# Dirac (delta) function

1. Aug 6, 2010

### abc def

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

2. Aug 6, 2010

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 $f$.

3. Aug 7, 2010

### 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"

4. Aug 7, 2010

### Petr Mugver

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

5. Aug 9, 2010

### arildno

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:

6. Aug 9, 2010