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Display information for equation id:math.2137.9 on revision:2137

* Page found: Wellenoptik und Beugung (eq math.2137.9)

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Hash: 0487b42e529b5a53c841c79d36d04b28

TeX (original user input): 

\begin{align}
& \#\Phi \left( \bar{r},t \right)=-\frac{\rho }{{{\varepsilon }_{0}}}=\left( \Delta -\frac{1}{{{c}^{2}}}\frac{{{\partial }^{2}}}{\partial {{t}^{2}}} \right)\Phi \left( \bar{r},t \right) \\
& \Rightarrow \left( \Delta +{{k}^{2}} \right)\Phi \left( {\bar{r}} \right)=-\frac{\rho \left( {\bar{r}} \right)}{{{\varepsilon }_{0}}} \\
& k:=\frac{\omega }{c} \\
\end{align}

TeX (checked): 

{\begin{aligned}&\#\Phi \left({\bar {r}},t\right)=-{\frac {\rho }{{\varepsilon }_{0}}}=\left(\Delta -{\frac {1}{{c}^{2}}}{\frac {{\partial }^{2}}{\partial {{t}^{2}}}}\right)\Phi \left({\bar {r}},t\right)\\&\Rightarrow \left(\Delta +{{k}^{2}}\right)\Phi \left({\bar {r}}\right)=-{\frac {\rho \left({\bar {r}}\right)}{{\varepsilon }_{0}}}\\&k:={\frac {\omega }{c}}\\\end{aligned}}

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MathML (23.417 KB / 2.894 KB) :

# ⁢ Φ ⁢ ( r ¯ , t ) = - ρ ε 0 = ( Δ - 1 c 2 ⁢ ∂ 2 ∂ ⁡ t 2 ) ⁢ Φ ⁢ ( r ¯ , t ) ⇒ ( Δ + k 2 ) ⁢ Φ ⁢ ( r ¯ ) = - ρ ⁢ ( r ¯ ) ε 0 k := ω c missing-subexpression # Φ ¯ 𝑟 𝑡 𝜌 subscript 𝜀 0 Δ 1 superscript 𝑐 2 superscript 2 superscript 𝑡 2 Φ ¯ 𝑟 𝑡 missing-subexpression ⇒ absent Δ superscript 𝑘 2 Φ ¯ 𝑟 𝜌 ¯ 𝑟 subscript 𝜀 0 missing-subexpression assign 𝑘 𝜔 𝑐 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\#\Phi\left(\bar{r},% t\right)=-\frac{\rho}{{{\varepsilon}_{0}}}=\left(\Delta-\frac{1}{{{c}^{2}}}% \frac{{{\partial}^{2}}}{\partial{{t}^{2}}}\right)\Phi\left(\bar{r},t\right)\\ &\displaystyle\Rightarrow\left(\Delta+{{k}^{2}}\right)\Phi\left({\bar{r}}% \right)=-\frac{\rho\left({\bar{r}}\right)}{{{\varepsilon}_{0}}}\\ &\displaystyle k:=\frac{\omega}{c}\\ \end{aligned}}}

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MathML (3.158 KB / 516 B) :

#Φ(r¯,t)=−ρε0=(Δ−1c2∂2∂t2)Φ(r¯,t)⇒(Δ+k2)Φ(r¯)=−ρ(r¯)ε0k:=ωc

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Calculated based on the variables occurring on the entire Wellenoptik und Beugung page

Identifiers

  • Φ
  • r¯
  • t
  • ρ
  • ε0
  • Δ
  • c
  • t
  • Φ
  • r¯
  • t
  • Δ
  • k
  • Φ
  • r¯
  • ρ
  • r¯
  • ε0
  • k
  • ω
  • c

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