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Display information for equation id:math.1667.60 on revision:1667
* Page found: Drehimpuls- Eigenzustände (eq math.1667.60)
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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}
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<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><mn>0</mn><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"><mo>−</mo></mrow></msub><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><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"><mi>max</mi></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="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><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"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><mi data-mjx-alternate="1">ℏ</mi><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><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>max</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>a</mi><mo>−</mo><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>max</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><mi data-mjx-alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>max</mi></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"><mi>max</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mn>0</mn><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"><mo>+</mo></mrow></msub><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><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"><mi>min</mi></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="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><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"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><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><mi>a</mi><mo>,</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>a</mi><mo>−</mo><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></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"><mi>min</mi></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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