Quantum Mechanics: Concepts and Applications · Problem 5.35

Three-Dimensional Problems — Nouredine Zettili

Physics — Quantum Mechanics · spin-three-halves-arbitrary-direction

Problem

Consider a particle of spin

\frac{3}{2}

. Find the matrix for the component of the spin along a unit vector with arbitrary direction

\vec{n}

. Find its eigenvalues and eigenvectors. Hint:

\vec{n} = (\sin\theta\cos\varphi)\vec{i} + (\sin\theta\sin\varphi)\vec{j} + (\cos\theta)\vec{k}.