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Angsaar

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I've been doing a math problem about the Legendre differential equation, and finding there are two linearly independent solutions. When I was taught about quantum mechanics the polynomial solutions were introduced to me as the basis for spherical harmonics and consequently the eigenfunctions of the hydrogen atom, etc etc.

But if there's a second type of solution (involving ln((1+x)/(1-x)) ), what significance to QM do they have? I've not been able to find any mention of them in the context of physics, only in math textbooks.

Thanks for any help!