Talk:Parabolic coordinates

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Could someone produce a diagram to show the concept of parabolic coordinates, ala the diagrams at Coordinates (elementary mathematics)? It would go a long way towards helping "visual learners" understand this. --Jacius 17:00, 30 Apr 2005 (UTC)

[edit] More up to date references

Hello. Can someone please update the reference section to include more recent literature on the subject. Currently all the references are from 1961 and the article quotes application in e.g the Stark Effect - though the Stark Effect article says nothing about parabolic coordinates... Some basic applications\examples and external links would also be appreciated. Thank you. (Sorry, I just can't glean from the article when one would want to consider using parabolic coordinates) Scribblesinmindscapes 20:49, 16 February 2007 (UTC)

Hi, I'll be glad to do this, but can you gve me a little time? My plate is a little full, since I'm working on setting up a new WikiProject, drafting an essay and brooding over how to bring Encyclopædia Britannica to FA status. Oh, and I actually have a few real-life jobs, too — wah! :O <- Willow freaks out!

Seriously, to answer your question quickly, you'll want to use parabolic coordinates in potential-type problems (e.g., diffusion equation, Laplace equation, Poisson equation) that feature a sharp edge of a half-infinite sheet (in 3 dimensions) or a half-infinite line in two. That's the sharp edge you see running vertically in the diagram; see how the potential lines wrap around the origin? That's where the edge is.

Another application of parabolic coordinates is in cases where you have an inverse square law for a central force, plus a force in the z-direction. That occurs for example when a hydrogen atom is placed in an electric field (the Stark effect). There's more on this subject (although it's "deep") at Laplace-Runge-Lenz vector.

Hoping that this helps, and please forgive my rushed answer, it's kindly meant nonetheless :) Willow 21:10, 16 February 2007 (UTC)

Thank you WillowW - that would be brilliant! Maybe I'll read something about it somewhere in due course though, but I've added this article to my watchlist. (Switched from engineering to physics this year so devouring a lot of physics now.) Thank you for the willingness to help - let me know if I can aid in any way. ps# Loved the pictures of Bouguereau on your profile by the way. Will add some of them to my blog :) Scribblesinmindscapes 20:29, 18 February 2007 (UTC)

Hey Scribbles, thanks for your nice message! :) I like Bouguereau, too, if only because he has such an affection for textile artists, especially knitters. A generalization of what I wrote before: check out Hamilton-Jacobi equation for the most general form of an energy function that can be solved by moving to parabolic coordinates, "solved" in the sense of "reduced to quadratures". Please send any suggestions for stuff that's poorly explained, so that we can fix it up together! :) Willow 23:24, 18 February 2007 (UTC)