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Why only l=1 of spherical harmonics survives?

  1. Jun 22, 2013 #1
    1. The problem statement, all variables and given/known data

    The question is about page 198 of Jackson's Classical Electrodynamics. The magnetic scalar potential is set to be:

    Phi = ∫ (dΩ' cosθ'/ |x-x'|).

    Using the spherical harmonics expansion of 1/|x-x'|, the book claims that only l=1 survives. I don't know why terms of l≠1 vanish


    3. The attempt at a solution

    I considered the addition theorem of 1/|x-x'| that contains on Y* (θ',ϕ'). I am trying to see whether the sin's and cos's inside Y* (θ',ϕ') are orthogonal to cosθ' for l≠1, but I had no success doing so. I could not think of other reasons why only l=1 terms survive.

    Any ideas
     
  2. jcsd
  3. Jun 22, 2013 #2

    Simon Bridge

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    Are sines and cosines not orthogonal?
    Don't forget the range of the integration.
     
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