INVARIANT IMBEDDING, WAVE PROPAGATION AND THE WKB APPROXIMATION
RAND CORP SANTA MONICA CA
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In previous papers, some applications of the principle of invariant imbedding to radiative transfer and neutron diffusion processes were presented. This use of invariance principles was stimulated by the fundamental work of Ambarzumian and Chandrasekhar, and strongly influenced by the point of regeneration technique of Bellman and Harris, and the theory of dynamic programming. Fundamental for the success of these techniques as applied to the above processes is the ability to consider the overall physical process as a sequence of local processes. For the case of particles, this is easily done. This paper indicates how wave propagation may be considered in these terms. It is rather remarkable that the results are based upon an algorithm that, in general, can yield divergent series. Following a provocative paper by Bremmer, the air is to show that wave propagation can be discussed in terms of reflection and refraction at infinitesimally separated interfaces. It was proven that the convergence of the Bremmer series can be established under a simple assumption concerning the slowly varying nature of the local wave number.
- Radiofrequency Wave Propagation