Dirac (delta) function

[abc def]

Main Question or Discussion Point

Where can i find the proof of dirac's function properties?

 

[adriank]

The delta "function" isn't an ordinary function; it's a distribution, and it only makes sense when you integrate it. It's *defined* by the property
$$\int_{-\infty}^\infty \delta(x) f(x) \;dx = f(0)$$
for suitable test functions $f$.

 

[HallsofIvy]

In other words, the delta function is the operator that maps f(x) to f(0).

This doesn't belong in this area. I am moving it to "Calculus and Analysis"

 

[Petr Mugver]

Where can i find the proof of dirac's function properties?

Look for a textbook that sounds like "Distribution theory" and you'll find what you need.

 

[arildno]

Where can i find the proof of dirac's function properties?

If you wish to understand what the Dirac delta "really is", and how it might be represented as a sort of "limit", then you may read the following tutorial:
https://www.physicsforums.com/showthread.php?t=73447

 

[HallsofIvy]

arilno, that link is invalid.

 

[arildno]

I've fixed it now.