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Display information for equation id:math.1667.39 on revision:1667
* Page found: Drehimpuls- Eigenzustände (eq math.1667.39)
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Hash: fdff6b4e5c50821b914cd1fd86d3cefa
TeX (original user input):
\begin{align}
& a=\left\langle a,b \right|{{{\hat{L}}}^{2}}\left| a,b \right\rangle =\sum\limits_{i=1}^{3}{{}}\left\langle a,b \right|{{{\hat{L}}}_{i}}^{+}{{{\hat{L}}}_{i}}\left| a,b \right\rangle \\
& \left\langle a,b \right|{{{\hat{L}}}_{i}}^{+}{{{\hat{L}}}_{i}}\left| a,b \right\rangle :=\left\langle \Phi | \Phi \right\rangle \ge 0 \\
& a=\left\langle a,b \right|{{{\hat{L}}}^{2}}\left| a,b \right\rangle =\sum\limits_{i=1}^{3}{{}}\left\langle a,b \right|{{{\hat{L}}}_{i}}^{+}{{{\hat{L}}}_{i}}\left| a,b \right\rangle \ge \left\langle a,b \right|{{{\hat{L}}}_{3}}^{2}\left| a,b \right\rangle \ge 0 \\
& \left\langle a,b \right|{{{\hat{L}}}_{3}}^{2}\left| a,b \right\rangle ={{b}^{2}} \\
& \to a\ge {{b}^{2}}\ge 0 \\
\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><mi>a</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></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"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mo>+</mo></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"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></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"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mo>+</mo></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"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mi>:</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi mathvariant="normal">Φ</mi><mo>|</mo><mi mathvariant="normal">Φ</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>≥</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mi>a</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></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"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mo>+</mo></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"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><mi>b</mi><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><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></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"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>≥</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">|</mo></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"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><msup><mi>b</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo accent="false">→</mo><mi>a</mi><mo>≥</mo><msup><mi>b</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>≥</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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