From 0757e0c7df78173ac7022188fc350d4e2ad9f171 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= <marek@necada.org>
Date: Wed, 6 Sep 2017 21:33:38 +0000
Subject: [PATCH] =?UTF-8?q?dudopr=C3=A1ce?=
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Former-commit-id: 64d6207472cc3684e2e3564e0e212b27c9c11faf
---
 notes/radpower.lyx | 76 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)

diff --git a/notes/radpower.lyx b/notes/radpower.lyx
index d7b0a39..8ecf05c 100644
--- a/notes/radpower.lyx
+++ b/notes/radpower.lyx
@@ -567,6 +567,82 @@ generated
 \end_inset
 
 .
+ Quantities without such indices apply 
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+se vztahují
+\end_layout
+
+\end_inset
+
+ to the whole system, so 
+\begin_inset Formula $P$
+\end_inset
+
+ will now denote the total power generated by the system.
+ Now 
+\begin_inset Formula $\ket{a_{0}^{\sci k}}$
+\end_inset
+
+ is the expansion of the external driving field in the location of nanoparticle
+ 
+\begin_inset Formula $\sci k$
+\end_inset
+
+ and 
+\begin_inset Formula $\ket{a^{\sci k}}$
+\end_inset
+
+ is the expansion of the external field together with the fields scattered
+ from other nanoparticles,
+\begin_inset Formula 
+\[
+\ket{a^{\sci k}}=\ket{a_{0}^{\sci k}}+\sum_{\sci l\ne\sci k}S_{\sci k\leftarrow\sci l}\ket{f^{\sci l}}.
+\]
+
+\end_inset
+
+Rewriting 
+\begin_inset Formula $\ket{f^{\sci l}}=T^{\sci l}\ket{a^{\sci l}}$
+\end_inset
+
+, this gives the scattering problem in terms of 
+\begin_inset Formula $\ket{a^{\sci k}}$
+\end_inset
+
+,
+\begin_inset Formula 
+\[
+\ket{a^{\sci k}}=\ket{a_{0}^{\sci k}}+\sum_{\sci l\ne\sci k}S_{\sci k\leftarrow\sci l}T^{\sci l}\ket{a^{\sci l}}
+\]
+
+\end_inset
+
+or, in the indexless notation for the whole system
+\begin_inset Formula 
+\begin{eqnarray*}
+\ket a & = & \ket{a_{0}}+ST\ket a,\\
+\left(1-ST\right)\ket a & = & \ket{a_{0}}
+\end{eqnarray*}
+
+\end_inset
+
+ Alternatively, multiplication by 
+\begin_inset Formula $T$
+\end_inset
+
+ from the left gives the problem in terms of the outgoing wave coefficients,
+\begin_inset Formula 
+\begin{eqnarray*}
+\ket f & = & T\ket{a_{0}}+TS\ket f,\\
+\left(1-TS\right)\ket f & = & T\ket{a_{0}}.
+\end{eqnarray*}
+
+\end_inset
+
+
 \end_layout
 
 \end_body