Quantum Mechanics: Concepts and Applications · Problem 7.13

Identical Particles — Nouredine Zettili

Physics — Quantum Mechanics · angular-momentum-rotation-transformation

Problem

(a) Show how the operator J^±\hat{J}_\pm transforms under a rotation of angle π\pi about the xx-axis. (b) Use the result of part (a) to show that J^±e−iπJ^x/ℏ=e−iπJ^x/ℏJ^∓\hat{J}_\pm e^{-i\pi\hat{J}_x/\hbar} = e^{-i\pi\hat{J}_x/\hbar}\hat{J}_\mp.

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