A Modern Approach to Quantum Mechanics · Problem 2.10

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · matrix-representation-jx-sz-basis

Problem

Determine the matrix representation of J^x\hat{J}_x in the SzS_z basis. Suggestion: Start with the matrix representation of the operator S^x\hat{S}_x using the states ∣+x⟩=12∣+z⟩+12∣−z⟩∣−x⟩=12∣+z⟩−12∣−z⟩|{+x}\rangle = \frac{1}{\sqrt{2}}|{+z}\rangle + \frac{1}{\sqrt{2}}|{-z}\rangle \qquad |{-x}\rangle = \frac{1}{\sqrt{2}}|{+z}\rangle - \frac{1}{\sqrt{2}}|{-z}\rangle as a basis and then transform to the SzS_z basis.

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