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Your reversal of my edit to Table of spherical harmonics is fine if "Quantum Theory of Angular Momentum by D.A. Varshalovich, A.N. Moskalev, V.K. Kershonskii (World Scientific 1988))" really does support the correction you made, but you did not add it as a reference to the article. You also wrote in your edit summary "see e.g. Quantum ..". Are there other sources? The current reference to the Serbian Astronomical Journal certainly does not support all the content of this article. I came across this article because I need the information for a program I am writing. I looked for references but found none. I have been putting off writing the most important part of this new code, but when I do, I will have to check everything myself. This wikipedia article is unreliable, because it is not clear that the content is supported by reliable sources. Recently there have been several small changes made without any reference to a reliable source. Are you sure that book supports everything that is written in the article? If so, I will try to get it, and we can add it as a reference. --Bduke (Discussion) 21:52, 21 January 2013 (UTC)
- Sorry for the lack of signature at your talk page and other technical deficiencies. Obvious newbie here. Short answer: real spherical harmonics are OK now for l=0, 1 and 2. You can check the complex ones in wolfram alpha: SphericalHarmonicY[l,m,theta,phi] gives you the answer (fortunately complex spherical harmonics with m=0 are real). I was guessing that wolfram alpha isn't a credible source either, that's why I stuck with the Russians' book. There should be a truckload of books containing the info you need. Meta-long answer: I'll see whether the book supports _everything_. It might take a while. If we're content with that, I can try and insert references up to some 'l' value. In my opinion, it might be better for your program to generate spherical harmonics with a fix, verified algorithm (I'm thinking recursion relation). It of course depends on your programming needs. As for the referencing of the article, it seems to me that I'll need a lot of time to figure out wikipedia and check the formulae... Loudandras (talk) 23:00, 21 January 2013 (UTC)
- First, my interest. I have coded what I need for l=2 but I will need reliable information soon on real spherical harmonics for l=3. Yes, I thought there would be a truckload of books and articles containing the info, but I have not found one that easily gives me what I want. Never mind, I'll find it. Second, this article. Yes, wolfram alpha will not really do as a source, but a link to it under "External links" would be fine and useful. These kind of articles are a real pain. Someone who really knows what they are doing writes it with no sources. Very few people look at it. It stays that way for years. Sometimes IP editors make small changes, but how do we know whether they are OK or whether they are vandalism? Maybe even nobody sees the edit. I have this paper on my watchlist, so I see the changes at least daily. Good luck learning the ropes here. It can take some time and it has got more, not less, difficult over the years as we get more and more policies and guidelines. --Bduke (Discussion) 23:38, 21 January 2013 (UTC)
- I understand how difficult it is with these types of articles (unfortunately, these articles tend to be crucial for a smaller group of people). Even though software like Mathematica and wolfram alpha will not do as a source, I think they should suffice to determine whether a minor edit is vandalism or a fix. If you're really desperate about your program, you can check your spherical harmonics yourself (assuming, of course, that most of them are fine): the orthonormality property of Laplace spherical harmonics (third equation in Spherical harmonics: Orthogonality and normalization) holds for both real and complex harmonics in the Table. Plugging the displayed functions into Mathematica or Maple or any other program capable of symbolic calculations, you can at least exclude trivial typos. Again, this is verification only on a personal level, but I believe this is the right thing to do until we find a proper source. (Real spherical harmonics up to l=2 are commonplace in physics, so the functional forms {1, x, y, z, xz, yz, xy, x2-y2, 3z2-1} are correct, only the normalization factors can be off → again, I'd use a symbolic math tool to convince myself one way or the other.) --Loudandras (talk) 10:11, 22 January 2013 (UTC)
- First, my interest. I have coded what I need for l=2 but I will need reliable information soon on real spherical harmonics for l=3. Yes, I thought there would be a truckload of books and articles containing the info, but I have not found one that easily gives me what I want. Never mind, I'll find it. Second, this article. Yes, wolfram alpha will not really do as a source, but a link to it under "External links" would be fine and useful. These kind of articles are a real pain. Someone who really knows what they are doing writes it with no sources. Very few people look at it. It stays that way for years. Sometimes IP editors make small changes, but how do we know whether they are OK or whether they are vandalism? Maybe even nobody sees the edit. I have this paper on my watchlist, so I see the changes at least daily. Good luck learning the ropes here. It can take some time and it has got more, not less, difficult over the years as we get more and more policies and guidelines. --Bduke (Discussion) 23:38, 21 January 2013 (UTC)