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Display information for equation id:math.1655.61 on revision:1655
* Page found: Der harmonische Oszillator (eq math.1655.61)
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Hash: 1eb1f37f28998f9b864478ddd712b9c6
TeX (original user input):
\begin{align}
& a\left| n \right\rangle =\frac{1}{\sqrt{n!}}a{{\left( {{a}^{+}} \right)}^{n}}\left| 0 \right\rangle =\frac{1}{\sqrt{n!}}\left\{ {{\left( {{a}^{+}} \right)}^{n}}a+\left[ a,{{\left( {{a}^{+}} \right)}^{n}} \right] \right\}\left| 0 \right\rangle =\frac{1}{\sqrt{n!}}n{{\left( {{a}^{+}} \right)}^{n-1}}\left| 0 \right\rangle =\sqrt{n}\left| n-1 \right\rangle \\
& {{a}^{+}}\left| n \right\rangle =\frac{1}{\sqrt{n!}}{{\left( {{a}^{+}} \right)}^{n+1}}\left| 0 \right\rangle =\sqrt{n+1}\left| n+1 \right\rangle \\
\end{align}
TeX (checked):
{\begin{aligned}&a\left|n\right\rangle ={\frac {1}{\sqrt {n!}}}a{{\left({{a}^{+}}\right)}^{n}}\left|0\right\rangle ={\frac {1}{\sqrt {n!}}}\left\{{{\left({{a}^{+}}\right)}^{n}}a+\left[a,{{\left({{a}^{+}}\right)}^{n}}\right]\right\}\left|0\right\rangle ={\frac {1}{\sqrt {n!}}}n{{\left({{a}^{+}}\right)}^{n-1}}\left|0\right\rangle ={\sqrt {n}}\left|n-1\right\rangle \\&{{a}^{+}}\left|n\right\rangle ={\frac {1}{\sqrt {n!}}}{{\left({{a}^{+}}\right)}^{n+1}}\left|0\right\rangle ={\sqrt {n+1}}\left|n+1\right\rangle \\\end{aligned}}
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