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I Understanding the Dirac Delta function

  1. May 28, 2017 #1
    I just want to make sure that I am understanding the Dirac Delta function properly. Is the following correct?:

    For two variables ##x## and ##y##:
    \begin{equation}
    \begin{split}
    \delta(x-y) f(x) &= f(y)
    \end{split}
    \end{equation}

    And:
    \begin{equation}
    \begin{split}
    \delta(x-x) f(x) &= f(x)
    \end{split}
    \end{equation}
     
  2. jcsd
  3. May 28, 2017 #2

    Vanadium 50

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    Neither of those is correct.
     
  4. May 29, 2017 #3

    Ssnow

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    The Dirac delta is not a function in the traditional sense, it can be rigorously defined either as a distribution or as a measure.
    Ssnow
     
  5. Jun 8, 2017 #4

    FactChecker

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    The Dirac delta function is defined as a generalized function by its behavior in an integral: ∫f(x)δ(x)dx = f(0).
    So in your question, ∫δ(x-y)f(x)dx = f(y) would make better sense than your expression (1). The integral can not be omitted. Your expression (2) does not make sense to me.
     
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