Jump to navigation
Jump to search
General
Display information for equation id:math.1825.8 on revision:1825
* Page found: Das Wasserstoffatom (relativistsich) (eq math.1825.8)
(force rerendering)Occurrences on the following pages:
Hash: 08590875f759189c5f0b3c2135f83bea
TeX (original user input):
\begin{align}
& {{\left( \hbar Q \right)}^{2}}=\beta \left( \tilde{\bar{\sigma }}\bar{L}+\hbar \right)\beta \left( \tilde{\bar{\sigma }}\bar{L}+\hbar \right)={{\beta }^{2}}{{\left( \tilde{\bar{\sigma }}\bar{L}+\hbar \right)}^{2}} \\
& \left[ \beta ,\tilde{\bar{\sigma }} \right]=0=\left( \begin{matrix}
\left[ 1,\tilde{\bar{\sigma }} \right] & {} \\
{} & -\left[ 1,\tilde{\bar{\sigma }} \right] \\
\end{matrix} \right) \\
& {{\beta }^{2}}=1 \\
& \Rightarrow {{\left( \hbar Q \right)}^{2}}=\left( \tilde{\bar{\sigma }}\bar{L} \right)\left( \tilde{\bar{\sigma }}\bar{L} \right)+2\hbar \left( \tilde{\bar{\sigma }}\bar{L} \right)+{{\hbar }^{2}} \\
& \left( \tilde{\bar{\sigma }}\bar{L} \right)\left( \tilde{\bar{\sigma }}\bar{L} \right)={{L}^{2}}+i\tilde{\bar{\sigma }}\left( \bar{L}\times \bar{L} \right) \\
& \left( \bar{L}\times \bar{L} \right)=i\hbar \bar{L} \\
& \Rightarrow \left( \tilde{\bar{\sigma }}\bar{L} \right)\left( \tilde{\bar{\sigma }}\bar{L} \right)={{L}^{2}}-\hbar \tilde{\bar{\sigma }}(\bar{L}) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\left(\hbar Q\right)}^{2}}=\beta \left({\tilde {\bar {\sigma }}}{\bar {L}}+\hbar \right)\beta \left({\tilde {\bar {\sigma }}}{\bar {L}}+\hbar \right)={{\beta }^{2}}{{\left({\tilde {\bar {\sigma }}}{\bar {L}}+\hbar \right)}^{2}}\\&\left[\beta ,{\tilde {\bar {\sigma }}}\right]=0=\left({\begin{matrix}\left[1,{\tilde {\bar {\sigma }}}\right]&{}\\{}&-\left[1,{\tilde {\bar {\sigma }}}\right]\\\end{matrix}}\right)\\&{{\beta }^{2}}=1\\&\Rightarrow {{\left(\hbar Q\right)}^{2}}=\left({\tilde {\bar {\sigma }}}{\bar {L}}\right)\left({\tilde {\bar {\sigma }}}{\bar {L}}\right)+2\hbar \left({\tilde {\bar {\sigma }}}{\bar {L}}\right)+{{\hbar }^{2}}\\&\left({\tilde {\bar {\sigma }}}{\bar {L}}\right)\left({\tilde {\bar {\sigma }}}{\bar {L}}\right)={{L}^{2}}+i{\tilde {\bar {\sigma }}}\left({\bar {L}}\times {\bar {L}}\right)\\&\left({\bar {L}}\times {\bar {L}}\right)=i\hbar {\bar {L}}\\&\Rightarrow \left({\tilde {\bar {\sigma }}}{\bar {L}}\right)\left({\tilde {\bar {\sigma }}}{\bar {L}}\right)={{L}^{2}}-\hbar {\tilde {\bar {\sigma }}}({\bar {L}})\\\end{aligned}}
LaTeXML (experimental; uses MathML) rendering
MathML (0 B / 8 B) :
SVG image empty. Force Re-Rendering
SVG (0 B / 8 B) :
MathML (experimental; no images) rendering
MathML (8.97 KB / 653 B) :
<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><mi data-mjx-alternate="1">ℏ</mi><mi>Q</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mi>β</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>β</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mi>β</mi><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><mn>0</mn><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd><mtd></mtd></mtr><mtr><mtd></mtd><mtd><mo>−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>β</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi data-mjx-alternate="1">ℏ</mi><mi>Q</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mn>2</mn><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><mi>L</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>i</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo>×</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo>×</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><mi>L</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>σ</mi><mo>¯</mo></mover></mrow></mrow><mo>~</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo></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
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results