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Display information for equation id:math.1661.6 on revision:1661
* Page found: Der harmonische Oszillator (eq math.1661.6)
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Hash: 0e67a230153ffa813594f85b6b06f738
TeX (original user input):
\hat{H}=\frac{1}{2}\hbar \omega \left( a{{a}^{+}}+{{a}^{+}}a \right)=\frac{1}{2}\hbar \omega \left( {{a}^{+}}a+1+{{a}^{+}}a \right)=\hbar \omega \left( {{a}^{+}}a+\frac{1}{2} \right)
TeX (checked):
{\hat {H}}={\frac {1}{2}}\hbar \omega \left(a{{a}^{+}}+{{a}^{+}}a\right)={\frac {1}{2}}\hbar \omega \left({{a}^{+}}a+1+{{a}^{+}}a\right)=\hbar \omega \left({{a}^{+}}a+{\frac {1}{2}}\right)
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MathML (1.659 KB / 317 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><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>a</mi><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mo>+</mo><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mi>a</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi><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>a</mi><mo>+</mo><mn>1</mn><mo>+</mo><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mi>a</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi data-mjx-alternate="1">ℏ</mi><mi>ω</mi><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>a</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>
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