A spin-half particle is in the pure state whose Bloch vector is .
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin
The Structure of Quantum Mechanics, Ch Spin one-half, SU(2) and two-level dynamics
Problem
A spin-half particle is in the pure state whose Bloch vector is n^=(0,3/2,−21).
((a)) Write the state as cos(θ/2)∣↑⟩+eiϕsin(θ/2)∣↓⟩, giving θ, ϕ and the two coefficients.
((b)) Find the probability that a measurement of spin along m^=(x^+z^)/2 gives +ℏ/2.