Quantum Mechanics: Concepts and Applications · Problem 7.14

Identical Particles — Nouredine Zettili

Physics — Quantum Mechanics · rotation-operators

Problem

Consider a rotation of finite angle

\alpha

about an axis

\vec{n}

which transforms unit vector

\vec{a}

into another unit vector

\vec{b}

. Show that

e^{-i\beta\hat{J}_b/\hbar} = e^{i\alpha\hat{J}_n/\hbar}\, e^{-i\beta\hat{J}_a/\hbar}\, e^{-i\alpha\hat{J}_n/\hbar}