– PhysikWiki

General

Display information for equation id:math.1786.17 on revision:1786

* Page found: Bornsche Näherung (eq math.1786.17)

Occurrences on the following pages:

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}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimentell; keine Bilder) rendering

MathML (4.457 KB / 623 B) :

\begin{matrix} \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{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>σ</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>Ω</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>f</mi><mo stretchy="false">(</mo><mi>ϑ</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">−</mo><mo>&gt;</mo><mi>σ</mi><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>Ω</mi></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>K</mi></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>d</mi><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow><mi>V</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><mi>sin</mi><mo>&#x2061;</mo><mi>K</mi><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>d</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>cos</mi><mo>&#x2061;</mo><mi>ϑ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ϕ</mi></mrow></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>K</mi></mrow></mfrac></mrow><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msubsup><mrow data-mjx-texclass="ORD"><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>d</mi><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow><mi>V</mi><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><mi>sin</mi><mo>&#x2061;</mo><mi>K</mi><mi>r</mi><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$d$

$σ$

$d$

$Ω$

$f$

$ϑ$

$σ$

$Ω$

$m$

$K$

$r$

$\overset{´}{}$

$r$

$\overset{´}{}$

$V$

$\bar{r}$

$\overset{´}{}$

$K$

$r$

$\overset{´}{}$

$ϑ$

$π$

$ϕ$

$m$

$K$

$r$

$\overset{´}{}$

$r$

$\overset{´}{}$

$V$

$\bar{r}$

$\overset{´}{}$

$K$

$r$

$\overset{´}{}$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

Suche