Talk:Multipole expansion

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To-do list for Multipole expansion: edit · history · watch · refresh

Tasks for expert:

  • derive the multipole expansion of a scalar field and explain relation to Taylor series,
  • stress immediated application to both electrostatics and Newtonian gravitostatics,
  • discuss some simple examples such as field of uniform rod, disk.
  • derive analogous expansions for vector and tensor fields (or at least give citations),
  • add annonated citations, e.g. 'Mathematical Methods for Physics by Arfken and Weber (alas, insufficiently readable, organization not good enough), Methods of Mathematical Physics by Jeffries and Jeffries (better, except for unfortunately nonstandard notation),
  • link to discussion of applications in gravitation, electromagnetism, etc.,
  • link to forthcoming article on relativistic multipoles (for general relativity)

[edit] Suggested improvements

This is a good start, but this is a big topic and we need to say more (see todo list for suggestions). Note that I came here while writing todo list for Talk:Linearized gravity. ---CH 00:52, 6 February 2006 (UTC)

Introduction to Electrodynamics, 3rd Edition by David Griffiths has a pretty straight forward derivation/analysis of the multipole expansion in the context of electromagnetism. Not very rigorous by a mathematician's standards, but a good start. RyanC. 17:43, 4 March 2007 (UTC)
I noticed that more than a year ago this page was much better, but that WillowW deleted quite some material without comment. Why did he do that?--P.wormer 16:07, 13 July 2007 (UTC)
That would be "she", and I forget my motivations from over a year ago when I had first arrived here at Wikipedia - forgive me? I'll try to look it over again and remember. I seem to recall that there was much overlap with multipole moments so perhaps I was eliminating redundancy? As an aside, we should all strive for simplicity, accessibility and clarity for lay-people; not everyone is going to have heard of solid harmonics by that name. The customary format nowadays at Wikipedia seems to use inline citations as in {{cite book}} or {{cite journal}}. Friendly suggestions from Willow 21:22, 13 July 2007 (UTC)
  • Dear Willow, I am sorry, I always try to write gender neutral, but somehow the nickname "Willow" triggered something masculine in my mind (perhaps because it reminded me of Willem, a Dutch boy's name). Anyway, with regard to technical level: the older article spherical multipole moments is not any more elementary than what I wrote :). In my opinion we should try to cater for all levels of proficiency (including senior/graduate level), not only for the proverbial "average reader", or "beginning student". But, of course, we should not forget the latter two categories, and I'll do my best. As you can see I embarked on some electrostatic related articles. The main reason is that I want to fix up intermolecular forces, where the electrostatic multipole expansion of the interaction is central.
I asked you before why you have hidden the complex conjugation star (*) in the definition of the spherical multipole. Now I want to add as a comment that this star conveys information, namely that the starred quantity transforms contragrediently to an unstarred one. Hence a starred/unstarred pair is an invariant [under SO(3)]. Our mutual august authority Jackson apparently wasn't aware of this, or didn't care. I also like to ask you where you found the concepts "interior" and "exterior" multipole moment? I've never heard of them. As a final comment: feel free to correct or augment my writings, particularly with didactic stuff. If you feel the urge to scratch some advanced material, then please explain this first on the talk page. Thank you. --P.wormer 09:09, 14 July 2007 (UTC) PS I understood that the use of macros is voluntary? I haven't mastered their use yet.


[edit] Rewriting the lede

The most common use of multipole decompositions is certainly in solutions of Laplace's equation in 3-d. Solutions are easily written as series of multipole decompositions in powers of r and 1/r. However, this is by no means the most basic use of multipole expansions. The correct definition of multipole expansion in the most authoritative texts I can find only defines it on an n-sphere, and makes no reference to distance. I think this article should really be referring to that basic version. I've rewritten the lede to make this clear, while also noting the common application. The rest of the article still needs a lot of cleanup. It looks like there's also a whole lot of work to be done on related pages, like quadrupole. --131.215.123.98 (talk) 05:02, 18 November 2007 (UTC)

[edit] sextupoles

In particle accelerators it is common to use dipole magnets for bending, quadrupole magnets for focusing and sextupole magnets for correcting chromatic aberrations (See Storage_ring). These should probably be mentioned on this page. I suspect that they only occur in a 2d multipole expansion, is that right? --194.36.2.144 (talk) 11:41, 29 November 2007 (UTC)