Optical Faraday rotation

Three calculations of optical Faraday rotation are presented in which a linearly polarized field is incident on a medium of harmonic oscillators in the presence of a longitudinal magnetic field. The rotation of the plane of polarization of the field is evaluated using classical oscillators and the Lorentz force equation, quantum oscillators and the Heisenberg equations of motion, and quantum oscillators and a Schroumldinger equation approach. It is shown that a simple argument, based on the assumption that a circularly polarized field drives either Delta m=1 or Delta m=-1 transitions on absorption (m is the magnetic quantum number), leads to an incorrect result for the Verdet constant.