Talk:Poisson's equation

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[edit] merge with Laplace equation (discussion)

I totally and completely disagree with the proposal to merge this page with that for the Laplace equation. Although they appear to be superficially similar, they lead in very different directions. The Laplace equation leads to the study of Harmonic functions, de Rham cohomology, and Hodge theory. On the other hand, Poisson's equation leads to the study of electrostatics, the Green's function, and anything that uses Green's functions or propagators, such as quantum field theory. Laplace's equation has absolutely no sense of a propagator, because it does not need one. Just because this article sucks, doesn't mean that it should be merged with another article that sucks even more. Both articles should be fixed. linas 14:00, 26 Apr 2005 (UTC)

Put another way, the wave equation is just the Laplace equation with signature +---, yet I notice there is no proposal to merge those two articles. That is because the Laplace equation is big enough to deserve multiple articles discussing it. linas 14:11, 26 Apr 2005 (UTC)

There is also the Poison-Boltzman equation concerning the distribution of ions around a macromolecule, that is solved to give the mapping of the epectrostatic potential around the molecule. From what i know it emerges from Poison equation and Boltzman distribution.

[edit] the real equation

this is the REAL Poisson's equation:

           /)))\
      ____/)))))\ 
     /    ))))))))))         <<<  
    / o    ))))))))))))  <<<<<<    
   |        ))))))))))))<<<<<<
    \      ))))))))))))  <<<<<<
     \_)__)))))))))          <<<
            \)))/
             \)/
    • And funnily enough, this one makes more sense to me than the actual article. Aquaman 09:51 (UTC)

[edit] Electrostatics

Recent edits on this article have changed it from being a discussion of Poisson's equation, to its application to the narrow, specific field of electrostatics. I strongly urge that this article be structured so that there is a general introduction, pointing out its general utility, and have the special case of electrostatics treated in a subsection. linas 17:11, 11 December 2005 (UTC)

Never mind, I did it myself. linas 17:33, 11 December 2005 (UTC)


[edit] Solutions ???

For completeness, I think this article needs to have a section describing the major solutions to the equation and some of the methods for finding the solutions. -- Metacomet 18:17, 11 December 2005 (UTC)

[edit] Where is the solution

No Poisson solution in this site?

[edit] less algebra, and more explanation please

This article is pretty poor IMHO. How about explaining what it is without resorting to algebra, and also explaining its applications... --Rebroad 10:21, 19 November 2006 (UTC)

I completely agree. I don't even know what it is supposed to be about. Psi is not explained, and there is no indication why Poisson would have dreamed it up in the first place. What does it solve? It's not clear here at all. Telling us that the LHS equals a number on the RHS is no more than trivial. I assume psi is to represent the wave function, but there is no clue from the article. --Centroyd

[edit] more applications

other applications include image processing. e.g. filtering light and shade effects from sequences of pictures. see: http://www.cs.huji.ac.il/course/2006/csip/iccv01.pdf

There should be something about how Poisson's equation is used as del-squared-phi=4(pi)G(rho) to compute gravitational forces in the universe, as an alternative to Newton's inverse-square law of gravitation. Phi is the potential field, and one gets to the force per unit mass (mass of the earth, say) by calculating -del(phi). —The preceding unsigned comment was added by 82.12.27.202 (talk) 12:10, August 23, 2007 (UTC)

[edit] Poisson's equation in Gravity's Rainbow

The Thomas Pynchon novel has a description of Poisson's equation that makes this article look like technical babble. pages 54-56. Fuzzform 22:39, 11 July 2007 (UTC)

[edit] Request for expansion

 Please help improve this with more applications (diffusion equation, ..) and solution methods (Green functions, ...) by expanding it.
Further information might be found on the talk page or at requests for expansion. (January 2007)

[edit] Del vs. Delta

There seems to be some confusion on this page between Del and Delta, that is:

\nabla (Del) vs. Δ (Delta)

This should be cleared up. I think that all of the Deltas should be turned into Dels. This is vector calculus here, not thermodynamics... but maybe I'm missing something.

askewchan 16:10, 25 October 2007 (UTC)

The explanation of the notation appears to already be in the article. Take a look at the paragraph after the first equation. Note that del squared is short hand for del dot del and both of these are equivalent to delta. Feel free to add expository text to clear that up in the article if you think it is needed. ChrisChiasson 17:02, 26 October 2007 (UTC)