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Display information for equation id:math.1709.14 on revision:1709

* Page found: Addition von Drehimpulsen (eq math.1709.14)

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Hash: 2b0904e94e92afad9bf2cc6be07ecd1e

TeX (original user input): 

\begin{align}

& \left[ {{{\hat{J}}}^{2}},{{{\hat{L}}}^{2}} \right]=\left[ {{{\hat{L}}}^{2}}+{{{\hat{\bar{S}}}}^{2}}+2\hat{\bar{L}}\cdot \hat{\bar{S}},{{{\hat{L}}}^{2}} \right]=0 \\

& \left[ {{{\hat{J}}}^{2}},{{{\hat{\bar{S}}}}^{2}} \right]=\left[ {{{\hat{L}}}^{2}}+{{{\hat{\bar{S}}}}^{2}}+2\hat{\bar{L}}\cdot \hat{\bar{S}},{{{\hat{\bar{S}}}}^{2}} \right]=0 \\

& \left[ {{{\hat{J}}}_{3}},{{{\hat{L}}}^{2}} \right]=\left[ {{{\hat{L}}}_{3}}+{{{\hat{\bar{S}}}}_{3}},{{{\hat{L}}}^{2}} \right]=0 \\

& \left[ {{{\hat{J}}}_{3}},{{{\hat{\bar{S}}}}^{2}} \right]=\left[ {{{\hat{L}}}_{3}}+{{{\hat{\bar{S}}}}_{3}},{{{\hat{\bar{S}}}}^{2}} \right]=0 \\

\end{align}

TeX (checked): 

{\begin{aligned}&\left[{{\hat {J}}^{2}},{{\hat {L}}^{2}}\right]=\left[{{\hat {L}}^{2}}+{{\hat {\bar {S}}}^{2}}+2{\hat {\bar {L}}}\cdot {\hat {\bar {S}}},{{\hat {L}}^{2}}\right]=0\\&\left[{{\hat {J}}^{2}},{{\hat {\bar {S}}}^{2}}\right]=\left[{{\hat {L}}^{2}}+{{\hat {\bar {S}}}^{2}}+2{\hat {\bar {L}}}\cdot {\hat {\bar {S}}},{{\hat {\bar {S}}}^{2}}\right]=0\\&\left[{{\hat {J}}_{3}},{{\hat {L}}^{2}}\right]=\left[{{\hat {L}}_{3}}+{{\hat {\bar {S}}}_{3}},{{\hat {L}}^{2}}\right]=0\\&\left[{{\hat {J}}_{3}},{{\hat {\bar {S}}}^{2}}\right]=\left[{{\hat {L}}_{3}}+{{\hat {\bar {S}}}_{3}},{{\hat {\bar {S}}}^{2}}\right]=0\\\end{aligned}}

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[Ĵ2,L̂2]=[L̂2+S¯̂2+2L¯̂⋅S¯̂,L̂2]=0[Ĵ2,S¯̂2]=[L̂2+S¯̂2+2L¯̂⋅S¯̂,S¯̂2]=0[Ĵ3,L̂2]=[L̂3+S¯̂3,L̂2]=0[Ĵ3,S¯̂2]=[L̂3+S¯̂3,S¯̂2]=0
<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="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mover><mi>J</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>,</mo><msup><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mn>2</mn><mover><mover><mi>L</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mo stretchy="false">⋅</mo><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mo>,</mo><msup><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mover><mi>J</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>,</mo><msup><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mn>2</mn><mover><mover><mi>L</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mo stretchy="false">⋅</mo><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mo>,</mo><msup><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mover><mi>J</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>,</mo><msup><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo stretchy="false">+</mo><msub><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>,</mo><msup><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mover><mi>J</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>,</mo><msup><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo stretchy="false">+</mo><msub><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo>,</mo><msup><mover><mover><mi>S</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Addition von Drehimpulsen page

Identifiers

  • Ĵ
  • L̂
  • L̂
  • S¯̂
  • L¯̂
  • S¯̂
  • L̂
  • Ĵ
  • S¯̂
  • L̂
  • S¯̂
  • L¯̂
  • S¯̂
  • S¯̂
  • Ĵ3
  • L̂
  • L̂3
  • S¯̂3
  • L̂
  • Ĵ3
  • S¯̂
  • L̂3
  • S¯̂3
  • S¯̂

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