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Display information for equation id:math.2158.32 on revision:2158

* Page found: Wellenausbreitung in Materie (eq math.2158.32)

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Wellenausbreitung in Materie Eq: math.2160.32

Hash: 99aec491e9fbce540c269e24d79bcbe5

TeX (original user input):

\begin{align}
& \bar{P}\left( \bar{r},t \right)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{\infty }{{}}d\omega \hat{\bar{P}}\left( \bar{r},\omega  \right){{e}^{-i\omega t}} \\
& \hat{\bar{E}}\left( \bar{r},\omega  \right)=\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{\infty }{{}}dt\bar{E}\left( \bar{r},t \right){{e}^{+i\omega t}} \\
& \Rightarrow \bar{P}\left( \bar{r},t \right)=\frac{1}{2\pi }\int_{-\infty }^{\infty }{{}}d\omega {{\varepsilon }_{0}}\hat{\chi }\left( \omega  \right)\int_{-\infty }^{\infty }{{}}dt\acute{\ }\bar{E}\left( \bar{r},t\acute{\ } \right){{e}^{+i\omega \left( t\acute{\ }-t \right)}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\bar {P}}\left({\bar {r}},t\right)={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{\infty }{}d\omega {\hat {\bar {P}}}\left({\bar {r}},\omega \right){{e}^{-i\omega t}}\\&{\hat {\bar {E}}}\left({\bar {r}},\omega \right)={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{\infty }{}dt{\bar {E}}\left({\bar {r}},t\right){{e}^{+i\omega t}}\\&\Rightarrow {\bar {P}}\left({\bar {r}},t\right)={\frac {1}{2\pi }}\int _{-\infty }^{\infty }{}d\omega {{\varepsilon }_{0}}{\hat {\chi }}\left(\omega \right)\int _{-\infty }^{\infty }{}dt{\acute {\ }}{\bar {E}}\left({\bar {r}},t{\acute {\ }}\right){{e}^{+i\omega \left(t{\acute {\ }}-t\right)}}\\\end{aligned}}

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\begin{matrix} \bar{P} (\bar{r}, t) = \frac{1}{\sqrt{2 π}} \int_{- \infty}^{\infty} d ω \hat{\bar{P}} (\bar{r}, ω) e^{- i ω t} \\ \hat{\bar{E}} (\bar{r}, ω) = \frac{1}{\sqrt{2 π}} \int_{- \infty}^{\infty} d t \bar{E} (\bar{r}, t) e^{+ i ω t} \\ \Rightarrow \bar{P} (\bar{r}, t) = \frac{1}{2 π} \int_{- \infty}^{\infty} d ω ε_{0} \hat{χ} (ω) \int_{- \infty}^{\infty} d t \overset{´}{} \bar{E} (\bar{r}, t \overset{´}{}) e^{+ i ω (t \overset{´}{} - t)} \end{matrix}

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Identifiers

$\bar{P}$

$\bar{r}$

$t$

$π$

$ω$

$\hat{\bar{P}}$

$\bar{r}$

$ω$

$e$

$i$

$ω$

$t$

$\hat{\bar{E}}$

$\bar{r}$

$ω$

$π$

$t$

$\bar{E}$

$\bar{r}$

$t$

$e$

$i$

$ω$

$t$

$\bar{P}$

$\bar{r}$

$t$

$π$

$ω$

$ε_{0}$

$\hat{χ}$

$ω$

$t$

$\overset{´}{}$

$\bar{E}$

$\bar{r}$

$t$

$\overset{´}{}$

$e$

$i$

$ω$

$t$

$\overset{´}{}$

$t$

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