Timeline for Addition of two angular momenta: general theory
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2021 at 7:47 | comment | added | ric.san | I'm sorry, but... what does change of basis has to do with $n$? | |
| Jul 18, 2021 at 23:04 | comment | added | ZeroTheHero | Yes but only $\ell$ - not $n$ - enters in angular momentum coupling, i.e. the change of basis does not depend on $n$. | |
| Jul 18, 2021 at 20:11 | comment | added | ric.san | Ok. That's really strange though. The atomic states are given by three quantum numbers $n , l$ and $m$, and $l$ goes from $0$ to $n-1$... | |
| Jul 18, 2021 at 19:49 | comment | added | ZeroTheHero | No. For fixed $j_1,j_2$ you have $\sum_{m_1m_2} \vert j_1m_1;j_2m_2\rangle \langle j_1m_1;j_2m_2\vert =\mathbb{I}$ and, for fixed $j_1m_1,j_2m_2$, you have $\sum_{j} \vert j m\rangle\langle j m \vert =\mathbb{I}$ where $m=m_1+m_2$. | |
| Jul 18, 2021 at 18:16 | comment | added | ric.san | @ZeroTheHero does that mean I cannot say if the set $\displaystyle \sum_{j1_,j_2,m_1,m_2} |j_1,j_2,m_1,m_2⟩⟨j_1,j_2,m_1,m_2|$ is complete or not, even if it is for each fixed value of $j_1$ and $j_2$? | |
| Jul 18, 2021 at 18:13 | vote | accept | ric.san | ||
| Jul 18, 2021 at 0:00 | comment | added | ZeroTheHero | Your last equation is incorrect: there is no sum on $j_1,j_2$ since $\mathbb{I}=\sum_{jm}\vert jm\rangle\langle jm\vert$. In the context of this equation $j_1,j_2$ are fixed. | |
| Jul 17, 2021 at 22:17 | answer | added | Cosmas Zachos | timeline score: 4 | |
| Jul 15, 2021 at 19:19 | comment | added | Davide Morgante | What do you know about group theory? You know the difference between reducible and irriducible representations? Do you know what a Casimir operator is? | |
| Jul 15, 2021 at 18:22 | history | edited | ric.san | CC BY-SA 4.0 |
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| Jul 15, 2021 at 18:11 | history | edited | ric.san |
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| Jul 15, 2021 at 17:51 | history | edited | ric.san | CC BY-SA 4.0 |
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| Jul 15, 2021 at 17:44 | history | asked | ric.san | CC BY-SA 4.0 |