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Display information for equation id:math.1714.15 on revision:1714

* Page found: Addition von Drehimpulsen (eq math.1714.15)

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TeX (original user input): 

\begin{align}

& {{{\hat{J}}}^{2}}\left| j{{m}_{j}}ls \right\rangle ={{\hbar }^{2}}(j(j+1))\left| j{{m}_{j}}ls \right\rangle  \\

& {{{\hat{J}}}_{3}}\left| j{{m}_{j}}ls \right\rangle =\hbar {{m}_{j}}\left| j{{m}_{j}}ls \right\rangle  \\

& {{{\hat{L}}}^{2}}\left| j{{m}_{j}}ls \right\rangle ={{\hbar }^{2}}(l(l+1)\left| j{{m}_{j}}ls \right\rangle  \\

& {{{\hat{\bar{S}}}}^{2}}\left| j{{m}_{j}}ls \right\rangle ={{\hbar }^{2}}(s(s+1)\left| j{{m}_{j}}ls \right\rangle  \\

\end{align}

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J ^ 2 ⁢ | j ⁢ m j ⁢ l ⁢ s ⟩ = ℏ 2 ⁢ ( j ⁢ ( j + 1 ) ) ⁢ | j ⁢ m j ⁢ l ⁢ s ⟩ J ^ 3 ⁢ | j ⁢ m j ⁢ l ⁢ s ⟩ = ℏ ⁢ m j ⁢ | j ⁢ m j ⁢ l ⁢ s ⟩ L ^ 2 | j m j l s ⟩ = ℏ 2 ( l ( l + 1 ) | j m j l s ⟩ S ¯ ^ 2 | j m j l s ⟩ = ℏ 2 ( s ( s + 1 ) | j m j l s ⟩ absent superscript ^ 𝐽 2 ket 𝑗 subscript 𝑚 𝑗 𝑙 𝑠 superscript Planck-constant-over-2-pi 2 𝑗 𝑗 1 ket 𝑗 subscript 𝑚 𝑗 𝑙 𝑠 absent subscript ^ 𝐽 3 ket 𝑗 subscript 𝑚 𝑗 𝑙 𝑠 Planck-constant-over-2-pi subscript 𝑚 𝑗 ket 𝑗 subscript 𝑚 𝑗 𝑙 𝑠 absent fragments superscript ^ 𝐿 2 | j subscript 𝑚 𝑗 l s ⟩ Planck-constant-over-2-pi 2 ( l fragments ( l 1 ) | j subscript 𝑚 𝑗 l s ⟩ absent fragments superscript ^ ¯ 𝑆 2 | j subscript 𝑚 𝑗 l s ⟩ Planck-constant-over-2-pi 2 ( s fragments ( s 1 ) | j subscript 𝑚 𝑗 l s ⟩ {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle{{{\hat{J}}}^{2}% }\left|j{{m}_{j}}ls\right\rangle={{\hbar}^{2}}(j(j+1))\left|j{{m}_{j}}ls\right% \rangle\\ \par&\displaystyle{{{\hat{J}}}_{3}}\left|j{{m}_{j}}ls\right\rangle=\hbar{{m}_{% j}}\left|j{{m}_{j}}ls\right\rangle\\ \par&\displaystyle{{{\hat{L}}}^{2}}\left|j{{m}_{j}}ls\right\rangle={{\hbar}^{2% }}(l(l+1)\left|j{{m}_{j}}ls\right\rangle\\ \par&\displaystyle{{{\hat{\bar{S}}}}^{2}}\left|j{{m}_{j}}ls\right\rangle={{% \hbar}^{2}}(s(s+1)\left|j{{m}_{j}}ls\right\rangle\\ \par\end{aligned}}}

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J^2|jmjls⟩=ℏ2(j(j+1))|jmjls⟩J^3|jmjls⟩=ℏmj|jmjls⟩L^2|jmjls⟩=ℏ2(l(l+1)|jmjls⟩S¯^2|jmjls⟩=ℏ2(s(s+1)|jmjls⟩

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