Talk:Solid harmonics

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Revision as of 10:35, 24 August 2007 by imported>Paul Wormer
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Article Checklist for "Solid harmonics"
Workgroup category or categories Physics Workgroup, Mathematics Workgroup [Categories OK]
Article status Developing article: beyond a stub, but incomplete
Underlinked article? Yes
Basic cleanup done? No
Checklist last edited by --Paul Wormer 04:18, 22 August 2007 (CDT)

To learn how to fill out this checklist, please see CZ:The Article Checklist.





This article (my own article from Wikipedia) gave LaTeX errors which I worked around. Added to WP version section on relation to regular and irregular solid harmonics and references. --Paul Wormer 04:18, 22 August 2007 (CDT)

Hi Paul. Is the definition of the orbital angular momentum (second displayed equation) correct? The factor seems out of place. -- Jitse Niesen 08:01, 24 August 2007 (CDT)
Hallo Jitse, I don't see what is wrong. Classically :
QM:
What do you think it should be? --Paul Wormer 09:21, 24 August 2007 (CDT)
I may well be misunderstanding what the article is saying. My issue is that you say first that, in spherical coordinates,
.
If I try to substitute
then I get
But the Laplacian should be independent of hbar. Perhaps the problem is in the first formula, and it should be
I hope you can make sense of it. It's ten years ago that I did this stuff, and I never did it properly. -- Jitse Niesen 09:53, 24 August 2007 (CDT)
Looking at the dimensions (sorry, I should have started with that; but I'm only a mathematician), it's indeed the formula for the Laplacian that's weird (or, more likely, me!). -- Jitse Niesen 10:09, 24 August 2007 (CDT)
You are right wrt to the Laplacian. My problem is that I 've worked my whole life with atomic units (). I have to be more careful with hbar, I'm a bit sloppy with it. I'm working on an article on spherical harmonics right now and there I specifically stated that I take hbar = 1. Maybe you can have a look at this article and also at Legendre polynomials, which is more up your street? --Paul Wormer 10:35, 24 August 2007 (CDT)