I've been reading Griffith's Introductory text on quantum mechanics, and I'm afraid I've hit a major roadblock. I don't understand his section on spin at all. I get the part about there being no classical analogy of quantum mechanical spin, but then he goes on to develop the algebraic theory of spin with no motivation apart from the fundamental angular momentum commutation relations. That suggests to me that spin has something, if not everything, to do with actual spinning. Where is the motivation behind there being an "intrinsic" angular momentum in addition to a particle's "extrinsic" angular momentum? Is it purely experimental ? And if you're developing the theory of "intrinsic" angular momentum entirely on the mathematical characteristics ( the commutation relations ) of the theory of "extrinsic" angular momentum, shouldn't they have a lot to do with each other? Further , in page 183 and 184 of the text, he does this(adsbygoogle = window.adsbygoogle || []).push({});

S[itex]^{2}[/itex]{sm} = h[itex]^{2}[/itex]s(s+1){sm} ; S[itex]_{z}[/itex]{sm} = hm{sm} to

S+-{sm} = h(s(s+1) - m(m+1))[itex]^{1/2}[/itex]{s(m+-1)}

( I couldn't find the appropriate mathematical notation in the menus, but the {} is a 'ket' , h is actually h/2[itex]\pi[/itex] and the +- should be a + on top of the - ) where S+- = S[itex]_{x}[/itex] +- iS[itex]_{y}[/itex]

I don't get what he did here at all. And finally, he claims this - "But this time eigenvectors are not spherical harmonics ( not functions of phi and theta at all), and there is no "a priori" reason to exclude half-integer values of s and m."

Why is the eigenvector not being a spherical harmonic a reason at all to include the half-integer values of s and m?

Sorry for the long post, but this has been causing me considerable distress. I'd be so eternally grateful for some help figuring this out :)

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# Can't understand the algebraic theory of spin.

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