Spin of electron and photon emitted How does the spin state of the electron affect the polarisation of the light emitted?
I am looking for a description in a detailed mathematical aspect, any suggestions on books ?
 A: An interesting question that I want to answer for the emission of photons in the case of the Lorentz force or Hall effect.
Electrons are aligned in the magnetic field with their magnetic dipole to the external magnetic field. As is known, an electron moving through the external field will emit photons and will be deflected sideways. The resulting EM radiation is polarised. Best studied in radiation from synchrotrons and other particle accelerators.
Conversely, it should be noted that from the polarised radiation of radio antennas, conclusions can be drawn about the behaviour of the surface electrons on an antenna rod. These electrons are aligned with their magnetic dipoles during their cyclic accelerations, otherwise there would be no emitted polarised radio wave.
You ask about spin and have to replace the term magnetic dipole from my answer with spin. If you think that is more intuitive or otherwise necessary.
Unfortunately, I can't help with mathematics. So take it more as a long comment than an answer.
A: I found a better description of the same in book by Bransden and Jochain. The spin of the electron changing is transferred to the photon. and a beutiful mathematical description is shown in the book.
Specifically, in the section.. 4.5 where the selection rules are discussed and the rules for angular momemntum of the photon is elaborated.
