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Spherical Harmonics

  1. Jan 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that

    {Y_{L}^{M}\left ( 0,\varphi \right )=\left ( \frac{2L+1}{4\pi } \right )^{1/2}\delta _{M,0}

    2. Relevant equations

    Y_{L}^{M}\left ( \theta,\varphi \right )=\left ( \frac{(2L+1)(L-M)!}{4\pi(L+M)! } \right )^{1/2}P_{L}^{M}(cos\theta )e^{im\varphi }

    \int_{\varphi =0}^{2\pi }\int_{\theta =0}^{\pi }Y_{L1}^{M1}\left ( \theta ,\varphi \right )Y_{L2}^{M2}\left ( \theta,\varphi \right )sin\theta d\theta d\varphi = \delta _{N1,N2}\delta _{M1,M2}

    3. The attempt at a solution

    I think i need integrate/combine relevant equations in first equation,but ....?

    Attached Files:

    Last edited: Jan 9, 2012
  2. jcsd
  3. Jan 10, 2012 #2
    written in latex
  4. Jan 15, 2012 #3
    I have proved the claim. Task completed.
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