1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Normalization of Bessel Functions

  1. Oct 18, 2009 #1

    Pengwuino

    User Avatar
    Gold Member

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

    [tex]
    \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

    [tex]
    \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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Normalization of Bessel Functions
Loading...