A Modern Approach to Quantum Mechanics · Problem 5.17

Wave Mechanics in One Dimension — John S. Townsend

Physics — Quantum Mechanics · density-operator-pure-state-check

Problem

Given the density operator ρ^=12(∣+z⟩⟨+z∣+∣−z⟩⟨−z∣−∣−z⟩⟨+z∣−∣+z⟩⟨−z∣)\hat{\rho} = \frac{1}{2}\left(|{+z}\rangle\langle{+z}| + |{-z}\rangle\langle{-z}| - |{-z}\rangle\langle{+z}| - |{+z}\rangle\langle{-z}|\right) construct the density matrix. Use the density operator formalism to calculate ⟨Sx⟩\langle S_x\rangle for this state. Is this the density operator for a pure state? Justify your answer in two different ways.

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