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Dirac-Delta functions

  • Thread starter zheng89120
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  • #1
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Homework Statement



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)

Homework Equations



calculus and Dirac-delta properties

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:

Answers and Replies

  • #2
33,265
4,965

Homework Statement



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

Homework Equations



calculus and Dirac-delta properties

The Attempt at a Solution



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

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?
 
  • #3
I like Serena
Homework Helper
6,577
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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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