A Modern Approach to Quantum Mechanics · Problem 2.15

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · jz-matrix-elements-linear-polarization

Problem

Evaluate the matrix elements

\begin{pmatrix} \langle x|\hat{J}_z|x\rangle & \langle x|\hat{J}_z|y\rangle \\ \langle y|\hat{J}_z|x\rangle & \langle y|\hat{J}_z|y\rangle \end{pmatrix}

by expressing the linear polarization states

|x\rangle

and

|y\rangle

in terms of the circular polarization states

|R\rangle

and

|L\rangle

. Compare your result with that given in Example 2.8.