- #1

caesius

- 24

- 0

## Homework Statement

Prove that [tex]\delta(at)=\frac{1}{abs(a)}\delta(t)[/tex]

Hint: Show that [tex]\int\phi(t)\delta(at)dt=\frac{1}{abs(a)}\phi(0)[/tex]

(the limits of integration are from -inf to +inf btw, I couldn't find how to put them in..)

## Homework Equations

## The Attempt at a Solution

Ok. I understand that the integral is only defined for at = 0, i.e., t = 0. But if I follow this logical then I evaluate the integral to be phi(0), not phi(0)/a. Where does the a come from?

And I'm not entirely sure how proving that relationship helps with the proof of the scaling function...