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## Main Question or Discussion Point

Given:

[tex]f(x)=\delta(x-a)[/tex]

Other than the standard definitions where f(x) equals zero everywhere except at a, where it's infinity, and that:

[tex]\int_{-\infty}^{\infty} g(x)\delta(x-a)\,dx=g(a)[/tex]

Is there some kind of other definition involving exponentials, like:

[tex]\int e^{ix(k'-k)}d^3x=\delta^3(k'-k)[/tex]

I remember learning something about this, but can't find a proof of it in any textbook or online at the moment, and I don't trust my memory enough to know if this is precise. Any thoughts?

[tex]f(x)=\delta(x-a)[/tex]

Other than the standard definitions where f(x) equals zero everywhere except at a, where it's infinity, and that:

[tex]\int_{-\infty}^{\infty} g(x)\delta(x-a)\,dx=g(a)[/tex]

Is there some kind of other definition involving exponentials, like:

[tex]\int e^{ix(k'-k)}d^3x=\delta^3(k'-k)[/tex]

I remember learning something about this, but can't find a proof of it in any textbook or online at the moment, and I don't trust my memory enough to know if this is precise. Any thoughts?