Quantum Mechanics: Concepts and Applications · Problem 5.23

Three-Dimensional Problems — Nouredine Zettili

Physics — Quantum Mechanics · angular-momentum-j1-jz-measurement

Problem

Consider a system of total angular momentum j=1j = 1. We want to carry out measurements on J^z=ℏ(10000000−1).\hat{J}_z = \hbar\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{pmatrix}. (a) What are the possible values will we obtain when measuring J^z\hat{J}_z? (b) Calculate ⟨J^x⟩\langle \hat{J}_x \rangle, ⟨J^x2⟩\langle \hat{J}_x^2 \rangle, and ΔJx\Delta J_x if the system is in the state jz=−ℏj_z = -\hbar. (c) Repeat (b) for ⟨J^y⟩\langle \hat{J}_y \rangle, ⟨J^y2⟩\langle \hat{J}_y^2 \rangle, and ΔJy\Delta J_y.

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