Ch 4 and Ap S REVIEWED

Ch 4 and App S PhL 9.22.14 Two interesting items here. 1. I was trying out averaging C and 1/V and 1/K, but that did not turn out to be useful in the end, so the final Appendix S only contains something called < > and then G(x1,x2) and C(x1,x2) are never mentioned and are not useful at all. 2. I noted that Le really ought to be complex, but in the end it is KL = K that forces it to be real, and this equality survives the averaging and now appears at the end of Appendix S. Reviewed on 9/24/14 and stored in Appendix S. Try this functional definition C'(x1,x2) ≡ q(z) / V(x1,x2) = 4πξd / K(x1,x2) Decompose C'(x1,x2) into its real and imaginary parts, C'(x1,x2) = G(x1,x2) + jωC(x1,x2) Double-averaging these equations gives C' = q(z) * <> = 4πξd <> C' = G + jωC How do I connect this with the main line progression leading to the new TL equations? There we obtain y ≡ jβd2/(ωLe) which we could decompose into real and imaginary parts like so y = G + jωC G ≡ Re[y] etc Question: In Chapter 4 when I do this W(z) = Le i(z) do I know that Le is real? Go back to φ1(x,ω) = ∫ ρ1(x',y',z',ω) dx'dy'dz' . R = |x - x'| (4.1.1) Now ρ1 could have some complex phase, and then so could φ1. And of course the expo is complex. You really must allow that everything could have a phase! How about ρ1(x,y,z) = α1(x,y) q1(z) . (4.1.2) Is this physical real stuff or could things be complex? ρ1(x,y,z,t) = ρ1(x,y,z) ejω1t ρ1(x,y,z) = physical at some instant in time = real ? ρ1(x,y,z,ω) = ρ1(x,y,z) 2πδ(ω-ω1) But things often have phase depending on r.