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Amok
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In various quantum chemistry books and course booklets I came across spin wave functions (usually referred to as alpha and beta for spin and up and down, respectively) that depend on a so called spin-variable. They are usually used to construct slater determinants. An example of this is Modern Quantum Chemistry (a great book). My problem is that sometimes, when matrix elements are computed, integrations over the spin-variable are made (e.g http://en.wikipedia.org/wiki/Franck–Condon_principle). My teacher told me this makes no sense since spin is supposed to be a discrete variable, so it should be a sum. What is this spin variable? Does it have anything to do with the actual 'spin' observable? I think it is a bit of a construct for when you actually have to write down matrix elements as integrals and not as scalar products using braket notation. Can anyone clarify this for me?