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I am working my way through Griffith's Introduction To Quantum Mechanics and I have got to the section on addition of spin angular momenta. I'll copy and paste the bit i'm struggling with, as it's easier than paraphrasing:

http://img714.imageshack.us/img714/2783/80183858.png [Broken]

http://img442.imageshack.us/img442/1294/20886932.png [Broken]

I'm assuming [itex]\chi_1[/itex] is the spin state of the electron and [itex]\chi_2[/itex] is the spin state of the proton. So why is the total state of the atom written as [itex]\chi_1\chi_2[/itex]? Why not [itex]\chi_1 + \chi_2[/itex] or something different?

Secondly, he says that [itex]S^{(1)}[/itex] acts only on [itex]\chi_1[/itex], and [itex]S^{(2)}[/itex] acts only on [itex]\chi_2[/itex]. Why is this, and how come [itex]S \equiv S^{(1)}+S^{(2)}[/itex]? If the two particles are both spin 1/2 then aren't the matrices [itex]S^{(1)}[/itex] and [itex]S^{(2)}[/itex] both the same (i.e. just given by the 2x2 Pauli spin matrices)?

I think if I was clearer on those two points maybe the rest will make sense, so I will leave it there.

Thanks for any help!

Jon.

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# Addition of spin angular momenta

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