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Display information for equation id:math.1783.3 on revision:1783

* Page found: Streuamplitude und Streuquerschnitt (eq math.1783.3)

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Streuamplitude und Streuquerschnitt Eq: math.1783.3

Hash: 04d1152f5e1848953b923be172b9b6c7

TeX (original user input):

\begin{align}
  & |\bar{r}-\bar{r}\acute{\ }|=\sqrt{{{\left( \bar{r}-\bar{r}\acute{\ } \right)}^{2}}}=\sqrt{\left( {{{\bar{r}}}^{2}}-2\bar{r}\bar{r}\acute{\ }+\bar{r}\acute{\ } \right)}=r\sqrt{\left( 1-2\frac{\bar{r}\bar{r}\acute{\ }}{{{r}^{2}}}+{{\left( \frac{r\acute{\ }}{r} \right)}^{2}} \right)}\approx r\sqrt{\left( 1-2\frac{\bar{r}\bar{r}\acute{\ }}{{{r}^{2}}} \right)\approx }r-\bar{r}\acute{\ }{{{\bar{e}}}_{r}} \\ 
 & {{{\bar{e}}}_{r}}=\frac{{\bar{r}}}{r} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&|{\bar {r}}-{\bar {r}}{\acute {\ }}|={\sqrt {{\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)}^{2}}}={\sqrt {\left({{\bar {r}}^{2}}-2{\bar {r}}{\bar {r}}{\acute {\ }}+{\bar {r}}{\acute {\ }}\right)}}=r{\sqrt {\left(1-2{\frac {{\bar {r}}{\bar {r}}{\acute {\ }}}{{r}^{2}}}+{{\left({\frac {r{\acute {\ }}}{r}}\right)}^{2}}\right)}}\approx r{\sqrt {\left(1-2{\frac {{\bar {r}}{\bar {r}}{\acute {\ }}}{{r}^{2}}}\right)\approx }}r-{\bar {r}}{\acute {\ }}{{\bar {e}}_{r}}\\&{{\bar {e}}_{r}}={\frac {\bar {r}}{r}}\\\end{aligned}}

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\begin{aligned} | \bar{r} - \bar{r} \overset{´}{} | = \sqrt{{(\bar{r} - \bar{r} \overset{´}{})}^{2}} = \sqrt{({\bar{r}}^{2} - 2 \bar{r} \bar{r} \overset{´}{} + \bar{r} \overset{´}{})} = r \sqrt{(1 - 2 \frac{\bar{r} \bar{r} \overset{´}{}}{r^{2}} + {(\frac{r \overset{´}{}}{r})}^{2})} \approx r \sqrt{(1 - 2 \frac{\bar{r} \bar{r} \overset{´}{}}{r^{2}}) \approx} r - \bar{r} \overset{´}{} {\bar{e}}_{r} \\ {\bar{e}}_{r} = \frac{\bar{r}}{r} \end{aligned}

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Identifiers

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$\bar{r}$

$\overset{´}{}$

$r$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$r$

$r$

$\overset{´}{}$

$r$

$r$

$\bar{r}$

$\bar{r}$

$\overset{´}{}$

$r$

$r$

$\bar{r}$

$\overset{´}{}$

${\bar{e}}_{r}$

${\bar{e}}_{r}$

$\bar{r}$

$r$

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