Fermi’s Golden Rule is a method to calculate the transition rate from an initial state α,k_{∥}⟩ to a final state α^{′ } , k _{∥ }^{′ }⟩ due to a perturbation. As described in the section 4.1.1.2, the general form of the transition probability is given by
 (5.2) 
The energy exchange between the electrons and the lattice occurs via phonons and the Delta distribution ensures energy conservation. Here, ℏω is the energy of the absorbed or emitted phonons. For the phonon interaction, the perturbation potential can be written in the following form
 (5.3) 
Inserting the wave function (3.1) into the matrix element appearing in Fermi’s Golden Rule, gives
 (5.5) 
In equation (5.2), the summation over q can be split into a sum over q_{z} and another sum over q_{∥}. Due to the momentum conservation, the sum over q_{∥} gives only one term for q_{∥} = k_{∥}^{′} k_{∥}. The remaining summation in the z direction can be tranformed to an integration over q_{z} according to

Thus, Fermi’s Golden Rule can be written as
 (5.6) 
Finally, the total scattering rate can be calculated as follows