diff --git a/notes/Scattering and Shit.lyx b/notes/Scattering and Shit.lyx index 554a94c..9e4afa1 100644 --- a/notes/Scattering and Shit.lyx +++ b/notes/Scattering and Shit.lyx @@ -1,5 +1,5 @@ -#LyX 2.0 created this file. For more info see http://www.lyx.org/ -\lyxformat 413 +#LyX 2.1 created this file. For more info see http://www.lyx.org/ +\lyxformat 474 \begin_document \begin_header \textclass report @@ -16,13 +16,13 @@ \font_roman TeX Gyre Pagella \font_sans default \font_typewriter default +\font_math auto \font_default_family default \use_non_tex_fonts true \font_sc false \font_osf true \font_sf_scale 100 \font_tt_scale 100 - \graphics default \default_output_format pdf4 \output_sync 0 @@ -44,15 +44,24 @@ \pdf_pdfusetitle true \papersize a5paper \use_geometry true -\use_amsmath 1 -\use_esint 1 -\use_mhchem 1 -\use_mathdots 1 +\use_package amsmath 1 +\use_package amssymb 1 +\use_package cancel 1 +\use_package esint 1 +\use_package mathdots 1 +\use_package mathtools 1 +\use_package mhchem 1 +\use_package stackrel 1 +\use_package stmaryrd 1 +\use_package undertilde 1 \cite_engine basic +\cite_engine_type default +\biblio_style plain \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false +\justification true \use_refstyle 1 \index Index \shortcut idx @@ -583,6 +592,46 @@ Definition [K](2.4.6); \end_layout +\begin_layout Subsection +Kristensson vs. + Xu +\end_layout + +\begin_layout Standard +As in +\begin_inset CommandInset citation +LatexCommand cite +after "eq. (36)" +key "xu_calculation_1996" + +\end_inset + + with unnormalised Legendre polynomials: +\begin_inset Formula +\begin{eqnarray*} +\left(\vect{u/v/w}\right)_{1lm} & = & \left(\mbox{CS}\right)^{m}\sqrt{\frac{2l+1}{4\pi}\frac{\left(l-m\right)!}{\left(l+m\right)!}}\frac{\vect N_{ml}^{(3/1/4)}}{\sqrt{l\left(l+1\right)}}\\ +\left(\vect{u/v/w}\right)_{1lm} & = & \left(\mbox{CS}\right)^{m}\sqrt{\frac{2l+1}{4\pi}\frac{\left(l-m\right)!}{\left(l+m\right)!}}\frac{\vect M_{ml}^{(3/1/4)}}{\sqrt{l\left(l+1\right)}} +\end{eqnarray*} + +\end_inset + +where CS is +\begin_inset Formula $-1$ +\end_inset + + in Kristensson's text. + N.B. + be careful about the translation coefficients and +\begin_inset CommandInset citation +LatexCommand cite +after "eq. (81)" +key "xu_calculation_1996" + +\end_inset + +, Xu's text is a bit confusing. +\end_layout + \begin_layout Subsection Relation between Kristensson and Taylor \begin_inset CommandInset label @@ -1245,7 +1294,7 @@ Quantisation of quasistatic modes of a sphere \begin_layout Standard \begin_inset CommandInset bibtex LatexCommand bibtex -bibfiles "Electrodynamics" +bibfiles "Electrodynamics,/home/mmn/repo/qpms/Electrodynamics" options "plain" \end_inset