In theoretical work that eventually led to the laser, Einstein considered a set of N two-level atoms,
Question:
In theoretical work that eventually led to the laser, Einstein considered a set of N two-level atoms, as shown in Figure 4.8, in a box with Nk photons, where
the energy h̄ωk corresponds to the energy difference between the two electron levels Based on the rules (4.7.19) above, one can straightforwardly write down rate equations for the populations of electrons in the different states and the photons:
where Nlo,i and Nhi,i are the electron occupation numbers for atom i and the bars indicate their average occupation numbers.
(a) Show that the rules for fermions imply that the (1−N) factors can be dropped, under the assumption that Ni,lo + Ni,hi = 1.
(b) Show that in equilibrium these equations are satisfied if
and Nk is a Planck distribution. This was one of the original arguments for stimulated emission.
Step by Step Answer:
a The fisrt term with electron numbers is Nihi 1 Nilo Nihi 1 1 Nihi Nhi Nihi since fo...View the full answer
