# Dirac-Delta functions

• zheng89120

## Homework Statement

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)

## Homework Equations

calculus and Dirac-delta properties

## 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:

## Homework Statement

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

## Homework Equations

calculus and Dirac-delta properties

## The Attempt at a Solution

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

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

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

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?