Spherical harmonics & Mathematica

[shetland]

I'm calculating the zz Component for the quadruple tensor.

$$Q_{zz} = 3cos^2\theta-1$$(r=1 in this case), and the $$Y_{lm}(\theta,\phi)$$ would be l=2, m=0.

I would like to calculate the result in either maple or mathematica - I have not used either very much - I want to check the result using the wigner-eckhart theorem against this - and if anyone feels like offering input here as well, much appreciated.

 

[Tide]

I don't know what your question is but, in the meantime, I think you intended to say quadrupole.

 

[shetland]

I don't know what your question is but, in the meantime, I think you intended to say quadrupole.

Yes, though even from mathworld it is spelled as I used: http://mathworld.wolfram.com/Quadruple.html

My question was lame, or showed off how ignorant I am - I am quite rusty - and realized how to do this in mathematica, and in addition sloughed through until I could use the wigner-eckhart theorem.

The integral was solved basically fiddling around with the spherical harmonic recursion relations (cosine * spherical harmonic).

 

[Tide]

Wolfram's "quadruple" refers to an entirely different concept.