Quantum Mechanics: Concepts and Applications · Problem 7.19

Identical Particles — Nouredine Zettili

Physics — Quantum Mechanics · rotation-matrices

Problem

Show that ⟨j, m′∣e−iβJ^y/ℏ J^z2 eiβJ^y/ℏ∣j, m′⟩=∑m=−jm=jm2 ∣dm′m(j)(β)∣2\langle j,\,m'\mid e^{-i\beta\hat{J}_y/\hbar}\,\hat{J}_z^2\, e^{i\beta\hat{J}_y/\hbar}\mid j,\,m'\rangle = \sum_{m=-j}^{m=j} m^2\,|d^{(j)}_{m'm}(\beta)|^2.

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