Consider an electron whose spin direction is located in the xy plane.
(a) Find the eigenvalues (call them λ1, λ2) and eigenstates (∣λ1⟩, ∣λ2⟩) of the electron's spin operator S.
(b) Assuming that the initial state of the electron is given by
∣ψ0⟩=31∣λ1⟩+322∣λ2⟩,
find the probability of obtaining a value of S^=−ℏ/2 after measuring the spin of the electron.