# Homework Help: Dirac-Delta functions

1. Oct 24, 2011

### zheng89120

1. The problem statement, all variables and given/known data

show that $\delta$(x-ct)$\delta$(x+ct) = $\delta$(x)$\delta$(t)

P.S. sorry I mean't:

show that 2C*$\delta$(x-ct)$\delta$(x+ct) = $\delta$(x)$\delta$(t)

2. Relevant equations

calculus and Dirac-delta properties

3. The attempt at a solution

$$d/dx \int_{-\infty}^x\delta(x-ct)\delta(x+ct) = \delta(x)\delta(t) dx$$

P.S. sorry I mean't:

$$2C*d/dx \int_{-\infty}^x\delta(x-ct)\delta(x+ct) = ...$$

there are a couple of really weird steps that somebody else used after the above

Last edited: Oct 24, 2011
2. Oct 24, 2011

### Staff: Mentor

Why are you taking the derivative? How is the Dirac delta function defined?

3. Oct 24, 2011

### I like Serena

Hi zheng89120!

Do you know how to calculate for any generic function f(u,v):
$$\iint f(x-ct, x+ct) 2c \delta(x-ct) \delta(x+ct) dxdt$$

And do you also know how to calculate this double integral after a parameter transformation to (u, v), where u=x-ct and v=x+ct?