altered-gravity
Aug23-04, 09:39 AM
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
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