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Display information for equation id:math.1661.62 on revision:1661
* Page found: Der harmonische Oszillator (eq math.1661.62)
(force rerendering)Occurrences on the following pages:
Hash: 2d8d24a3366391aa7ae0055bcbb1c2e7
TeX (original user input):
\begin{align}
& N:={{a}^{+}}a \\
& N\left| n \right\rangle ={{a}^{+}}a\left| n \right\rangle ={{a}^{+}}\sqrt{n}\left| n-1 \right\rangle =\sqrt{n}\sqrt{n}\left| n \right\rangle =n\left| n \right\rangle \\
\end{align}
TeX (checked):
{\begin{aligned}&N:={{a}^{+}}a\\&N\left|n\right\rangle ={{a}^{+}}a\left|n\right\rangle ={{a}^{+}}{\sqrt {n}}\left|n-1\right\rangle ={\sqrt {n}}{\sqrt {n}}\left|n\right\rangle =n\left|n\right\rangle \\\end{aligned}}
LaTeXML (experimentell; verwendet MathML) rendering
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MathML (experimentell; keine Bilder) rendering
MathML (1.619 KB / 351 B) :
<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>N</mi><mi>:</mi><mo>=</mo><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mi>a</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>N</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mi>a</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mrow data-mjx-texclass="ORD"><msqrt><mi>n</mi></msqrt></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><msqrt><mi>n</mi></msqrt></mrow><mrow data-mjx-texclass="ORD"><msqrt><mi>n</mi></msqrt></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mi>n</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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