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Display information for equation id:math.1661.50 on revision:1661

* Page found: Der harmonische Oszillator (eq math.1661.50)

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TeX (original user input): 

\begin{align}

& 1=!=\left\langle  n | n \right\rangle ={{\left| {{\alpha }_{n}} \right|}^{2}}\left\langle  0 \right|{{a}^{n}}{{\left( {{a}^{+}} \right)}^{n}}\left| 0 \right\rangle  \\
& \left\langle  0 \right|{{a}^{n}}{{\left( {{a}^{+}} \right)}^{n}}\left| 0 \right\rangle =\left\langle  0 \right|{{a}^{n-1}}\left( {{\left( {{a}^{+}} \right)}^{n}}a+\left[ a,{{\left( {{a}^{+}} \right)}^{n}} \right] \right)\left| 0 \right\rangle  \\
\end{align}

TeX (checked): 

{\begin{aligned}&1=!=\left\langle n|n\right\rangle ={{\left|{{\alpha }_{n}}\right|}^{2}}\left\langle 0\right|{{a}^{n}}{{\left({{a}^{+}}\right)}^{n}}\left|0\right\rangle \\&\left\langle 0\right|{{a}^{n}}{{\left({{a}^{+}}\right)}^{n}}\left|0\right\rangle =\left\langle 0\right|{{a}^{n-1}}\left({{\left({{a}^{+}}\right)}^{n}}a+\left[a,{{\left({{a}^{+}}\right)}^{n}}\right]\right)\left|0\right\rangle \\\end{aligned}}

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1=!=⟨n|n⟩=|αn|2⟨0|an(a+)n|0⟩⟨0|an(a+)n|0⟩=⟨0|an−1((a+)na+[a,(a+)n])|0⟩
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  • αn
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