# Photoelectric effect — quantum mechanical treatment

I'm curious if anyone knows a paper or a book where authors computed the probability of exciting an electron by sending a photon on a solid.

For example, my photon starts in state $| \sigma_+ \rangle$ and scatters on the solid which is in the ground state $|0 \rangle$, and they end up with the photon destroyed, i.e. $|0_{ph}\rangle$ and the solid with one excited electron, like $| 1\rangle$. It would be nice to know the probability of that happening depending on the photon's initial state ($\alpha |\sigma_-\rangle +\beta |\sigma_+ \rangle$).

• Beyond Fermi's golden rule? – Mikael Kuisma Jul 26 '16 at 10:39
• The probability of the photoelectric effect occurring is measured by the cross section, σ. There is an approximation for this σ for photons above the energy of the highest atomic binding energy. Presumably that is not what you want. However, in case you did, you can read that here: ocw.mit.edu/courses/nuclear-engineering/… – Matt Jul 26 '16 at 10:43
• @Mikael Kuisma The Fermi golden rule computes the probability that your system scatters from state $| i \rangle$ to state $| f \rangle$, assuming a given scattering potential. So, the creation/destruction of particles is not there. The details of the scatterer are, if I remember correctly, encoded in the details of the potential. – Magicsowon Jul 26 '16 at 11:08
• @user3653831 The scattering potential in this case is A.p You can then second quantize the vector potential A if you wish, and calculate the matrix element between second quantized states, but I believe it adds nothing. – Mikael Kuisma Jul 26 '16 at 11:48
• Look for theory papers of numerical simulations of ARPES measurements. There is the initial effect, multiple scattering and some of the papers might use diagrams and second quantization as well. – Mikael Kuisma Jul 26 '16 at 11:50