A Modern Approach to Quantum Mechanics · Problem 5.18

Wave Mechanics in One Dimension — John S. Townsend

Physics — Quantum Mechanics · density-operator-mixed-state-spin-half

Problem

Given the density operator ρ^=34∣+z⟩⟨+z∣+14∣−z⟩⟨−z∣\hat{\rho} = \frac{3}{4}|{+z}\rangle\langle{+z}| + \frac{1}{4}|{-z}\rangle\langle{-z}| construct the density matrix. Show that this is the density operator for a mixed state. Determine ⟨Sx⟩\langle S_x\rangle, ⟨Sy⟩\langle S_y\rangle, and ⟨Sz⟩\langle S_z\rangle for this state.

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