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Display information for equation id:math.1667.56 on revision:1667
* Page found: Drehimpuls- Eigenzustände (eq math.1667.56)
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Hash: 9503dac3c2e1c3ba83997419b4369d67
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 \sqrt{a}\ge b\ge -\sqrt{a} \\
\end{align}
TeX (checked):
{\begin{aligned}&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 \geq 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 \geq \left\langle a,b\right|{{\hat {L}}_{3}}^{2}\left|a,b\right\rangle \geq 0\\&\left\langle a,b\right|{{\hat {L}}_{3}}^{2}\left|a,b\right\rangle ={{b}^{2}}\\&\to {\sqrt {a}}\geq b\geq -{\sqrt {a}}\\\end{aligned}}
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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><mrow data-mjx-texclass="ORD"><msqrt><mi>a</mi></msqrt></mrow><mo>≥</mo><mi>b</mi><mo>≥</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><msqrt><mi>a</mi></msqrt></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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