Talk:Table of spherical harmonics

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Sources

This article is almost entirely unsupported by sources and several small edits have recently been made. User:Loudandras has just supported a small correction with "Quantum Theory of Angular Momentum by D.A. Varshalovich, A.N. Moskalev, V.K. Kershonskii (World Scientific 1988))" mentioned in the edit summary. Can anyone support that this reference supports the content of all or part.duke of this article, so it can be added as a suitable reference? I do not have access to it. Other references would also be welcome and particularly welcome if there were more easily available. --Bduke (Discussion) 22:14, 21 January 2013 (UTC)[reply]

Mathworld is an web-accessible source that can be taken to reliable. Xxanthippe (talk) 23:15, 21 January 2013 (UTC).[reply]

OK, so add the appropriate specific link to the article as a reference. I am not familiar with Mathworld but it looks interesting. --Bduke (Discussion) 23:38, 21 January 2013 (UTC)[reply]

Putting it in the article as an external link, as you have done, is fine, but I do not think it can be used as a source for the material. How would mathworld be used to get the material? --Bduke (Discussion) 05:04, 22 January 2013 (UTC)[reply]

By going to the Mathworld home page and searching for "spherical harmonic". Xxanthippe (talk) 09:57, 22 January 2013 (UTC).[reply]

OK, so as you seem to know more about this than I do, put some specific links as references to support specific parts of this article. A general link is not enough. --Bduke (Discussion) 10:40, 22 January 2013 (UTC)[reply]

I added cited references to an accessible article and the Varshalovich-book. The former gives real spherical harmonics up to l=2, the latter complex ones up to l=5. I checked every single harmonic on the page, and added references to the sections corresponding to the checked l's. The spherical-to-cartesian transcriptions are also fine for complex harmonics. I added the citations at the end of section titles, what might be frowned upon, but I couldn't think of anything better. I also added a direct link to Wolfram Alpha. Sorry if some cleanup is needed after my edit, I tried to be as efficient as possible.--Loudandras (talk) 22:08, 23 January 2013 (UTC)[reply]

Fixed transcription error for l=10, m=0 to agree with http://www.wolframalpha.com/input/?i=SphericalHarmonicY%5B10%2C0%2Ctheta%2C0%5D . ThaeliosActual 14:21, 25 January 2013 (UTC)[reply]

Found a decent source for real spherical harmonics, unfortunately g orbitals are not tabulated there. I checked every single function and their transformation from complex spherical harmonics, all are according to the Chisholm book and the other cited article.--Loudandras (talk) 14:03, 1 February 2013 (UTC)[reply]

Great. I can find the Chisholm book. I even thought I had it, but it seems not, but it will be in the university library. It is a good source for chemists. --Bduke (Discussion) 19:59, 1 February 2013 (UTC)[reply]

Splendid work. Xxanthippe (talk) 00:02, 2 February 2013 (UTC).[reply]

Contraction of +-m harmonics

I just noticed that anonymous 193.175.8.58 made some edits in the middle of November, contracting the formulae of spherical harmonics with $l=2$ . While this notation is indeed more concise, I have some objections. Firstly, the choice of only $l=2$ for the edit seems arbitrary. Why not fix the other ones as well? Secondly, I think the expanded version would be much more useful in the case of this specific article. As the article is a table, it doesn't matter that 2 (or $l$ ) more lines are used for these functions. However, when users access the page and want to use/check these functions, the expanded notation (I mean having separate $+|m|$ and $-|m|$ harmonics) is much more transparent, and provides much less room for errors. If it was up to me, I would revert to a preceding version, but others might argue to change all the other spherical harmonics instead. Either way, I'm hoping for some input from others. --Loudandras (talk) 20:36, 3 January 2014 (UTC)[reply]