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Display information for equation id:math.1667.19 on revision:1667

* Page found: Drehimpuls- Eigenzustände (eq math.1667.19)

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Hash: d5636e2e9013cf2480413016f1d03837

TeX (original user input): 

\left[ {{\left( {{{\hat{L}}}_{+}} \right)}^{n+1}},{{{\hat{L}}}_{3}} \right]={{\left( {{{\hat{L}}}_{+}} \right)}^{n}}\left[ \left( {{{\hat{L}}}_{+}} \right),{{{\hat{L}}}_{3}} \right]+\left[ {{\left( {{{\hat{L}}}_{+}} \right)}^{n}},{{{\hat{L}}}_{3}} \right]\left( {{{\hat{L}}}_{+}} \right)={{\left( {{{\hat{L}}}_{+}} \right)}^{n}}\left( -\hbar \left( {{{\hat{L}}}_{+}} \right) \right)-n\hbar {{\left( {{{\hat{L}}}_{+}} \right)}^{n}}{{\hat{L}}_{+}}=-(n+1)\hbar {{\left( {{{\hat{L}}}_{+}} \right)}^{n+1}}

TeX (checked): 

\left[{{\left({{\hat {L}}_{+}}\right)}^{n+1}},{{\hat {L}}_{3}}\right]={{\left({{\hat {L}}_{+}}\right)}^{n}}\left[\left({{\hat {L}}_{+}}\right),{{\hat {L}}_{3}}\right]+\left[{{\left({{\hat {L}}_{+}}\right)}^{n}},{{\hat {L}}_{3}}\right]\left({{\hat {L}}_{+}}\right)={{\left({{\hat {L}}_{+}}\right)}^{n}}\left(-\hbar \left({{\hat {L}}_{+}}\right)\right)-n\hbar {{\left({{\hat {L}}_{+}}\right)}^{n}}{{\hat {L}}_{+}}=-(n+1)\hbar {{\left({{\hat {L}}_{+}}\right)}^{n+1}}

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[(L^+)n+1,L^3]=(L^+)n[(L^+),L^3]+[(L^+)n,L^3](L^+)=(L^+)n(−ℏ(L^+))−nℏ(L^+)nL^+=−(n+1)ℏ(L^+)n+1
<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="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mrow></msup><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><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><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2212;</mo><mi>n</mi><mi data-mjx-alternate="1">&#x210F;</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo>=</mo><mo>&#x2212;</mo><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi data-mjx-alternate="1">&#x210F;</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mrow></msup></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Drehimpuls- Eigenzustände page

Identifiers

  • L^+
  • n
  • L^3
  • L^+
  • n
  • L^+
  • L^3
  • L^+
  • n
  • L^3
  • L^+
  • L^+
  • n
  • L^+
  • n
  • L^+
  • n
  • L^+
  • n
  • L^+
  • n

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