– PhysikWiki

General

Display information for equation id:math.1756.21 on revision:1756

* Page found: Stark Effekt im H- Atom (eq math.1756.21)

Occurrences on the following pages:

Stark Effekt im H- Atom Eq: math.1756.21

Hash: 2ac16641de1e48257f3993640667a329

TeX (original user input):

\begin{align}

& {{d}_{13}}=\left\langle  200 \right|e{{{\hat{x}}}_{3}}\left| 210 \right\rangle  \\

& =e\int_{0}^{\infty }{{}}{{d}^{3}}r{{r}^{2}}\frac{2}{{{\left( 2{{a}_{0}} \right)}^{\frac{3}{2}}}}\left( 1-\frac{r}{2{{a}_{0}}} \right){{e}^{-\frac{r}{2{{a}_{0}}}}}r\frac{1}{\sqrt{3}{{\left( 2{{a}_{0}} \right)}^{\frac{3}{2}}}{{a}_{0}}}r{{e}^{-\frac{r}{2{{a}_{0}}}}}\int_{0}^{2\pi }{d\phi \int_{0}^{\pi }{d\vartheta \sin \vartheta \sqrt{\frac{1}{4\pi }}\cos \vartheta \sqrt{\frac{3}{4\pi }}\cos \vartheta }} \\

& \frac{{{u}_{20}}(r)}{r}=\frac{2}{{{\left( 2{{a}_{0}} \right)}^{\frac{3}{2}}}}\left( 1-\frac{r}{2{{a}_{0}}} \right){{e}^{-\frac{r}{2{{a}_{0}}}}} \\

& \frac{{{u}_{21}}(r)}{r}=\frac{1}{\sqrt{3}{{\left( 2{{a}_{0}} \right)}^{\frac{3}{2}}}{{a}_{0}}}r{{e}^{-\frac{r}{2{{a}_{0}}}}} \\

& \sqrt{\frac{1}{4\pi }}={{Y}_{0}}^{0} \\

& \sqrt{\frac{3}{4\pi }}\cos \vartheta ={{Y}_{1}}^{0} \\

& \int_{0}^{2\pi }{d\phi \int_{0}^{\pi }{d\vartheta \sin \vartheta \sqrt{\frac{1}{4\pi }}\cos \vartheta \sqrt{\frac{3}{4\pi }}\cos \vartheta }}=\frac{1}{\sqrt{3}} \\

& \Rightarrow {{d}_{13}}=\left\langle  200 \right|e{{{\hat{x}}}_{3}}\left| 210 \right\rangle =\frac{e}{\sqrt{3}}\int_{0}^{\infty }{{}}{{d}^{3}}r{{r}^{2}}\frac{2}{{{\left( 2{{a}_{0}} \right)}^{\frac{3}{2}}}}\left( 1-\frac{r}{2{{a}_{0}}} \right){{e}^{-\frac{r}{2{{a}_{0}}}}}r\frac{1}{\sqrt{3}{{\left( 2{{a}_{0}} \right)}^{\frac{3}{2}}}{{a}_{0}}}r{{e}^{-\frac{r}{2{{a}_{0}}}}}=-3e{{a}_{0}} \\

\end{align}

TeX (checked):

{\begin{aligned}&{{d}_{13}}=\left\langle 200\right|e{{\hat {x}}_{3}}\left|210\right\rangle \\&=e\int _{0}^{\infty }{}{{d}^{3}}r{{r}^{2}}{\frac {2}{{\left(2{{a}_{0}}\right)}^{\frac {3}{2}}}}\left(1-{\frac {r}{2{{a}_{0}}}}\right){{e}^{-{\frac {r}{2{{a}_{0}}}}}}r{\frac {1}{{\sqrt {3}}{{\left(2{{a}_{0}}\right)}^{\frac {3}{2}}}{{a}_{0}}}}r{{e}^{-{\frac {r}{2{{a}_{0}}}}}}\int _{0}^{2\pi }{d\phi \int _{0}^{\pi }{d\vartheta \sin \vartheta {\sqrt {\frac {1}{4\pi }}}\cos \vartheta {\sqrt {\frac {3}{4\pi }}}\cos \vartheta }}\\&{\frac {{{u}_{20}}(r)}{r}}={\frac {2}{{\left(2{{a}_{0}}\right)}^{\frac {3}{2}}}}\left(1-{\frac {r}{2{{a}_{0}}}}\right){{e}^{-{\frac {r}{2{{a}_{0}}}}}}\\&{\frac {{{u}_{21}}(r)}{r}}={\frac {1}{{\sqrt {3}}{{\left(2{{a}_{0}}\right)}^{\frac {3}{2}}}{{a}_{0}}}}r{{e}^{-{\frac {r}{2{{a}_{0}}}}}}\\&{\sqrt {\frac {1}{4\pi }}}={{Y}_{0}}^{0}\\&{\sqrt {\frac {3}{4\pi }}}\cos \vartheta ={{Y}_{1}}^{0}\\&\int _{0}^{2\pi }{d\phi \int _{0}^{\pi }{d\vartheta \sin \vartheta {\sqrt {\frac {1}{4\pi }}}\cos \vartheta {\sqrt {\frac {3}{4\pi }}}\cos \vartheta }}={\frac {1}{\sqrt {3}}}\\&\Rightarrow {{d}_{13}}=\left\langle 200\right|e{{\hat {x}}_{3}}\left|210\right\rangle ={\frac {e}{\sqrt {3}}}\int _{0}^{\infty }{}{{d}^{3}}r{{r}^{2}}{\frac {2}{{\left(2{{a}_{0}}\right)}^{\frac {3}{2}}}}\left(1-{\frac {r}{2{{a}_{0}}}}\right){{e}^{-{\frac {r}{2{{a}_{0}}}}}}r{\frac {1}{{\sqrt {3}}{{\left(2{{a}_{0}}\right)}^{\frac {3}{2}}}{{a}_{0}}}}r{{e}^{-{\frac {r}{2{{a}_{0}}}}}}=-3e{{a}_{0}}\\\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 (13.978 KB / 899 B) :

\begin{aligned} d_{13} = ⟨ 200 | e {\hat{x}}_{3} | 210 ⟩ \\ = e \int_{0}^{\infty} d^{3} r r^{2} \frac{2}{{(2 a_{0})}^{\frac{3}{2}}} (1 - \frac{r}{2 a_{0}}) e^{- \frac{r}{2 a_{0}}} r \frac{1}{\sqrt{3} {(2 a_{0})}^{\frac{3}{2}} a_{0}} r e^{- \frac{r}{2 a_{0}}} \int_{0}^{2 π} d ϕ \int_{0}^{π} d ϑ \sin ϑ \sqrt{\frac{1}{4 π}} \cos ϑ \sqrt{\frac{3}{4 π}} \cos ϑ \\ \frac{u_{20} (r)}{r} = \frac{2}{{(2 a_{0})}^{\frac{3}{2}}} (1 - \frac{r}{2 a_{0}}) e^{- \frac{r}{2 a_{0}}} \\ \frac{u_{21} (r)}{r} = \frac{1}{\sqrt{3} {(2 a_{0})}^{\frac{3}{2}} a_{0}} r e^{- \frac{r}{2 a_{0}}} \\ \sqrt{\frac{1}{4 π}} = {Y_{0}}^{0} \\ \sqrt{\frac{3}{4 π}} \cos ϑ = {Y_{1}}^{0} \\ \int_{0}^{2 π} d ϕ \int_{0}^{π} d ϑ \sin ϑ \sqrt{\frac{1}{4 π}} \cos ϑ \sqrt{\frac{3}{4 π}} \cos ϑ = \frac{1}{\sqrt{3}} \\ \Rightarrow d_{13} = ⟨ 200 | e {\hat{x}}_{3} | 210 ⟩ = \frac{e}{\sqrt{3}} \int_{0}^{\infty} d^{3} r r^{2} \frac{2}{{(2 a_{0})}^{\frac{3}{2}}} (1 - \frac{r}{2 a_{0}}) e^{- \frac{r}{2 a_{0}}} r \frac{1}{\sqrt{3} {(2 a_{0})}^{\frac{3}{2}} a_{0}} r e^{- \frac{r}{2 a_{0}}} = - 3 e a_{0} \end{aligned}

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msub><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>3</mn></mrow></mrow></msub><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mn>2</mn><mn>0</mn><mn>0</mn><mo data-mjx-texclass="CLOSE">|</mo></mrow><mi>e</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mn>2</mn><mn>1</mn><mn>0</mn><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mi>e</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mrow></msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mn>3</mn></msqrt></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mi>r</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mrow></msup><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>&#x03C0;</mi></mrow></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>&#x03D5;</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03C0;</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>&#x03D1;</mi><mi>sin</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>&#x03C0;</mi></mrow></mrow></mfrac></mrow></msqrt></mrow><mi>cos</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>&#x03C0;</mi></mrow></mrow></mfrac></mrow></msqrt></mrow><mi>cos</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>0</mn></mrow></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>1</mn></mrow></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mn>3</mn></msqrt></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mi>r</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>&#x03C0;</mi></mrow></mrow></mfrac></mrow></msqrt></mrow><mo>=</mo><msup><msub><mi>Y</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>&#x03C0;</mi></mrow></mrow></mfrac></mrow></msqrt></mrow><mi>cos</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi><mo>=</mo><msup><msub><mi>Y</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>&#x03C0;</mi></mrow></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>&#x03D5;</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03C0;</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>&#x03D1;</mi><mi>sin</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>&#x03C0;</mi></mrow></mrow></mfrac></mrow></msqrt></mrow><mi>cos</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>&#x03C0;</mi></mrow></mrow></mfrac></mrow></msqrt></mrow><mi>cos</mi><mo>&#x2061;</mo><mi>&#x03D1;</mi></mrow></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mn>3</mn></msqrt></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msub><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>3</mn></mrow></mrow></msub><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mn>2</mn><mn>0</mn><mn>0</mn><mo data-mjx-texclass="CLOSE">|</mo></mrow><mi>e</mi><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mn>2</mn><mn>1</mn><mn>0</mn><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mn>3</mn></msqrt></mrow></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">&#x221E;</mi></mrow></munderover></mstyle><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mrow></msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mn>3</mn></msqrt></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow><mi>r</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></mfrac></mrow></mrow></mrow></msup><mo>=</mo><mo>&#x2212;</mo><mn>3</mn><mi>e</mi><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$d_{13}$

$e$

${\hat{x}}_{3}$

$e$

$r$

$r$

$a_{0}$

$r$

$a_{0}$

$e$

$r$

$a_{0}$

$r$

$a_{0}$

$a_{0}$

$r$

$e$

$r$

$a_{0}$

$π$

$ϕ$

$π$

$ϑ$

$ϑ$

$π$

$ϑ$

$π$

$ϑ$

$u_{20}$

$r$

$r$

$a_{0}$

$r$

$a_{0}$

$e$

$r$

$a_{0}$

$u_{21}$

$r$

$r$

$a_{0}$

$a_{0}$

$r$

$e$

$r$

$a_{0}$

$π$

$Y_{0}$

$π$

$ϑ$

$Y_{1}$

$π$

$ϕ$

$π$

$ϑ$

$ϑ$

$π$

$ϑ$

$π$

$ϑ$

$d_{13}$

$e$

${\hat{x}}_{3}$

$e$

$r$

$r$

$a_{0}$

$r$

$a_{0}$

$e$

$r$

$a_{0}$

$r$

$a_{0}$

$a_{0}$

$r$

$e$

$r$

$a_{0}$

$e$

$a_{0}$

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