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but doing this requires you have to deal with convergence, boundaries, orthonormality, perturbative expansions, etc. I guess you don't have to actually expand over a basis like this, but ... well ... this is the lock-stock-and-barrel trade of textbooks on classical electrodynamics... and quantum ...
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Someone had edited the text such that f was used both as the solution to the differential equation as well as the fundamental solution (which was elsewhere referred to as F). I tried to clear this up everywhere. Further clean-up is certainly possible! One major thing that should be fixed is the
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I also agree, no difference whatsoever for practical matters between widely known Green's functions and alledged 'Fundamental
Solution Theory'. Definitively all results here are also illustrated in the Green's function article. The alternative insight if any is not described here at
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in the very same sentence. Roughly speaking, you can't "do anything" with a Greens function, unless you know how to integrate over it. In physics, you write greens functions aka "propagators" as expansions over some
Hilbert space:
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example: If the convolution doesn't cleanly produce the correct result in this case, why are we using it as an example? Might a polynomial work better? Someone else can consider it and hopefully fix it!
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The convolution integral of the example doesn't exist. You certainly can't "easily find it" as is stated directly above.
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Heh. Per my comment at bottom, I'm flabbergasted as to how anyone could say "Green's function" without blurting out
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This article does not mark the difference between the Green's function and the fundamental solution!
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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467:{\displaystyle L|n\rangle =\lambda _{n}|n\rangle }
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578:{\displaystyle LG=\delta }
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