Talk:Multipole expansion

message: 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)
replies: text: What are these authoritative texts? Are they the books on angular momentum that you have cited? Your definition departs from the vast majority of uses of multipole expansions and contradicts parts of this article - for example, the idea of multipoles expressed in Cartesian or cylindrical coordinates. In every use of multipole expansions that I have seen (and some of them are very authoritative references like Morse and Feshbach, Methods of Theoretical Physics), they represent the potential of a body or radiation at a distance, and their purpose is to reduce the complexity of a source covering some finite region to point sources ("poles") at the origin. Multipole expansions do not include the positive powers of r, which increase with increasing distance.--RockMagnetist (talk) 17:17, 12 October 2010 (UTC)
thread_title:  Rewriting the lede 

message: 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)
replies: text: To my knowledge the naming conventions in high energy physics and the corresponding engineering differ from standard conventions. Hence, a single magnet already is a dipole and does not show a monopole. The quadrupole magnet consist of four coils such that the naming is  incorrect (see origin of naming below). Within naming conventions in a multipole expansion and the standard expansion itself a sextupole, which actually consist of six coils, does not exist. So, it might be mentioned and linked to an article on synchrotron rings (or similar), but it is not part of a multipole expansion. I guess in 2D everything is slightly different, as the potential becomes logarithmic etc. (infinite line charge).(mikuszefski)  — Preceding unsigned comment added by Mikuszefski (talk • contribs) 09:14, 17 August 2012 (UTC)
replies: text:  I agree that numerous related topics should be clarified (e.g. hexapole). Octupole should be fixed to octopole. A line should be drawn between 2D and 3D expansion. This article needs attention of an expert. --FDominec (talk) 07:40, 27 October 2021 (UTC)
thread_title:  sextupoles 

message: I think that somewhere in the first paragraph it should be explained why this expansion is called multipole expnsion. What is a pole in this context by the way?
Paranoidhuman (talk) 03:45, 26 September 2009 (UTC)
replies: text: For the name one might check the book from Maxwell on electrodynamics. Here the argument is actually the other way around. Maxwell does not make a series expansion of an existing potential, but claims that in the far field any potential can be generated by special sources of a specific symmetry. He then constructs these sources starting with a singe charge, a pole. In a next step two charges are combined showing no total net charge. Hence the name dipole. These two charges are brought together such that the product of distance and charge remains constant.  This object obviously creates a potential with a symmetry different to the one of the monopole. As it is necessarily related to the direction at which the two charges are brought together it is represented as a vector, the dipole moment. However, in the context of the multipole expansion one should consider this vector as a first order tensor. The next object is supposed to have neither monopole not dipole moment. This is achieved by properly combining two dipoles; hence they must be of equal strength and opposite direction. However, one is free in the direction in which these two approach each other (using the same limit conditions as before, i.e. strength times distance stays constant). Note that an additional vector comes into play. At the end one gets a second order tensor, the quadrupole. In each step an object of new symmetry is created by combining two objects of the next lower symmetry. In total one starts with 1 charge then 2, 4, 8, and so on. Each object consists virtually of 2^n charges/poles such that it can be called multipole. The standard naming convention is monopole, dipole, quadrupole, octopole (from octo - eight and not octupole as it is often found), hexadecapole, dotriacontapole, etc. (mikuszefski)  — Preceding unsigned comment added by Mikuszefski (talk • contribs) 09:37, 17 August 2012 (UTC)
thread_title: Reason of the name

message: I don't see any particular reason why there should be separate pages for multipole expansion and multipole moments. You cannot discuss the one without the other. Hence it makes sense to try to merge the two pages. TimothyRias (talk) 08:59, 22 February 2010 (UTC)
replies: text: I agree. The lead section for multipole moments would make an improved lead section for multipole expansion, and the multipole moments#Molecular electrostatic multipole moments is an application of multipole expansion#Expansion in Cartesian coordinates.--RockMagnetist (talk) 22:00, 12 October 2010 (UTC)
thread_title:  Merge? 

message: In the section "Interaction of two non-overlaping charge distributions"
I am missing a hint that for molecules (for example) the formula is certainly
only catching the electrostatic interaction of the classical Coulomb
interaction, missing all the exchange-correlation energy
(This point is also very obscure in Distributed multipole analysis.) R. J. Mathar (talk)
Based on my experience, it is very common for basic quantum mechanics treatments to implicitly assume that exchange and correlation, as well as relativistic perturbations, are left out.  The treatment in this article is basically what you would expect to find in an advanced undergraduate textbook or a basic graduate textbook in theoretical chemistry/computational chemistry.  Its not even really a true "theoretical physics" treatment.  To a degree, it makes sense to mention that this treatment leaves out more complicated (mathematically or physically) interactions and/or those that are only solvable in terms of approximation.  Then again, this is the standard and you will find this implicit assumption in textbooks written from 1920 to 2014.  It is by no means restricted to quantum mechanics.  Fluid mechanics texts typically leave out magnetohydrodynamics until chapter 27.  By that point it is assumed that you are studying using software and have implemented various forms of numerical tools to solve intractable problems.184.189.220.114 (talk) 16:11, 5 April 2014 (UTC)
thread_title:  Quantum mechanics