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Display information for equation id:math.1713.2 on revision:1713

* Page found: Addition von Drehimpulsen (eq math.1713.2)

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TeX (original user input): 

\begin{align}

& \Rightarrow \left[ {{{\hat{J}}}_{j}},{{{\hat{J}}}_{k}} \right]=\left[ {{{\hat{L}}}_{j}},{{{\hat{L}}}_{k}} \right]+\left[ {{{\hat{S}}}_{j}},{{{\hat{S}}}_{k}} \right] \\

& \left[ {{{\hat{L}}}_{j}},{{{\hat{L}}}_{k}} \right]=i\hbar {{\varepsilon }_{jkl}}{{{\hat{L}}}_{l}} \\

& \left[ {{{\hat{S}}}_{j}},{{{\hat{S}}}_{k}} \right]=i\hbar {{\varepsilon }_{jkl}}{{{\hat{S}}}_{l}} \\

& \Rightarrow \left[ {{{\hat{J}}}_{j}},{{{\hat{J}}}_{k}} \right]=i\hbar {{\varepsilon }_{jkl}}{{{\hat{J}}}_{l}} \\

\end{align}

TeX (checked): 

{\begin{aligned}&\Rightarrow \left[{{\hat {J}}_{j}},{{\hat {J}}_{k}}\right]=\left[{{\hat {L}}_{j}},{{\hat {L}}_{k}}\right]+\left[{{\hat {S}}_{j}},{{\hat {S}}_{k}}\right]\\&\left[{{\hat {L}}_{j}},{{\hat {L}}_{k}}\right]=i\hbar {{\varepsilon }_{jkl}}{{\hat {L}}_{l}}\\&\left[{{\hat {S}}_{j}},{{\hat {S}}_{k}}\right]=i\hbar {{\varepsilon }_{jkl}}{{\hat {S}}_{l}}\\&\Rightarrow \left[{{\hat {J}}_{j}},{{\hat {J}}_{k}}\right]=i\hbar {{\varepsilon }_{jkl}}{{\hat {J}}_{l}}\\\end{aligned}}

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⇒[Ĵj,Ĵk]=[L̂j,L̂k]+[Ŝj,Ŝk][L̂j,L̂k]=iℏεjklL̂l[Ŝj,Ŝk]=iℏεjklŜl⇒[Ĵj,Ĵk]=iℏεjklĴl
<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"><mo stretchy="false">⇒</mo><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"><mi>j</mi></mrow></msub><mo>,</mo><msub><mover><mi>J</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><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"><mi>j</mi></mrow></msub><mo>,</mo><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><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>S</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>,</mo><msub><mover><mi>S</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow></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>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>,</mo><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mi>i</mi><mi alternate="1">ℏ</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mi>k</mi><mi>l</mi></mrow></mrow></msub><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub></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>S</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>,</mo><msub><mover><mi>S</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mi>i</mi><mi alternate="1">ℏ</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mi>k</mi><mi>l</mi></mrow></mrow></msub><msub><mover><mi>S</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><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"><mi>j</mi></mrow></msub><mo>,</mo><msub><mover><mi>J</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">=</mo><mi>i</mi><mi alternate="1">ℏ</mi><msub><mi>ε</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mi>k</mi><mi>l</mi></mrow></mrow></msub><msub><mover><mi>J</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub></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

  • Ĵj
  • Ĵk
  • L̂j
  • L̂k
  • Ŝj
  • Ŝk
  • L̂j
  • L̂k
  • i
  • εjkl
  • L̂l
  • Ŝj
  • Ŝk
  • i
  • εjkl
  • Ŝl
  • Ĵj
  • Ĵk
  • i
  • εjkl
  • Ĵl

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