A Modern Approach to Quantum Mechanics · Problem 2.12

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · photon-polarization-probability-torque

Problem

A photon polarization state for a photon propagating in the

z

direction is given by

|\psi\rangle = \sqrt{\frac{2}{3}}|x\rangle + \frac{i}{\sqrt{3}}|y\rangle

(a) What is the probability that a photon in this state will pass through an ideal polarizer with its transmission axis oriented in the

y

direction? (b) What is the probability that a photon in this state will pass through an ideal polarizer with its transmission axis

y'

making an angle

\phi

with the

y

axis? (c) A beam carrying

N

photons per second, each in the state

|\psi\rangle

, is totally absorbed by a black disk with its normal to the surface in the

z

direction. How large is the torque exerted on the disk? In which direction does the disk rotate? Reminder: The photon states

|R\rangle

and

|L\rangle

each carry a unit

\hbar

of angular momentum parallel and antiparallel, respectively, to the direction of propagation of the photons. (d) How would the result for each of these questions differ if the polarization state were

|\psi'\rangle = \sqrt{\frac{2}{3}}|x\rangle + \frac{1}{\sqrt{3}}|y\rangle

that is, the ``

i

'' in the state

|\psi\rangle

is absent?

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