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Dirac-Delta functions

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data

    show that [itex]\delta[/itex](x-ct)[itex]\delta[/itex](x+ct) = [itex]\delta[/itex](x)[itex]\delta[/itex](t)

    P.S. sorry I mean't:

    show that 2C*[itex]\delta[/itex](x-ct)[itex]\delta[/itex](x+ct) = [itex]\delta[/itex](x)[itex]\delta[/itex](t)

    2. Relevant equations

    calculus and Dirac-delta properties

    3. The attempt at a solution

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

    P.S. sorry I mean't:

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

    there are a couple of really weird steps that somebody else used after the above
     
    Last edited: Oct 24, 2011
  2. jcsd
  3. Oct 24, 2011 #2

    Mark44

    Staff: Mentor

    Why are you taking the derivative? How is the Dirac delta function defined?
     
  4. Oct 24, 2011 #3

    I like Serena

    User Avatar
    Homework Helper

    Hi zheng89120! :smile:

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

    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?
     
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