1. ## Dirac delta function

Can someone explain or provide a reference to a treatment of the well known Dirac delta function which places it on a better foundation (not too rigorous!) than a switching of orders of integration or of limit taking?

An expression of the delta function that particularly interests me is the Fourier transform of the function f(x) = 1.

2. ## Re: Dirac delta function

Did you check out the wiki? You can define it as a distribution with the sifting property as its defining characteristic.

3. ## Re: Dirac delta function

Originally Posted by Ackbeet
Did you check out the wiki? You can define it as a distribution with the sifting property as its defining characteristic.
I have checked wiki, and I find that my math is not strong enough to understand the more rigorous discussions. When I studied physics in the 1950s at Brooklyn College, my professor, a distinguished physicist, seemed to discourage interest in such matters. Since the advent of string theory, he may have changed his mind.

I'll just plod along. Thanks!

4. ## Re: Dirac delta function

Well, like I said, I'd say the sifting property is the best way to think about the Dirac Delta "function". Under an integration, the Dirac Delta function "picks out" the value of the function at the point where the argument of the Dirac Delta function is zero.

5. ## Re: Dirac delta function

Yes, that is clear, as were other non-rigorous explanations, including Dirac's in his "Principles of Quantum Mechanics" (1927?)
Thanks!