Representations of a delta function

• I
Gold Member
There are many representations of the delta function. Is there a place/reference that lists AND proves them? I am interested in proofs that would satisfy a physicist not a mathematician.

marcusl
Gold Member
By representations, do you mean the generating functions that produce the delta in the limit? Physics references do not generally provide proofs so much as demonstrations or explanations, so if you want a proof you should stick to math texts. The list of texts containing demonstrations/discussions, on the other hand, is nearly limitless. Open up your favorite one. Here are a few examples
• Arfken, Mathematical Methods for Physicists
• Bracewell, The Fourier Transform and Its Applications
• Dirac, The Principles of Quantum Mechanics (of course!)

S.G. Janssens
BvU
Homework Helper
representations of the delta function. Is there a place/reference that lists AND proves them
I wonder what you would consider a proof of a representation . A delta function is a something with certain well described properties. The word distributions comes to mind (out of the dust of ages). Showing that the representation exhibits such properties is just that: a showing.

[Links added after commenting; plenty references for further study. As a physicist I'm comfortable with 'infinitely narrow and high needle with area 1' but I would never claim that would prove anything]

Gold Member
I am actually comfortable with the delta function. It’s just that I am many years past grad school and was reading something (Intermediate Quantum Mechanics by Bethe) that piqued my interest in how to to show that these representations have the correct properties.

WWGD
Gold Member
I am actually comfortable with the delta function. It’s just that I am many years past grad school and was reading something (Intermediate Quantum Mechanics by Bethe) that piqued my interest in how to to show that these representations have the correct properties.
What are the properties you refer to?

Gold Member
That the integral over all space of the representations equals one. I am interested in how to do the integrals. Some of them I can solve, some of them I cannot. I do not want to look them up in an integral table.

S.G. Janssens