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Dirac's delta and units

  1. Jan 11, 2005 #1
    Consider :

    [tex] E = \int P(\tau) d\tau = \int A\delta(\tau) d\tau [/tex]

    E is in Joules and [tex]P(\tau)[/tex] is in Watts, what are the units of A? What about [tex]\delta[/tex]?

    I have a hunch, but need to have all doubts removed.
  2. jcsd
  3. Jan 11, 2005 #2


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    The delta function has the dimension of the reciprocal of the variable of integration. Thus delta(tau)d(tau) is non-dimensional. Therefore A has the same dimension as E, i.e. Joules.
  4. Jan 11, 2005 #3


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    And you can see why the dirac delta has units of the reciprocal of the integration variable from

    [tex] \int _{-\infty} ^{\infty} \delta (p-p_0) dp = 1 [/tex],
    where p is any parameter.
  5. Jan 11, 2005 #4
    Thanks guys!
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