L13.2 Transition rates induced by thermal radiation (continued)
PROFESSOR: We have now expressed in terms of the energy density on this mode omega I the contribution to the transition amplitude. The fact that all these modes act incoherently means that each one has a shot in producing the transition. And the probabilities now must be added. So the way to sum probabilities now is the following. If you have a sum over I of this frequency sum I of some energy density u of I times any function of omega I, you can replace it by an integral d omega. Instead of little omega I's that you're summing, you now integrate over omega the energy density of your radiation field times the function of omega. So instead of having a sum of these things, you now integrate over a continuous variable. And this represents the energy density in the range. This whole thing is the energy density in the range d omega, which is in that range d omega, the energy range. The energy density is the sum of the energy densities of each of the contributions. So t...