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I'm having a hard time grasping the logical flow from orbital angular momentum to spherical harmonics. It feels like it's just sort of been sprung out of nowhere from both my lecture notes and the textbook. Can anyone help fill in the gaps that clearly must link them somehow?

How did I get from eigenvectors of L

How did I get from eigenvectors of L

^{2}and L_{z}being functions that depend only on theta and psi to the spherical harmonics [tex]|lm>=Y^{m}_{l}(\theta,\phi)[/tex]?
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