Field electromagnetic average

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

ChaumeL P. C. and Nieto-Vesperinas, M. (2000) Time-averaged total force on a dipolar sphere in an electromagnetic field. Opt Lett., 25, 1065-1067. 

In the above expressions for C(t), the averaging over initial rotational, vibrational, and electronic states is explicitly shown. There is also an average over the translational motion implicit in all of these expressions. Its role has not (yet) been emphasized because the molecular energy levels, whose spacings yield the characteristic frequencies at which light can be absorbed or emitted, do not depend on translational motion. However, the frequency of the electromagnetic field experienced by moving molecules does depend on the velocities of the molecules, so this issue must now be addressed. 

Once we have obtained the electromagnetic fields inside and scattered by the particle, we can determine the Poynting vector at any point. However, we are usually interested only in the Poynting vector at points outside the particle. The time-averaged Poynting vector S at any point in the medium surrounding the particle can be written as the sum of three terms ... 

The instantaneous direction of propagation is, of course, perpendicular to the plane defined by the instantaneous electromagnetic fields E and B. But this time-dependent direction need not be parallel to the z axis, physically defined as the direction for the average propagation of energy. Let us illustrate the point with variations of the same simple example of previous section, for additional details see Munera and Guzman [67]. 

All we need to do is to estimate the average of the potential. To do this, the form of the electric and magnetic fields are used in the normalized energy density of the electromagnetic field... 

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