For an electron we have $n$ (energy level), $m$ (orbital s p d f), $m_\ell$ (sub-orbital s px py pz d1 d2 d3 d4 d5 and the 7 f orbitals), $m_s$ (spin up or down with or opposed to the external magnetic field). Anyone familiar with electron configuration can get it on a physical level but what are the quantum numbers for a photon? We have polarization, momentum and frequency but what else? Also how can these properties be used for spectroscopy? I am aware of how frequency is used in FTIR and polarization in optical rotation spectroscopy.
What are the quantum numbers of a photon?
In the standard model of particle physics, the photon is an elementary particle of mass zero,charge zero, spin 1 and energy equal to $hν$ where $h$ is Plancks' constant and $ν$ the frequency of the classical wave that can be built up by the quantum mechanical superposition of the same energy photons. These are its intrinsic quantum numbers.
For an electron we have n (energy level), m (orbital s p d f), mℓ (sub-orbital s px py pz d1 d2 d3 d4 d5 and the 7 f orbitals), ms (spin up or down with or opposed to the external magnetic field).
If you look at the table of elementary particles you will see that the intrinsic quantum numbers of an electron have little to do with the ones you are talking about. The ones you quote are the particular quantum numbers coming up in a solution of the electron being in a potential well. To be precise it is the atom that has these quantum numbers assigned to the energy levels. Because of the great difference in mass between a nucleus and an electron, one assigns them to electron orbitals , assuming the nucleus is at rest.
Anyone familiar with electron configuration can get it on a physical level but what are the quantum numbers for a photon?
The photon having zero charge cannot be caught in a Coulomb potential the way charged particles can. It can interact with an atom that has an electron with the specific quantum numbers, if its energy is appropriate to change the energy level of the atom, and at the time has spin projection appropriate to the l and m quantum numbers of that level.
If its energy is high enough it can ionize the atom, kicking the electron off. Angular momentum conservation has to be obeyed, by the appropriate spin of the photon, depending on the l and m of the level the atom was in before the interaction.