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Derivative of Spherical Harmonic for negative m

  1. Mar 8, 2014 #1

    VVS

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    Hello!

    1. The problem statement, all variables and given/known data
    I want to evaluate the derivative of spherical harmonics with respect to the azimuthal angle and express it in terms of spherical harmonics.


    2. Relevant equations and 3. The attempt at a solution
    I have calculated the derivative of the spherical harmonic with respect to the azimuthal angle.
    I know how to express the derivative of the spherical harmonic in terms of spherical harmonics for positive m. But I don't know how to do this for negative m.

    View attachment Spherical_Harmonics.pdf


    Thanks for your help.
     
  2. jcsd
  3. Mar 8, 2014 #2
    Isn't the azimuthal angle the argument of the Exp[], in this case θ?
     
  4. Mar 8, 2014 #3

    VVS

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    Yes you're right. I meant that I want the derivative wrt the polar angle.
     
  5. Mar 8, 2014 #4
    Hope this is what you were looking for.

    It isn't the final answer because you can still express Cot ø and Exp(iθ) in terms of the spherical harmonics but that part is not the worst. May even be able to find them in a table somewhere.
     

    Attached Files:

  6. Mar 8, 2014 #5

    VVS

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    Hello!

    Yes!! That is exactly what I was looking for.
    Although I recalculated it and I get a slightly different result.
    I will upload my calculations tomorrow or so. Right now I am too tired.

    thanks
     
  7. Mar 10, 2014 #6

    VVS

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