- #1
caesius
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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...