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Display information for equation id:math.2158.33 on revision:2158

* Page found: Wellenausbreitung in Materie (eq math.2158.33)

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Wellenausbreitung in Materie Eq: math.2160.33

Hash: b281528376a7cf320042359106b10e5e

TeX (original user input):

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

TeX (checked):

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

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

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data-mjx-texclass="ORD"><mi>t</mi></mrow></msubsup><mi>d</mi><mi>t</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>χ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo stretchy="false">−</mo><mi>t</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mover><mi>E</mi><mo>¯</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$π$

$ω$

$ε_{0}$

$\hat{χ}$

$ω$

$t$

$\overset{´}{}$

$e$

$i$

$ω$

$t$

$\overset{´}{}$

$t$

$ε_{0}$

$π$

$χ$

$t$

$t$

$\overset{´}{}$

$\bar{P}$

$\bar{r}$

$t$

$π$

$ω$

$ε_{0}$

$\hat{χ}$

$ω$

$t$

$\overset{´}{}$

$\bar{E}$

$\bar{r}$

$t$

$\overset{´}{}$

$e$

$i$

$ω$

$t$

$\overset{´}{}$

$t$

$ε_{0}$

$π$

$t$

$t$

$\overset{´}{}$

$χ$

$t$

$t$

$\overset{´}{}$

$\bar{E}$

$\bar{r}$

$t$

$\overset{´}{}$

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