Calculating Spherical Harmonics Cuadratic Dispersion

AI Thread Summary
The discussion focuses on calculating quadratic dispersion in quantum systems by expanding x^2 in terms of spherical harmonics using Clebsch-Gordan coefficients. The user initially expands x as a linear combination of spherical harmonics but encounters issues when squaring x to obtain the correct form of x^2. Despite achieving a sum of spherical harmonics multiplied by coefficients, the results are incorrect. The user seeks assistance in resolving this calculation challenge. The thread highlights the complexities of applying spherical harmonics in quantum mechanics.
altered-gravity
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Greetings,

I´m calculating cuadratic dispersion of some quantum systems. I need to expand x^2 in terms of spherical harmonics (using Clebsch-Gordan coefficients, or threeJ as well) in order to be able to use Gaunt espression in the integral solving.

I start from the expansion of x as linnear combination of Spherical Harmonics (with Clebsch-Gordan coef.). Then, in order to get x^2, I calculate x*x (studying the couplings of the state vectors term by term) and I get what I need: a sum of Spherical Harmonics (each multiplied by a C-G coef.) but it´s not the correct one!

Could anyone help me? Thanks
 
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wow K-12 got really hard really fast!
sorry, maybe a different forum should be addressed
 
oops! Excuse me.
 

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