A Modern Approach to Quantum Mechanics · Problem 2.14

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · circular-linear-polarization-basis-transformation

Problem

(a) Determine a

2\times 2

matrix

\mathbb{S}

that can be used to transform a column vector representing a photon polarization state using the linear polarization vectors

|x\rangle

and

|y\rangle

as a basis to one using the circular polarization vectors

|R\rangle

and

|L\rangle

as a basis. (b) Using matrix multiplication, verify explicitly that the matrix

\mathbb{S}

that you found in (a) is unitary.