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Display information for equation id:math.1787.17 on revision:1787

* Page found: Bornsche Näherung (eq math.1787.17)

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Bornsche Näherung Eq: math.1790.17

Hash: 9310e3b62b977611d57311a76310825f

TeX (original user input):

\begin{align}

& \frac{d\sigma }{d\Omega }={{\left| f(\vartheta ) \right|}^{2}} \\
& ->\sigma =\int_{{}}^{{}}{d\Omega }{{\left| \frac{2m}{{{\hbar }^{2}}}\frac{1}{K}\int_{0}^{\infty }{r\acute{\ }dr\acute{\ }}V(\bar{r}\acute{\ })\sin Kr\acute{\ } \right|}^{2}} \\
& =\int_{-1}^{1}{d\left( \cos \vartheta  \right)\int_{0}^{2\pi }{d\phi }}{{\left| \frac{2m}{{{\hbar }^{2}}}\frac{1}{K}\int_{0}^{\infty }{r\acute{\ }dr\acute{\ }}V(\bar{r}\acute{\ })\sin Kr\acute{\ } \right|}^{2}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {d\sigma }{d\Omega }}={{\left|f(\vartheta )\right|}^{2}}\\&->\sigma =\int _{}^{}{d\Omega }{{\left|{\frac {2m}{{\hbar }^{2}}}{\frac {1}{K}}\int _{0}^{\infty }{r{\acute {\ }}dr{\acute {\ }}}V({\bar {r}}{\acute {\ }})\sin Kr{\acute {\ }}\right|}^{2}}\\&=\int _{-1}^{1}{d\left(\cos \vartheta \right)\int _{0}^{2\pi }{d\phi }}{{\left|{\frac {2m}{{\hbar }^{2}}}{\frac {1}{K}}\int _{0}^{\infty }{r{\acute {\ }}dr{\acute {\ }}}V({\bar {r}}{\acute {\ }})\sin Kr{\acute {\ }}\right|}^{2}}\\\end{aligned}}

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\begin{aligned} \frac{d σ}{d Ω} = {| f (ϑ) |}^{2} \\ - > σ = \int_{}^{} d Ω {| \frac{2 m}{ℏ^{2}} \frac{1}{K} \int_{0}^{\infty} r \overset{´}{} d r \overset{´}{} V (\bar{r} \overset{´}{}) \sin K r \overset{´}{} |}^{2} \\ = \int_{- 1}^{1} d (\cos ϑ) \int_{0}^{2 π} d ϕ {| \frac{2 m}{ℏ^{2}} \frac{1}{K} \int_{0}^{\infty} r \overset{´}{} d r \overset{´}{} V (\bar{r} \overset{´}{}) \sin K r \overset{´}{} |}^{2} \end{aligned}

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Identifiers

$d$

$σ$

$d$

$Ω$

$f$

$ϑ$

$σ$

$Ω$

$m$

$K$

$r$

$\overset{´}{}$

$r$

$\overset{´}{}$

$V$

$\bar{r}$

$\overset{´}{}$

$K$

$r$

$\overset{´}{}$

$ϑ$

$π$

$ϕ$

$m$

$K$

$r$

$\overset{´}{}$

$r$

$\overset{´}{}$

$V$

$\bar{r}$

$\overset{´}{}$

$K$

$r$

$\overset{´}{}$

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