - \bar{r} \overset{´}{} |} \end{aligned}

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Identifiers

$Φ$

$\bar{r}$

$\overset{´}{}$

$t$

$π$

$V$

${\bar{f}}_{R}$

$e$

$i$

$k$

$R$

$R$

$r$

$Φ$

$\bar{r}$

$Φ$

$\bar{r}$

$r$

$e$

$i$

$k$

$R$

$R$

$r$

$e$

$i$

$k$

$R$

$R$

$e$

$i$

$k$

$R$

$R$

$i$

$k$

$R$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

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