Einstein transition probabilities for electric dipole transitions

Einstein transition probabilities for electric dipole transitions 

As promised at the end of section 6.11.1 we now consider a specific example of the time-dependent perturbation introduced in equations (6.263) and (6.272). The radiation density for electromagnetic radiation with unit dielectric constant and magnetic permeability is given by [5, 72] 

Ex(v) represents the component of the electric field in the X direction, and we may describe the time variation, by analogy with (6.272), by writing 

Since the average value of cos227tvt is 1 /2, we find that 

The perturbation of a molecular system of electrically charged particles (electrons and nuclei) by an oscillating electric field applied parallel to the X axis is represented by the operator 

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