Spherical harmonics & Mathematica

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Discussion Overview

The discussion revolves around the calculation of the zz component of a quadrupole tensor using spherical harmonics, specifically focusing on the expression Q_{zz} = 3cos^2θ - 1 and the spherical harmonic Y_{lm}(θ, φ) with l=2, m=0. Participants explore the use of Mathematica or Maple for this calculation and reference the Wigner-Eckhart theorem.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents the formula for the zz component of the quadrupole tensor and expresses a desire to calculate it using Mathematica or Maple.
  • Another participant points out a potential misunderstanding in terminology, suggesting the term "quadrupole" instead of "quadruple."
  • A later reply acknowledges the initial confusion and indicates that the participant has figured out how to perform the calculation in Mathematica, mentioning the use of spherical harmonic recursion relations.
  • There is a clarification regarding the term "quadruple," with a participant noting that it refers to a different concept according to Wolfram's resources.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the terminology used, with differing views on the correct term ("quadrupole" vs. "quadruple"). The discussion also reflects varying levels of familiarity with Mathematica and the mathematical concepts involved.

Contextual Notes

Some assumptions about the definitions and applications of the terms used may be unclear, and there are unresolved aspects regarding the calculation methods and the application of the Wigner-Eckhart theorem.

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

[tex]Q_{zz} = 3cos^2\theta-1[/tex](r=1 in this case), and the [tex]Y_{lm}(\theta,\phi)[/tex] 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.
 
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I don't know what your question is but, in the meantime, I think you intended to say quadrupole.
 
Tide said:
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).
 
Wolfram's "quadruple" refers to an entirely different concept.
 

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