Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.1826.74 on revision:1826

* Page found: Das Wasserstoffatom (relativistsich) (eq math.1826.74)

(force rerendering)

Occurrences on the following pages:

Hash: dc0b2dcec3e86d4d87b507508e827e70

TeX (original user input): 

\begin{align}

& {{\left( \frac{1}{\lambda +n\acute{\ }} \right)}^{2}}=\frac{1}{{{\left[ n\acute{\ }+|q|-\frac{1}{2}\left( \frac{{{\gamma }^{2}}}{\left| q \right|} \right) \right]}^{2}}}+O\left( {{\gamma }^{4}} \right) \\
& n=n\acute{\ }+\left| q \right| \\
& n\acute{\ }=0,1,2,... \\
& \left| q \right|=j+\frac{1}{2}=1,2,.... \\
& {{\left( \frac{1}{\lambda +n\acute{\ }} \right)}^{2}}=\frac{1}{{{n}^{2}}}{{\left[ 1-\frac{1}{2}\left( \frac{{{\gamma }^{2}}}{\left| q \right|n} \right) \right]}^{-2}}+O\left( {{\gamma }^{4}} \right)=\frac{1}{{{n}^{2}}}\left[ 1+\left( \frac{{{\gamma }^{2}}}{\left| q \right|n} \right) \right]+O\left( {{\gamma }^{4}} \right)=\frac{1}{{{n}^{2}}}+\left( \frac{{{\gamma }^{2}}}{\left| q \right|{{n}^{3}}} \right)+O\left( {{\gamma }^{4}} \right) \\
& \left| q \right|=j+\frac{1}{2}=l\pm s+\frac{1}{2} \\
\end{align}

TeX (checked): 

{\begin{aligned}&{{\left({\frac {1}{\lambda +n{\acute {\ }}}}\right)}^{2}}={\frac {1}{{\left[n{\acute {\ }}+|q|-{\frac {1}{2}}\left({\frac {{\gamma }^{2}}{\left|q\right|}}\right)\right]}^{2}}}+O\left({{\gamma }^{4}}\right)\\&n=n{\acute {\ }}+\left|q\right|\\&n{\acute {\ }}=0,1,2,...\\&\left|q\right|=j+{\frac {1}{2}}=1,2,....\\&{{\left({\frac {1}{\lambda +n{\acute {\ }}}}\right)}^{2}}={\frac {1}{{n}^{2}}}{{\left[1-{\frac {1}{2}}\left({\frac {{\gamma }^{2}}{\left|q\right|n}}\right)\right]}^{-2}}+O\left({{\gamma }^{4}}\right)={\frac {1}{{n}^{2}}}\left[1+\left({\frac {{\gamma }^{2}}{\left|q\right|n}}\right)\right]+O\left({{\gamma }^{4}}\right)={\frac {1}{{n}^{2}}}+\left({\frac {{\gamma }^{2}}{\left|q\right|{{n}^{3}}}}\right)+O\left({{\gamma }^{4}}\right)\\&\left|q\right|=j+{\frac {1}{2}}=l\pm s+{\frac {1}{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 (7.59 KB / 640 B) :

(1λ+n´)2=1[n´+|q|−12(γ2|q|)]2+O(γ4)n=n´+|q|n´=0,1,2,...|q|=j+12=1,2,....(1λ+n´)2=1n2[1−12(γ2|q|n)]−2+O(γ4)=1n2[1+(γ2|q|n)]+O(γ4)=1n2+(γ2|q|n3)+O(γ4)|q|=j+12=l±s+12
<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><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</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"><mi>&#x03BB;</mi><mo>+</mo><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>+</mo><mo>|</mo><mi>q</mi><mo>|</mo><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>+</mo><mi>O</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>n</mi><mo>=</mo><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>=</mo><mi>j</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo></mtd></mtr><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</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"><mi>&#x03BB;</mi><mo>+</mo><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><msup><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"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mi>n</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mn>2</mn></mrow></mrow></msup><mo>+</mo><mi>O</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mi>n</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>+</mo><mi>O</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mi>O</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>&#x03B3;</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>q</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>=</mo><mi>j</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo>=</mo><mi>l</mi><mo>&#x00B1;</mo><mi>s</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></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:

Similar pages

Calculated based on the variables occurring on the entire Das Wasserstoffatom (relativistsich) page

Identifiers

  • λ
  • n
  • ´
  • n
  • ´
  • q
  • γ
  • q
  • O
  • γ
  • n
  • n
  • ´
  • q
  • n
  • ´
  • q
  • j
  • λ
  • n
  • ´
  • n
  • γ
  • q
  • n
  • O
  • γ
  • n
  • γ
  • q
  • n
  • O
  • γ
  • n
  • γ
  • q
  • n
  • O
  • γ
  • q
  • j
  • l
  • s

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“