5

I am reading the QED book by Landau and Lifshitz and I am having a confusion with the angular momentum of a photon.

In the book, they show that the total angular momentum $j$ cannot be zero and takes the values 1,2,3,...., and that the "spin" is 1. So that means that $j=l+s=l\pm 1$. So that means $l=0,1,2,3,\dots$, but only when $l+s \ne 0$.

My question is, what is the physical meaning of $l$? In the case of the Hydrogen atom, $l$ makes sense to me since it corresponds to different energy levels the electron is in, but what is the explanation in terms of a photon? How does a photon physically obtain different values of $l$? Furthermore, why can we assume that the angular momentum of a photon is in terms of spherical harmonics? If I remember correctly, when solving the Hydrogen atom, one obtains the spherical harmonics by using separation of variables and solving the angular part of Schrodingers equation. The book just kind of starts by assuming the solutions are of the form of the spherical harmonics. Can anyone help me understand?

Vincent Thacker
  • 7,926
user41178
  • 981
  • 1
    The representation of angular momentum is simply the consequence of spatial symmetry. These are all the forms that angular momentum can take on. The symmetry can't tell you which of these forms is actually implemented in a physical system. For the states of the hydrogen atom it's all of the above, for a photon it's just one. That's part of the differences between a hydrogen atom and a photon. That angular momentum is a good variable at all (for any system) is a consequence of the isotropy of space. Break that isotropy (completely) and angular momentum goes away (completely). – CuriousOne Feb 23 '16 at 22:19
  • Ah I see, that makes sense. So for a photon, what value of $l$ does it take on? Does this depend on the system? What about for a free photon? Thanks for your comment. – user41178 Feb 23 '16 at 22:35
  • That's a non-trivial question because you have to distinguish between the spin of photons and the angular momentum of electromagnetic waves. The spin of a photon is 1, which would predict that there are three different eigenstates with quantum numbers -1, 0 and +1, but 0 is forbidden, see e.g. http://physics.stackexchange.com/questions/46643/why-is-the-s-z-0-state-forbidden-for-photons. Once you combine multiple photons into an actual electromagnetic wave state, you can build up an arbitrary large angular momentum of the wave: https://en.wikipedia.org/wiki/Angular_momentum_of_light. – CuriousOne Feb 23 '16 at 22:46

0 Answers0