Implement some of Javier's notes.

Former-commit-id: 3881eccd2bbca4975d50c4a749751b7c134d6698

lepaper/finite.lyx

@@ -481,7 +481,11 @@ The single-particle scattering problem at frequency
 \end_inset
 
 .
- Inside this volume, the electric field can be expanded as
+ Inside 
+\begin_inset Formula $\openball 0{R^{>}}\backslash B_{0}\left(R\right)$
+\end_inset
+
+, the electric field can be expanded as
 \begin_inset Note Note
 status open
 
@@ -770,7 +774,7 @@ literal "false"
 
  its (maximum) refractive index.
 \begin_inset Note Note
-status open
+status collapsed
 
 \begin_layout Plain Layout
 \begin_inset Formula 
@@ -1281,7 +1285,7 @@ In practice, the multiple-scattering problem is solved in its truncated
 \begin_inset Formula $l\le L_{p}$
 \end_inset
 
-, laeving only 
+, leaving only 
 \begin_inset Formula $N_{p}=2L_{p}\left(L_{p}+2\right)$
 \end_inset
 
@@ -1428,11 +1432,7 @@ Let
 
 \end_inset
 
-where an explicit formula for the (regular) 
+where an explicit formula for the regular translation operator 
-\emph on
-translation operator
-\emph default
- 
 \begin_inset Formula $\tropr$
 \end_inset
 
@@ -1547,7 +1547,7 @@ reference "eq:regular vswf translation"
 , 
 \begin_inset Formula 
 \[
-\vect E\left(\vect r,\omega\right)=\sum_{\tau,l,m}\rcoeffptlm p{\tau}lm\sum_{\tau'l'm'}\tropr_{\tau lm;\tau'l'm'}\left(k\left(\vect r_{q}-\vect r_{p}\right)\right)\vswfrtlm{\tau'}{l'}{m'}\left(\vect r-\vect r_{q}\right)
+\vect E\left(\vect r,\omega\right)=\sum_{\tau,l,m}\rcoeffptlm p{\tau}lm\sum_{\tau'l'm'}\tropr_{\tau lm;\tau'l'm'}\left(k\left(\vect r_{q}-\vect r_{p}\right)\right)\vswfrtlm{\tau'}{l'}{m'}\left(k\left(\vect r-\vect r_{q}\right)\right)
 \]
 
 \end_inset
@@ -1579,7 +1579,12 @@ reference "eq:regular vswf coefficient translation"
 
 \end_inset
 
-(note the reversed indices; TODO redefine them in 
+(note the reversed indices
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+; TODO redefine them in 
 \begin_inset CommandInset ref
 LatexCommand eqref
 reference "eq:regular vswf translation"
@@ -1593,7 +1598,12 @@ reference "eq:singular vswf translation"
 
 \end_inset
 
-? Similarly, if we had only outgoing waves in the original expansion around
+?
+\end_layout
+
+\end_inset
+
+) Similarly, if we had only outgoing waves in the original expansion around
  
 \begin_inset Formula $\vect r_{p}$
 \end_inset

lepaper/infinite.lyx

@@ -329,6 +329,16 @@ noprefix "false"
 
 \begin_layout Standard
 As in the case of a finite system, eq.
+ 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:Multiple-scattering problem unit cell"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
  can be written in a shorter block-matrix form,
 \begin_inset Formula 
 \begin{equation}
@@ -526,7 +536,17 @@ noprefix "false"
 \begin_inset Formula $\left|\vect k\right|=\sqrt{\epsilon\mu}\omega/c_{0}$
 \end_inset
 
- (modulo lattice points; TODO write this a clean way).
+ (modulo reciprocal lattice points
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+TODO write this in a clean way
+\end_layout
+
+\end_inset
+
+).
  A somehow challenging step is to distinguish the different bands that can
  all be very close to the empty lattice approximation, especially if the
  particles in the systems are small.

lepaper/symmetries.lyx

@@ -98,11 +98,11 @@ If the system has nontrivial point group symmetries, group theory gives
 \end_layout
 
 \begin_layout Standard
-As an example, if our system has a 
+As an example, if the system has a 
 \begin_inset Formula $D_{2h}$
 \end_inset
 
- symmetry and our truncated 
+ symmetry and the corresponding truncated 
 \begin_inset Formula $\left(I-T\trops\right)$
 \end_inset
 
@@ -961,7 +961,7 @@ where
 \begin_inset Formula $1$
 \end_inset
 
- through 
+ to 
 \begin_inset Formula $d_{n}$
 \end_inset
 
@@ -969,7 +969,7 @@ where
 \begin_inset Formula $i$
 \end_inset
 
- goes from 1 through the multiplicity of irreducible representation 
+ goes from 1 to the multiplicity of irreducible representation 
 \begin_inset Formula $\Gamma_{n}$
 \end_inset