By Edminister J.
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Extra resources for Elettromagnetismo: 301 problemi risolti
3), D and H are termed response fields. 119) are based on primitive moments. 119) can also be obtained using series expansions of the averaged microscopic charge and current densities, (rj) and (j), in coordinate space. Explicit calculations to electric quadrupole-magnetic dipole order are given in [21-23]. The averaging techniques referred to in this section are an essential aspect of the transition from microscopic to macroscopic electromagnetism. Detailed accounts of this topic are available in the literature [21-23], and here we make some brief comments.
33, and the need to take account of the traces of multipole moments has also been emphasized by Melrose and McPhedran . They point out that even in the simple example of multipole radiation, it is only for transverse radiated fields that traceless moments may be used. In media where the radiated fields have longitudinal components, it is necessary to use primitive moments . 13). 11), it therefore seems desirable to retain these traces in the response fields rather than incorporating them in the free source densities.
We assume that this state, but not necessarily the others, is non-degenerate. The energy of the system is expanded in powers of the perturbation where from time-independent non-degenerate perturbation theory  Here, and in what follows, we use the notation for the matrix elements of an operator fj on the vector space describing the system, where s^} and n^} denote unperturbed orthonormal eigenvectors of the system. 14) where ujns is the angular frequency of the transition between the unperturbed states n and a.
Elettromagnetismo: 301 problemi risolti by Edminister J.