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up or down. We now index the eigenstates with the spinors in the basis:

:

where and denote spin-up and spin-down states respectively. As previously discussed, the magnitudes of the complex coefficients give the probability of finding the electron in either definite spin state:

:
:
:

where the probability of finding the particle with either spin up or down is normalized to 1. Notice that and are complex numbers, so that

:

is an example of an

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