# Physical significane and context in which Dirac introduced the Dirac Delta function

I'd like to know the exact context in which Paul Dirac introduced the Dirac delta function. What was the physical significance of the Dirac delta function when he first used it in Physics ?

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www.ece.unm.edu/summa/notes/Mathematics/0041.pdf –  Bernhard Heijstek Jul 31 '11 at 16:46
According to Wikipedia, he was not the first to introduce the concept of point mass distribution, but he introduced the notation (see library.du.ac.in/dspace/bitstream/1/92/11/…) by analogy with the Kronecker delta. –  Scott Carnahan Aug 1 '11 at 14:59

Plane-wave states are of the form $\exp(ikx)$, and these are clearly a useful quasi-basis for continuous functions. But when you Fourier transform, their x-fourier transform is a delta functions at position $k$. So if you want a representation of wavefunctions which is symmetric between x-space and p-space, you are forced to consider delta functions.