Quantum mechanical treatment of radiation theory

The previous expressions for the intensity decrease per imit time and per unit area will now be treated by quantum mechanics. It is related to the transition probability d fl p/df. This is the probability per unit of time that a photon of energy hv = Eja) is absorbed and induces a transition from a state a to a state j. The decrease in intensity given by Eq. (55) can be written as the product of the energy of the transition with the number of molecules on the absorption area and with the transition probability. 

Calculation of d flmf/df is done by the standard time-dependent perturbation theory with being the unperturbed Hamiltonian and 3li the Hamiltonian describing the interaction with light. 

In MCD literature (Piepho and Schatz, 1983 Schellman, 1975 Stephens, 1976) and in the paper written by Judd (Gorller-Walrand and Binnemans, 1998 Judd, 1962) the electric dipole perturbation Hamiltonian is given as 

E ic- the electric field due to the light wave, including medium effects. 

For linearly polarized light along x and y the Hamiltonian is written as 

---