Various methods of introducing polarization moments

All the aforesaid also applies to the classical limit of the quantum density operator p, namely to the probability density p(0, p) if one performs its expansion over the classical analogue of tensor operators to which the spherical functions Ykq 0, p) belong. Unfortunately, different ways of expansion are used by different authors, both in the quantum approach and in the classical limit. This complicates considerably comparison of the results obtained by these authors, including experimental data. 

In this appendix we aim briefly to compare and analyze a number of frequently used approaches to the problem of introducing polarization moments into the description of atomic and molecular angular momenta polarization. 

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Appendix D. Various methods of introducing polarization moments D.l Polarization moments in quantum physics... 

Thus, we have attempted to give, in the present appendix, an idea of the various methods of determining classical and quantum mechanical polarization moments and some related coefficients. We have considered only those methods which are most frequently used in atomic, molecular and chemical physics. An analysis of a great variety of different approaches creates the impression that sometimes the authors of one or other investigation find it easier to introduce new definitions of their own multipole moments, rather than find a way in the rather muddled system of previously used ones. This situation complicates comparison between the results obtained by various authors considerably. We hope that the material contained in the present appendix might, to some extent, simplify such a comparison. 

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