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Dirac Delta Integral

  1. Aug 30, 2011 #1
    1. The problem statement, all variables and given/known data
    For some reason these are just messing me up. I need to prove:

    1. [itex]\delta(y)=\delta(-y)[/itex]

    2.[itex]\delta^{'}(y) = -\delta^{'}(-y)[/itex]

    3.[itex]\delta(ay) = (1/a)\delta(y)[/itex]

    In 2, those are supposed to be first derivatives of the delta functions

    2. Relevant equations
    Use an integral with a test function


    3. The attempt at a solution
    Need a small hint
     
  2. jcsd
  3. Aug 30, 2011 #2

    Dick

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    Homework Helper

    You need to prove the integral of delta(y)*f(y)*dy (what is that?) is equal to the integral of delta(-y)*f(y)*dy where y goes from -infinity to infinity and f is a test function. Try a change of variable u=(-y) and use the properties of the delta function. Don't forget to pay attention to what happens to the limits of integration when you change the variable.
     
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