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Can someone explain to me what the spin functions are? I understand that a spin up is described by a function which is often called [tex]\alpha[/tex] and spin down is described by a similar function called [tex]\beta[/tex]. But what are these functions? What do they look like and what parameters do they take? Are they orthonormal like spatial wave functions?

If you have a good source for information on this I'd be grateful. I've tried searching Google but that didn't really give me any good information.

Thanks