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Consider an electron whose spin direction is located in the xy plane.
(a) Find the eigenvalues (call them,) and eigenstates (1),2)) of the
electron's spin operator S.
(b) Assuming that the initial state of the electron is given by
2√2₁
|40) = 13|12) + ²√² | 2₂),
3
Find the probability of obtaining a value of S
8=-½ 4 after measuring the spin of the
2
electron.

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