A spin- particle is prepared in the state | = 3| ! +4| ! 5
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · Symmetry, angular momentum and spin
The Structure of Quantum Mechanics, Ch The wave function is not the state
Problem
A spin-21 particle is prepared in the state ∣ψ⟩=53∣↑⟩+4∣↓⟩, written in the S^z eigenbasis {∣↑⟩,∣↓⟩} with eigenvalues ±ℏ/2. The S^x eigenstates are ∣+⟩x=2∣↑⟩+∣↓⟩,∣−⟩x=2∣↑⟩−∣↓⟩.
((a)) Using the Born rule in the z-representation, give P(Sz=+ℏ/2) and P(Sz=−ℏ/2).
((b)) Translate ∣ψ⟩ into the x-representation by computing ⟨+∣xψ⟩ and ⟨−∣xψ⟩, and hence give P(Sx=+ℏ/2) and P(Sx=−ℏ/2).