Introduction to Quantum Mechanics · Problem 4.31

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · general_spinor

Problem

For the most general normalized spinor χ\chi (Equation 4.139), compute ⟨Sx⟩\langle S_x \rangle, ⟨Sy⟩\langle S_y \rangle, ⟨Sz⟩\langle S_z \rangle, ⟨Sx2⟩\langle S_x^2 \rangle, ⟨Sy2⟩\langle S_y^2 \rangle, and ⟨Sz2⟩\langle S_z^2 \rangle. Check that ⟨Sx2⟩+⟨Sy2⟩+⟨Sz2⟩=⟨S2⟩\langle S_x^2 \rangle + \langle S_y^2 \rangle + \langle S_z^2 \rangle = \langle S^2 \rangle.

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