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Delta dirac

  1. Feb 21, 2010 #1
    if [tex]\phi[/tex] is a angular coordinate , between ([tex]-\pi,\pi[/tex])

    ¿how much is [tex]\delta(\phi-\pi)[/tex] with [tex]\phi=-\pi+\epsilon[/tex]????
     
  2. jcsd
  3. Feb 21, 2010 #2

    SpectraCat

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    The Dirac delta function yield zero unless it's argument is zero, in which case it yields 1 (this is an oversimplification, but it should do for the present discussion). In your case, the argument of the delta function is [tex]-2*\pi + \epsilon[/tex], so it should be zero. Did you mean to type, [tex]\phi=\pi + \epsilon[/tex]? In that case, the argument of the delta function would be just [tex]\epsilon[/tex], and then you need to get a bit more specific about how you are defining the delta function. Have you looked at this thread? https://www.physicsforums.com/showthread.php?t=73447
     
  4. Feb 21, 2010 #3
    then the dirac delta evaluated in (-2pi+epsilon) is 0 or infinite??????
     
  5. Feb 21, 2010 #4
    specifically, i need to find T, in the follows equation:

    [tex]\delta(\phi-\pi)+k=T\delta(\phi-\pi)[/tex]
    where [tex]\phi[/tex] is between ([tex]-\pi,\pi[/tex])
     
  6. Feb 22, 2010 #5

    haushofer

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    With that specific range the delta distribution is zero; phi can't become equal to pi. So you get the equation 0 + k = T*0.
     
  7. Feb 22, 2010 #6
    but, if i do:

    [tex]\int^{\pi-\epsilon}_{-\pi+\epsilon}\delta(\phi-\pi)d\phi+\int^{\pi-\epsilon}_{-\pi+\epsilon} k=T\int^{\pi-\epsilon}_{-\pi+\epsilon}\delta(\phi-\pi)[/tex]

    is correct????????????

    pd: [tex]\phi[/tex] can be equal to [tex]\pi[/tex].......[tex]\phi[/tex] is between [tex](-\pi,\pi)[/tex]
     
    Last edited: Feb 22, 2010
  8. Feb 22, 2010 #7

    Matterwave

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    You want to integrate from pi-epsilon to pi+epsilon. That will include the relevant range of the dirac delta.
     
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