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Homework Help: Normalization of Bessel Functions

  1. Oct 18, 2009 #1


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    Jackson 3.16 has one derive the orthonormality of the bessel functions, that is:

    \int\limits_0^\infty {\rho J_v (kp)J_v (k'p)d\rho } = \frac{{\delta (k - k')}}{k}[/tex]

    Now, I was able to show that infact, they are orthogonal, but I haven't been able to figure out the 1/k term. Basically, I'm looking to see what

    \int\limits_0^\infty {\rho J_v (kp)J_v (k'p)d\rho } = N\delta (k - k')[/tex]

    produces where N is the normalization constant that I need to determine. I've been stumped on how to show that the normalization constant is infact, 1/k. Any ideas anyone? :)
  2. jcsd
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