Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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 ?

share|improve this question
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
add comment

1 Answer

The delta function was used to give the x-operator eigenstates in quantum mechanics. The original papers are relatively obscure, because all the material in them was incorporated into the Principles of Quantum Mechanics, which is in print and very popular. The first mathematical chapters contains a bunch of delta-function identities.

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.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.