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Display information for equation id:math.1661.39 on revision:1661
* Page found: Der harmonische Oszillator (eq math.1661.39)
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Hash: 6470d70d1b788a905744e6ecd503caac
TeX (original user input):
\hat{H}{{a}^{+}}\left| 0 \right\rangle =\left( {{a}^{+}}H+\hbar \omega {{a}^{+}} \right)\left| 0 \right\rangle ={{a}^{+}}\left( \hat{H}+\hbar \omega \right)\left| 0 \right\rangle ={{a}^{+}}\left( \frac{\hbar \omega }{2}+\hbar \omega \right)\left| 0 \right\rangle =\frac{3\hbar \omega }{2}{{a}^{+}}\left| 0 \right\rangle
TeX (checked):
{\hat {H}}{{a}^{+}}\left|0\right\rangle =\left({{a}^{+}}H+\hbar \omega {{a}^{+}}\right)\left|0\right\rangle ={{a}^{+}}\left({\hat {H}}+\hbar \omega \right)\left|0\right\rangle ={{a}^{+}}\left({\frac {\hbar \omega }{2}}+\hbar \omega \right)\left|0\right\rangle ={\frac {3\hbar \omega }{2}}{{a}^{+}}\left|0\right\rangle
LaTeXML (experimentell; verwendet MathML) rendering
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MathML (experimentell; keine Bilder) rendering
MathML (2.437 KB / 355 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"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mi>H</mi><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mn>0</mn><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="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mn>0</mn><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="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>3</mn><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mn>0</mn><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mstyle></mrow></math>
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