Talk:Green function

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Contents 1 Page name 2 All functions are equal, and discontinous functions aren't less equal than others, are they? 3 Applications to Quantum Mechanics 4 bad form 5 Minus sign missing 6 More Examples 7 Green's functions in condensed matter physics 8 Intuition

[edit] Page name

People, let's call it a Green function. This use of Green's is killing me!

I've always heard it called a Green's function. This case seems somewhat specific, would it be possible to generalise it to a degree n? - 3mta3 01:23, 20 Jun 2005 (UTC)

It should be 'Green function': compare Hermite polynomial, Abelian Group, Grothendieck topology, etc.--88.104.215.243 11:05, 9 July 2006 (UTC)

I'm going to rename the page accordingly. AMS 108, Applied Functional Analysis by Zeidler calls it "Green function". —Ben FrantzDale 00:17, 13 November 2006 (UTC)

[edit] All functions are equal, and discontinous functions aren't less equal than others, are they?

The article says "Green's functions are distributions in general, not functions, meaning they can have discontinuities.". This cannot possibly be correct, can it? I mean, a function having discontinuities sure doesn't make it any less of a function. The author must have had something else in mind. Please rephrase. Jonas Olson 21:36, 27 September 2005 (UTC)

Umh. Not totally satisfactory formulation. More discontinous than any function, so to say, like Dirac delta function, which isn't a function. --Pjacobi 23:01, 27 September 2005 (UTC)

You raise a good point about the Green's being called stricly a distribution, and not a 'true' function. What of the case of a dimensionless operator L=1? Would not the Green's be identified with the Dirac Delta (assuming infinitesimal integration)? I.E. - it is only a function in the sense that it acts locally on said operator.

[edit] Applications to Quantum Mechanics

I'd love to see an elaboration of the applications to QM. --User:TobinFricke

[edit] bad form

"we leave it to the reader to fill in the in-between steps" Is something contained in bad textbooks and bad lectures. Can anyone fill in the blanks here?

[edit] Minus sign missing

shouldn't there be a minus sign in the Laplacian Green's function 1/|x-x'| (and in the expressionwith the charge density \rho)? maybe I'm confused at the moment, but I'm pretty sure there should be... If no one answers I'll change it. Dan Gluck 16:35, 10 October 2006 (UTC)

[edit] More Examples

I think we all know the best way to learn stuff is Examples, Like actual problems. I think it would be great if we could get many examples from some text books or somewhere, to give readers (and hopless students) an idea of how to use the this function. this is a more General statement to the applications to Quantum Mechanics Section.24.25.211.241 04:48, 24 October 2006 (UTC)

[edit] Green's functions in condensed matter physics

I think there's a little confusion with regards to this section. Until someone disagrees (Andywall?), I'd like to replace it with a section explaining the connections and differences between this kind of Green('s) function — the inverse of a linear operator — and what's meant by the term in quantum/statistical field theory, where it essentially just means correlation function. Stevvers 03:15, 5 November 2006 (UTC)

I have added a sentence in the introduction to mention this distinction and will add something to Correlation function (quantum field theory).Stevvers 01:16, 10 November 2006 (UTC)

[edit] Intuition

After looking at my math text, I think I just "got" this topic, at least for the case of − u'' = f. I would add my understanding to the page, but am not sure it is a complete understanding. Is this right?:

The Green function, , can be thought of as the response of the solution variable, u, to a delta function, δ(x − y). Because the system is linear, we can apply superposition: we can represent our given f as the sum of delta functions and expect our solution to be a sum of the responses to each of those delta functions.

For example, suppose we have a horizontal string with distributed and point weights on it and we want to know its deflection along its length. Assume small deflection (so that the problem is linear). We could hang a unit mass at every point, y, along the string and record the deflection as a function of x. This would be our . (Obviously we would expect a V shape centered on the point). The the solution will be

.

Is that about right? —Ben FrantzDale 00:16, 13 November 2006 (UTC)

Yes, that sounds exactly right. If you put this into the page, make sure you explicitly write the differential equation that the string satisfies. Stevvers 21:27, 15 November 2006 (UTC)