Before progressing in the math, and trying to find a more explicit expression for the proportionality constant α α ( ω ω ) , there's an important aspect that we need to discuss. That is that we have found that the potential felt by an atom in a light induced potential follows the square of the time averaged electric field. This is important to a lot of experimental physics in cold atom physics where physicists use this fact to understand what potential is applied to the atoms using the known intensity of the laser light applied to atoms since the intensity of light is proportional itself to the square of the time averaged electric field, i.e. I ∝ ∝ E 2 ( r → → , t ) ¯ ¯ .