(Solved): 10. (a) Determine a 2 x 2 matrix S that can be used to transform a column vector representing a phot ...

10. (a) Determine a 2 x 2 matrix S that can be used to transform a column vector representing a photon polarization state using the linear polarization vectors |x) and ly) as a basis to one using the circular polarization vectors R) and IL) as a basis (b) Using matrix multiplication, verify explicitly that the matrix S that you found in (a) is unitary 2.14. (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.