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Display information for equation id:math.1665.48 on revision:1665
* Page found: Drehimpuls- Eigenzustände (eq math.1665.48)
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Hash: 83ab29054be577642938fb3875e8764e
TeX (original user input):
\begin{align}
& {{{\hat{L}}}^{2}}{{{\hat{L}}}_{\pm }}\left| a,b \right\rangle ={{{\hat{L}}}_{\pm }}{{{\hat{L}}}^{2}}\left| a,b \right\rangle =a{{{\hat{L}}}_{\pm }}\left| a,b \right\rangle \\
& {{{\hat{L}}}_{3}}{{{\hat{L}}}_{\pm }}\left| a,b \right\rangle =\left( {{{\hat{L}}}_{\pm }}{{{\hat{L}}}_{3}}-\left[ {{{\hat{L}}}_{\pm }},{{{\hat{L}}}_{3}} \right] \right)\left| a,b \right\rangle \\
& \left[ {{{\hat{L}}}_{\pm }},{{{\hat{L}}}_{3}} \right]=\mp \hbar {{{\hat{L}}}_{\pm }} \\
& \to \left( {{{\hat{L}}}_{\pm }}{{{\hat{L}}}_{3}}-\left[ {{{\hat{L}}}_{\pm }},{{{\hat{L}}}_{3}} \right] \right)\left| a,b \right\rangle ={{{\hat{L}}}_{\pm }}\left( {{{\hat{L}}}_{3}}\pm \hbar \right)\left| a,b \right\rangle ={{{\hat{L}}}_{\pm }}\left( b\pm \hbar \right)\left| a,b \right\rangle \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\hat {L}}^{2}}{{\hat {L}}_{\pm }}\left|a,b\right\rangle ={{\hat {L}}_{\pm }}{{\hat {L}}^{2}}\left|a,b\right\rangle =a{{\hat {L}}_{\pm }}\left|a,b\right\rangle \\&{{\hat {L}}_{3}}{{\hat {L}}_{\pm }}\left|a,b\right\rangle =\left({{\hat {L}}_{\pm }}{{\hat {L}}_{3}}-\left[{{\hat {L}}_{\pm }},{{\hat {L}}_{3}}\right]\right)\left|a,b\right\rangle \\&\left[{{\hat {L}}_{\pm }},{{\hat {L}}_{3}}\right]=\mp \hbar {{\hat {L}}_{\pm }}\\&\to \left({{\hat {L}}_{\pm }}{{\hat {L}}_{3}}-\left[{{\hat {L}}_{\pm }},{{\hat {L}}_{3}}\right]\right)\left|a,b\right\rangle ={{\hat {L}}_{\pm }}\left({{\hat {L}}_{3}}\pm \hbar \right)\left|a,b\right\rangle ={{\hat {L}}_{\pm }}\left(b\pm \hbar \right)\left|a,b\right\rangle \\\end{aligned}}
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