Timeline for How should we think about Spherical Harmonics?
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 7, 2020 at 3:52 | comment | added | Myridium | @PM2Ring - I agree with that. Wikipedia is nice if you're already well-versed in surrounding subjects. But it's impenetrable for someone trying to enter. You may enjoy this article: larrysanger.org/2020/05/wikipedia-is-badly-biased | |
| Dec 6, 2020 at 22:58 | comment | added | PM 2Ring | @Myridium I know what you mean, but I think it depends on the topic. Maybe I'm just being nostalgic, but I think it used to be better. But these days, many maths & science articles have become bloated with excessive detail and you virtually need to be an expert in the topic to understand them. So it can be useful to refresh your memory, but not much use for beginners. | |
| Dec 6, 2020 at 20:53 | comment | added | wyphan | @leftaroundabout Yes, that's exactly what I meant, thanks for the clarification. I was trying to insert the definition in $\mathbb{L}^2$ space, but messed it up. | |
| Dec 6, 2020 at 4:57 | comment | added | Myridium | @CosmasZachos - please, Wikipedia is god-awful for any mathematical topic. Its pedagogical value is near zero. | |
| Dec 5, 2020 at 17:50 | vote | accept | Noumeno | ||
| Dec 5, 2020 at 16:16 | comment | added | leftaroundabout | @wyphan your “definition” of completeness doesn't make sense as such (that sum actually diverges), and certainly doesn't capture the idea behind completeness. The point is, any (sufficiently regular) function on the sphere can be represented by a series of spherical harmonics. I think what you actually meant was $\sum_{l,m}|Y_{l,m}\rangle\langle Y_{l,m}| = \mathrm{id}_{\mathcal{L}^2(S^2)}$, which indeed could also be written in integral form but not the one you wrote. Yours is actually saying $\sum_{l,m}\langle Y_{l,m} | Y_{l,m}\rangle = 1\in\mathbb{C}$, which is wrong. | |
| Dec 5, 2020 at 0:38 | history | became hot network question | |||
| Dec 5, 2020 at 0:00 | history | tweeted | twitter.com/StackPhysics/status/1335011170193989632 | ||
| Dec 4, 2020 at 19:54 | answer | added | Emilio Pisanty | timeline score: 28 | |
| Dec 4, 2020 at 17:50 | comment | added | jacob1729 | But "the simultaneous eigenstates of $L_z,L^2$" and "complete orthonormal basis of functions on the sphere" mean exactly the same thing... | |
| Dec 4, 2020 at 17:50 | answer | added | JEB | timeline score: 11 | |
| Dec 4, 2020 at 17:39 | answer | added | Thomas Fritsch | timeline score: 10 | |
| Dec 4, 2020 at 17:36 | comment | added | Cosmas Zachos | Isn't Wikipedia enough? You want much more discussion? I mean, it has enough references for you to focus on what bothers you, and you are the best judge of what you need to know. At the very least you could use it to focus your question. | |
| Dec 4, 2020 at 17:32 | comment | added | wyphan | @Noumeno Vector spaces, where the words "complete" and "orthonormal" are defined, is usually covered in a first-year graduate-level course in physics. | |
| Dec 4, 2020 at 17:30 | comment | added | Noumeno | @CosmasZachos What do you mean by going beyond Wikipedia? | |
| Dec 4, 2020 at 17:29 | answer | added | Himanshu | timeline score: 7 | |
| Dec 4, 2020 at 17:26 | comment | added | wyphan | The spherical harmonics form a complete orthonormal basis. "Complete" in mathematical notation is $\sum_{l,m} \int \mathrm{d} \Omega | Y_{l,m} (\theta, \pi) |^2 = 1$, where $\mathrm{d} \Omega = sin \theta \mathrm{d} \theta \mathrm{d} \phi$, the usual solid angle differential. "Orthonormal" in mathematical notation is $\int \mathrm{d} \Omega Y^*_{l,m} Y_{l',m'} = 0$ if $l \neq l'$ and $m \neq m'$ | |
| Dec 4, 2020 at 17:16 | comment | added | Cosmas Zachos | So you wish to go beyond WP? | |
| Dec 4, 2020 at 16:46 | history | edited | Gert | CC BY-SA 4.0 |
added 4 characters in body
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| Dec 4, 2020 at 16:35 | history | asked | Noumeno | CC BY-SA 4.0 |