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Display information for equation id:math.1199.663 on revision:1199

* Page found: Elektrodynamik Schöll (eq math.1199.663)

Occurrences on the following pages:

Retardierte Potenziale Eq: math.2129.17

Hash: 8c2d8da66fe39f0022fc2dc30588ac29

TeX (original user input):

\begin{align}
& u\left( \bar{r},t \right)=\frac{1}{{{\left( 2\pi  \right)}^{2}}}\int_{{{R}^{3}}}^{{}}{{{d}^{3}}q\int_{-\infty }^{\infty }{d\omega }}\hat{u}\left( \bar{q},\omega  \right){{e}^{i\left( \bar{q}\bar{r}-\omega t \right)}} \\
& \Rightarrow \#u\left( \bar{r},t \right)=\frac{1}{{{\left( 2\pi  \right)}^{2}}}\int_{{{R}^{3}}}^{{}}{{{d}^{3}}q\int_{-\infty }^{\infty }{d\omega }}\hat{u}\left( \bar{q},\omega  \right)\#{{e}^{i\left( \bar{q}\bar{r}-\omega t \right)}} \\
& \#{{e}^{i\left( \bar{q}\bar{r}-\omega t \right)}}=-\left( {{q}^{2}}-\frac{{{\omega }^{2}}}{{{c}^{2}}} \right){{e}^{i\left( \bar{q}\bar{r}-\omega t \right)}} \\
\end{align}

TeX (checked):

{\begin{aligned}&u\left({\bar {r}},t\right)={\frac {1}{{\left(2\pi \right)}^{2}}}\int _{{R}^{3}}^{}{{{d}^{3}}q\int _{-\infty }^{\infty }{d\omega }}{\hat {u}}\left({\bar {q}},\omega \right){{e}^{i\left({\bar {q}}{\bar {r}}-\omega t\right)}}\\&\Rightarrow \#u\left({\bar {r}},t\right)={\frac {1}{{\left(2\pi \right)}^{2}}}\int _{{R}^{3}}^{}{{{d}^{3}}q\int _{-\infty }^{\infty }{d\omega }}{\hat {u}}\left({\bar {q}},\omega \right)\#{{e}^{i\left({\bar {q}}{\bar {r}}-\omega t\right)}}\\&\#{{e}^{i\left({\bar {q}}{\bar {r}}-\omega t\right)}}=-\left({{q}^{2}}-{\frac {{\omega }^{2}}{{c}^{2}}}\right){{e}^{i\left({\bar {q}}{\bar {r}}-\omega t\right)}}\\\end{aligned}}

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\begin{aligned} u (\bar{r}, t) = \frac{1}{{(2 π)}^{2}} \int_{R^{3}}^{} d^{3} q \int_{- \infty}^{\infty} d ω \hat{u} (\bar{q}, ω) e^{i (\bar{q} \bar{r} - ω t)} \\ \Rightarrow # u (\bar{r}, t) = \frac{1}{{(2 π)}^{2}} \int_{R^{3}}^{} d^{3} q \int_{- \infty}^{\infty} d ω \hat{u} (\bar{q}, ω) # e^{i (\bar{q} \bar{r} - ω t)} \\ # e^{i (\bar{q} \bar{r} - ω t)} = - (q^{2} - \frac{ω^{2}}{c^{2}}) e^{i (\bar{q} \bar{r} - ω t)} \end{aligned}

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Identifiers

$u$

$\bar{r}$

$t$

$π$

$R$

$q$

$ω$

$\hat{u}$

$\bar{q}$

$ω$

$e$

$i$

$\bar{q}$

$\bar{r}$

$ω$

$t$

$u$

$\bar{r}$

$t$

$π$

$R$

$q$

$ω$

$\hat{u}$

$\bar{q}$

$ω$

$e$

$i$

$\bar{q}$

$\bar{r}$

$ω$

$t$

$e$

$i$

$\bar{q}$

$\bar{r}$

$ω$

$t$

$q$

$ω$

$c$

$e$

$i$

$\bar{q}$

$\bar{r}$

$ω$

$t$

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