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Display information for equation id:math.1653.10 on revision:1653
* Page found: Der harmonische Oszillator (eq math.1653.10)
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Hash: 9c15cc805ed8ce86fb051fa5fb291858
TeX (original user input):
\begin{align}
& \left( a{{a}^{+}} \right)a=\frac{1}{\hbar \omega }\hat{H}a+\frac{1}{2}a \\
& =a\left( {{a}^{+}}a \right)=\frac{1}{\hbar \omega }a\hat{H}-\frac{1}{2}a \\
& \Rightarrow \left[ a,\hat{H} \right]=a\hat{H}-\hat{H}a=\hbar \omega a \\
\end{align}
TeX (checked):
{\begin{aligned}&\left(a{{a}^{+}}\right)a={\frac {1}{\hbar \omega }}{\hat {H}}a+{\frac {1}{2}}a\\&=a\left({{a}^{+}}a\right)={\frac {1}{\hbar \omega }}a{\hat {H}}-{\frac {1}{2}}a\\&\Rightarrow \left[a,{\hat {H}}\right]=a{\hat {H}}-{\hat {H}}a=\hbar \omega a\\\end{aligned}}
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MathML (2.527 KB / 452 B) :
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