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Display information for equation id:math.1438.103 on revision:1438

* Page found: Elektromagnetische Wellen (eq math.1438.103)

Occurrences on the following pages:

Retardierte Potenziale Eq: math.2129.18

Hash: dc63ce625a35a4c907309135f2747f43

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{f}\left( \bar{q},\omega  \right){{e}^{i\left( \bar{q}\bar{r}-\omega t \right)}} \\
& \Rightarrow \left( {{q}^{2}}-\frac{{{\omega }^{2}}}{{{c}^{2}}} \right)\hat{u}\left( \bar{q},\omega  \right)=\hat{f}\left( \bar{q},\omega  \right) \\
& \Rightarrow \hat{u}\left( \bar{q},\omega  \right)=\frac{\hat{f}\left( \bar{q},\omega  \right)}{\left( {{q}^{2}}-\frac{{{\omega }^{2}}}{{{c}^{2}}} \right)} \\
& \Rightarrow \hat{G}=\frac{1}{\left( {{q}^{2}}-\frac{{{\omega }^{2}}}{{{c}^{2}}} \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 {f}}\left({\bar {q}},\omega \right){{e}^{i\left({\bar {q}}{\bar {r}}-\omega t\right)}}\\&\Rightarrow \left({{q}^{2}}-{\frac {{\omega }^{2}}{{c}^{2}}}\right){\hat {u}}\left({\bar {q}},\omega \right)={\hat {f}}\left({\bar {q}},\omega \right)\\&\Rightarrow {\hat {u}}\left({\bar {q}},\omega \right)={\frac {{\hat {f}}\left({\bar {q}},\omega \right)}{\left({{q}^{2}}-{\frac {{\omega }^{2}}{{c}^{2}}}\right)}}\\&\Rightarrow {\hat {G}}={\frac {1}{\left({{q}^{2}}-{\frac {{\omega }^{2}}{{c}^{2}}}\right)}}\\\end{aligned}}

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MathML (5.94 KB / 623 B) :

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

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Identifiers

$u$

$\bar{r}$

$t$

$π$

$R$

$q$

$ω$

$\hat{f}$

$\bar{q}$

$ω$

$e$

$i$

$\bar{q}$

$\bar{r}$

$ω$

$t$

$q$

$ω$

$c$

$\hat{u}$

$\bar{q}$

$ω$

$\hat{f}$

$\bar{q}$

$ω$

$\hat{u}$

$\bar{q}$

$ω$

$\hat{f}$

$\bar{q}$

$ω$

$q$

$ω$

$c$

$\hat{G}$

$q$

$ω$

$c$

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