A Modern Approach to Quantum Mechanics · Problem 2.17

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · rotation-operator-circular-polarization-eigenstates

Problem

Use the matrix representation of the rotation operator

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

in the

|x\rangle

|y\rangle

basis as given in (2.113) to establish that the photon circular polarization states (2.114), expressed as column vectors in the

|x\rangle

|y\rangle

basis, are eigenstates of the rotation operator with the eigenvalues that appear in (2.116) and (2.119).