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Display information for equation id:math.1661.52 on revision:1661
* Page found: Der harmonische Oszillator (eq math.1661.52)
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TeX (original user input):
\begin{align}
& \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 =\left\langle 0 \right|{{a}^{n-1}}{{\left( {{a}^{+}} \right)}^{n}}a\left| 0 \right\rangle +n\left\langle 0 \right|{{a}^{n-1}}{{\left( {{a}^{+}} \right)}^{n-1}}\left| 0 \right\rangle \\
& \left\langle 0 \right|{{a}^{n-1}}{{\left( {{a}^{+}} \right)}^{n}}a\left| 0 \right\rangle =0 \\
& \Rightarrow n\left\langle 0 \right|{{a}^{n-1}}{{\left( {{a}^{+}} \right)}^{n-1}}a\left| 0 \right\rangle =n\left( n-1 \right)\left\langle 0 \right|{{a}^{n-2}}{{\left( {{a}^{+}} \right)}^{n-2}}a\left| 0 \right\rangle \Rightarrow ...\Rightarrow \\
\end{align}
TeX (checked):
{\begin{aligned}&\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 =\left\langle 0\right|{{a}^{n-1}}{{\left({{a}^{+}}\right)}^{n}}a\left|0\right\rangle +n\left\langle 0\right|{{a}^{n-1}}{{\left({{a}^{+}}\right)}^{n-1}}\left|0\right\rangle \\&\left\langle 0\right|{{a}^{n-1}}{{\left({{a}^{+}}\right)}^{n}}a\left|0\right\rangle =0\\&\Rightarrow n\left\langle 0\right|{{a}^{n-1}}{{\left({{a}^{+}}\right)}^{n-1}}a\left|0\right\rangle =n\left(n-1\right)\left\langle 0\right|{{a}^{n-2}}{{\left({{a}^{+}}\right)}^{n-2}}a\left|0\right\rangle \Rightarrow ...\Rightarrow \\\end{aligned}}
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