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Dirac (delta) function

  1. Aug 6, 2010 #1
    Where can i find the proof of dirac's function properties?
     
  2. jcsd
  3. Aug 6, 2010 #2
    The delta "function" isn't an ordinary function; it's a distribution, and it only makes sense when you integrate it. It's *defined* by the property
    [tex]\int_{-\infty}^\infty \delta(x) f(x) \;dx = f(0)[/tex]
    for suitable test functions [itex]f[/itex].
     
  4. Aug 7, 2010 #3

    HallsofIvy

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    In other words, the delta function is the operator that maps f(x) to f(0).

    This doesn't belong in this area. I am moving it to "Calculus and Analysis"
     
  5. Aug 7, 2010 #4
    Look for a textbook that sounds like "Distribution theory" and you'll find what you need.
     
  6. Aug 9, 2010 #5

    arildno

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    If you wish to understand what the Dirac delta "really is", and how it might be represented as a sort of "limit", then you may read the following tutorial:
    https://www.physicsforums.com/showthread.php?t=73447
     
  7. Aug 9, 2010 #6

    HallsofIvy

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    arilno, that link is invalid.
     
  8. Aug 9, 2010 #7

    arildno

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    I've fixed it now.
     
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