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Display information for equation id:math.1796.28 on revision:1796

* Page found: Drehimpulsdarstellung und Streuphasen (eq math.1796.28)

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Drehimpulsdarstellung und Streuphasen Eq: math.1796.28

Hash: 0e81e3a751fed490d60e203e0e33cfc0

TeX (original user input):

\begin{align}
& \begin{matrix}
\lim   \\
r\to \infty   \\
\end{matrix}\Psi (\bar{r})={{e}^{ikr\cos \vartheta }}+f(\vartheta )\frac{{{e}^{ikr}}}{r} \\
& \begin{matrix}
\lim   \\
r\to \infty   \\
\end{matrix}\sum\limits_{l}{{}}\frac{{{u}_{l}}}{r}{{P}_{l}}(\xi )=\sum\limits_{l}{{}}\left\{ \left( 2l+1 \right)\frac{{{i}^{l}}}{kr}\sin \left( kr-l\frac{\pi }{2} \right)+{{f}_{l}}\frac{{{e}^{ikr}}}{r} \right\}{{P}_{l}}(\xi ) \\
\end{align}

TeX (checked):

{\begin{aligned}&{\begin{matrix}\lim \\r\to \infty \\\end{matrix}}\Psi ({\bar {r}})={{e}^{ikr\cos \vartheta }}+f(\vartheta ){\frac {{e}^{ikr}}{r}}\\&{\begin{matrix}\lim \\r\to \infty \\\end{matrix}}\sum \limits _{l}{}{\frac {{u}_{l}}{r}}{{P}_{l}}(\xi )=\sum \limits _{l}{}\left\{\left(2l+1\right){\frac {{i}^{l}}{kr}}\sin \left(kr-l{\frac {\pi }{2}}\right)+{{f}_{l}}{\frac {{e}^{ikr}}{r}}\right\}{{P}_{l}}(\xi )\\\end{aligned}}

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MathML (3.553 KB / 626 B) :

\begin{aligned} \begin{matrix} \lim \\ r \to \infty \end{matrix} Ψ (\bar{r}) = e^{i k r \cos ϑ} + f (ϑ) \frac{e^{i k r}}{r} \\ \begin{matrix} \lim \\ r \to \infty \end{matrix} \sum_{l} \frac{u_{l}}{r} P_{l} (ξ) = \sum_{l} {(2 l + 1) \frac{i^{l}}{k r} \sin (k r - l \frac{π}{2}) + f_{l} \frac{e^{i k r}}{r}} P_{l} (ξ) \end{aligned}

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Identifiers

$r$

$Ψ$

$\bar{r}$

$e$

$i$

$k$

$r$

$ϑ$

$f$

$ϑ$

$e$

$i$

$k$

$r$

$r$

$r$

$l$

$u_{l}$

$r$

$P_{l}$

$ξ$

$l$

$l$

$i$

$l$

$k$

$r$

$k$

$r$

$l$

$π$

$f_{l}$

$e$

$i$

$k$

$r$

$r$

$P_{l}$

$ξ$

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