Hi all, I'm studying the spherical harmonics, specifically the zonals (set m=0). With the equatorial harmonics(set m=l), the classical limit is pretty darn clear; the particle just accumulates to a Dirac delta along the equator, but I've proven that the zonals don't converge to a Dirac Delta at the north and south pole. They certainly(adsbygoogle = window.adsbygoogle || []).push({}); accumulatethere, but they converge to a fixed Bessel function instead of a genuine Dirac. Does anyone have any ideas on the classical picture emerging here? I've heard some talk of quantum scattering but I'm really not sure.

My personal thought is that with the equatorials, there is really only one plane perpendicular to the z axis and we know the angular momentum vector converges to the z-axis ==> by symmetry, they must necessarily be "orbiting" in a plane in the limit. However, with the zonals, all we know is that the z component of the angular momentum is zero. But there are infinitely many planes with normals vectors of zero z component. Is there some kind up superposition going on here that's preventing us from getting a genuine Dirac?

Thanks!

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# Quantum-Classical limit of Zonal Harmonics

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