If spherical harmonics are simultaneous eigenfunctions of [itex]\hat{L}[/itex] and [itex]\hat{L}_{z}[/itex], then that means for a state at which l=1, and where you have three possible values of m (1, 0 , -1) that the value of L and L[itex]_{z}[/itex] cannot really be determined simultaneously. Because the three fold degeneracy of the state implies that the rigid rotator exists in a three dimensional subspace with the eigenkets given by the three spherical harmonics determined by l=1. Is this true, or am I getting something wrong? My textbook says that they can be determined simultaneously, but I'm pretty sure this is only true if the particle exists in a state given by one of the eigen-kets of the degenerate subspace.(adsbygoogle = window.adsbygoogle || []).push({});

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# The rigid rotator and Angular momentum.

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