Talk:Poisson's equation

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Contents 1 merge with Laplace equation (discussion) 2 the real equation 3 Electrostatics 4 Solutions ??? 5 Where is the solution 6 less algebra, and more explanation please

[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