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Display information for equation id:math.1666.48 on revision:1666

* Page found: Drehimpuls- Eigenzustände (eq math.1666.48)

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Drehimpuls- Eigenzustände Eq: math.1667.48

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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\begin{matrix} {\hat{L}}^{2} {\hat{L}}_{\pm} | a, b ⟩ = {\hat{L}}_{\pm} {\hat{L}}^{2} | a, b ⟩ = a {\hat{L}}_{\pm} | a, b ⟩ \\ {\hat{L}}_{3} {\hat{L}}_{\pm} | a, b ⟩ = ({\hat{L}}_{\pm} {\hat{L}}_{3} - [{\hat{L}}_{\pm}, {\hat{L}}_{3}]) | a, b ⟩ \\ [{\hat{L}}_{\pm}, {\hat{L}}_{3}] = \mp ℏ {\hat{L}}_{\pm} \\ \to ({\hat{L}}_{\pm} {\hat{L}}_{3} - [{\hat{L}}_{\pm}, {\hat{L}}_{3}]) | a, b ⟩ = {\hat{L}}_{\pm} ({\hat{L}}_{3} \pm ℏ) | a, b ⟩ = {\hat{L}}_{\pm} (b \pm ℏ) | a, b ⟩ \end{matrix}

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Identifiers

$\hat{L}$

$\hat{L}$

$a$

$b$

$\hat{L}$

$\hat{L}$

$a$

$b$

$a$

$\hat{L}$

$a$

$b$

${\hat{L}}_{3}$

$\hat{L}$

$a$

$b$

$\hat{L}$

${\hat{L}}_{3}$

$\hat{L}$

${\hat{L}}_{3}$

$a$

$b$

$\hat{L}$

${\hat{L}}_{3}$

$\hat{L}$

$\hat{L}$

${\hat{L}}_{3}$

$\hat{L}$

${\hat{L}}_{3}$

$a$

$b$

$\hat{L}$

${\hat{L}}_{3}$

$a$

$b$

$\hat{L}$

$b$

$a$

$b$

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