A Modern Approach to Quantum Mechanics · Problem 2.3

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · rotation-operator-matrix-representation

Problem

Determine the matrix representation of the rotation operator

\hat{R}(\phi\mathbf{k})

using the states

|{+z}\rangle

and

|{-z}\rangle

as a basis. Using your matrix representation, verify that the rotation operator is unitary, that is, it satisfies

\hat{R}^\dagger(\phi\mathbf{k})\hat{R}(\phi\mathbf{k}) = 1