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Display information for equation id:math.1665.60 on revision:1665

* Page found: Drehimpuls- Eigenzustände (eq math.1665.60)

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TeX (original user input): 

\begin{align}

& 0={{{\hat{L}}}_{-}}{{{\hat{L}}}_{+}}\left| a,{{b}_{\max }} \right\rangle =\left( {{{\hat{L}}}^{2}}-{{{\hat{L}}}_{3}}^{2}-\hbar {{{\hat{L}}}_{3}} \right)\left| a,{{b}_{\max }} \right\rangle =\left( a-{{b}_{\max }}^{2}-\hbar {{b}_{\max }} \right)\left| a,{{b}_{\max }} \right\rangle  \\

& 0={{{\hat{L}}}_{+}}{{{\hat{L}}}_{-}}\left| a,{{b}_{\min }} \right\rangle =\left( {{{\hat{L}}}^{2}}-{{{\hat{L}}}_{3}}^{2}+\hbar {{{\hat{L}}}_{3}} \right)\left| a,{{b}_{\min }} \right\rangle =\left( a-{{b}_{\min }}^{2}+\hbar {{b}_{\min }} \right)\left| a,{{b}_{\min }} \right\rangle  \\

\end{align}

TeX (checked): 

{\begin{aligned}&0={{\hat {L}}_{-}}{{\hat {L}}_{+}}\left|a,{{b}_{\max }}\right\rangle =\left({{\hat {L}}^{2}}-{{\hat {L}}_{3}}^{2}-\hbar {{\hat {L}}_{3}}\right)\left|a,{{b}_{\max }}\right\rangle =\left(a-{{b}_{\max }}^{2}-\hbar {{b}_{\max }}\right)\left|a,{{b}_{\max }}\right\rangle \\&0={{\hat {L}}_{+}}{{\hat {L}}_{-}}\left|a,{{b}_{\min }}\right\rangle =\left({{\hat {L}}^{2}}-{{\hat {L}}_{3}}^{2}+\hbar {{\hat {L}}_{3}}\right)\left|a,{{b}_{\min }}\right\rangle =\left(a-{{b}_{\min }}^{2}+\hbar {{b}_{\min }}\right)\left|a,{{b}_{\min }}\right\rangle \\\end{aligned}}

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0=L̂−L̂+|a,bmax⟩=(L̂2−L̂32−ℏL̂3)|a,bmax⟩=(a−bmax2−ℏbmax)|a,bmax⟩0=L̂+L̂−|a,bmin⟩=(L̂2−L̂32+ℏL̂3)|a,bmin⟩=(a−bmin2+ℏbmin)|a,bmin⟩
<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"><mn>0</mn><mo stretchy="false">=</mo><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">−</mo></mrow></msub><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>max</mo></mrow></msub><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><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">−</mo><mi alternate="1">ℏ</mi><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>max</mo></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>a</mi><mo stretchy="false">−</mo><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>max</mo></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">−</mo><mi alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>max</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>max</mo></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"><mn>0</mn><mo stretchy="false">=</mo><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">−</mo></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><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><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mi alternate="1">ℏ</mi><msub><mover><mi>L</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>a</mi><mo stretchy="false">−</mo><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mi alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></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 Drehimpuls- Eigenzustände page

Identifiers

  • L̂−
  • L̂+
  • a
  • b
  • L̂
  • L̂3
  • L̂3
  • a
  • b
  • a
  • b
  • b
  • a
  • b
  • L̂+
  • L̂−
  • a
  • b
  • L̂
  • L̂3
  • L̂3
  • a
  • b
  • a
  • b
  • b
  • a
  • b

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