alt Hacker NewsDistribution theory has lots of applications in physics. The charge density of a point particle is the delta function.
Also when Fourier transforming over the whole real line (not just an interval where the function is periodic), one has identities that involve delta functions. E.g. \int dx e^(i * k1 * x) e^(-i * k2 * x) = 2 * pi * delta (k1 - k2).
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elcritch • 12/09/2024
That's fascinating about charge density of a particle being a dirac delta function. Is that a mathematical convenience or something deeper in the theory?
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The article showed that Dirac deltas could be defined WITHOUT distributions. You ignored the article when answering my question.
The question is why distribution theory is a particularly good approach to notions like the Dirac delta.