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Display information for equation id:math.1438.236 on revision:1438

* Page found: Elektromagnetische Wellen (eq math.1438.236)

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Hash: d09fa1d864703f9c23a56a592f1055cc

TeX (original user input): 

\begin{align}
& \Phi \left( \bar{r},t \right)=\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }\tilde{G}\left( \bar{r}-\bar{r}\acute{\ } \right){{e}^{-i\omega t}}\frac{\rho \left( \bar{r}\acute{\ } \right)}{{{\varepsilon }_{0}}}}=\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }\frac{{{e}^{ik\left| \bar{r}-\bar{r}\acute{\ } \right|}}}{4\pi \left| \bar{r}-\bar{r}\acute{\ } \right|}{{e}^{-i\omega t}}\frac{\rho \left( \bar{r}\acute{\ } \right)}{{{\varepsilon }_{0}}}} \\
& \Phi \left( \bar{r},t \right)=\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }\frac{{{e}^{i\left( k\left| \bar{r}-\bar{r}\acute{\ } \right|-\omega t \right)}}}{4\pi \left| \bar{r}-\bar{r}\acute{\ } \right|}\frac{\rho \left( \bar{r}\acute{\ } \right)}{{{\varepsilon }_{0}}}} \\
\end{align}

TeX (checked): 

{\begin{aligned}&\Phi \left({\bar {r}},t\right)=\int _{}^{}{{{d}^{3}}r{\acute {\ }}{\tilde {G}}\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right){{e}^{-i\omega t}}{\frac {\rho \left({\bar {r}}{\acute {\ }}\right)}{{\varepsilon }_{0}}}}=\int _{}^{}{{{d}^{3}}r{\acute {\ }}{\frac {{e}^{ik\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{4\pi \left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{{e}^{-i\omega t}}{\frac {\rho \left({\bar {r}}{\acute {\ }}\right)}{{\varepsilon }_{0}}}}\\&\Phi \left({\bar {r}},t\right)=\int _{}^{}{{{d}^{3}}r{\acute {\ }}{\frac {{e}^{i\left(k\left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|-\omega t\right)}}{4\pi \left|{\bar {r}}-{\bar {r}}{\acute {\ }}\right|}}{\frac {\rho \left({\bar {r}}{\acute {\ }}\right)}{{\varepsilon }_{0}}}}\\\end{aligned}}

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Φ(r¯,t)=∫d3r´G~(r¯−r¯´)e−iωtρ(r¯´)ε0=∫d3r´eik|r¯−r¯´|4π|r¯−r¯´|e−iωtρ(r¯´)ε0Φ(r¯,t)=∫d3r´ei(k|r¯−r¯´|−ωt)4π|r¯−r¯´|ρ(r¯´)ε0
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Calculated based on the variables occurring on the entire Elektromagnetische Wellen page

Identifiers

  • Φ
  • r¯
  • t
  • r
  • ´
  • G~
  • r¯
  • r¯
  • ´
  • e
  • i
  • ω
  • t
  • ρ
  • r¯
  • ´
  • ε0
  • r
  • ´
  • e
  • i
  • k
  • r¯
  • r¯
  • ´
  • π
  • r¯
  • r¯
  • ´
  • e
  • i
  • ω
  • t
  • ρ
  • r¯
  • ´
  • ε0
  • Φ
  • r¯
  • t
  • r
  • ´
  • e
  • i
  • k
  • r¯
  • r¯
  • ´
  • ω
  • t
  • π
  • r¯
  • r¯
  • ´
  • ρ
  • r¯
  • ´
  • ε0

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“