\batchmode
%
\documentclass[12pt,letterpaper,oneside,onecolumn]{article}
\makeatletter
\usepackage[]{fontenc}
\usepackage[dvips]{epsfig}


\makeatletter












\makeatother


\pagestyle{plain}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}

\def\LyX{L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\spacefactor1000}

\newcommand {\lyxtitle}[1] {\thispagestyle{empty}
\global\@topnum\z@
\section*{\LARGE \centering \sffamily \bfseries \protect#1 }
}

\newcommand {\lyxline}[1]{
{#1 \vspace{1ex} \hrule width \columnwidth \vspace{1ex}}
}

\newenvironment {lyxbibliography}
{
\begin{thebibliography}{99}}
{\end{thebibliography}}

\def\lxq{"}

\newenvironment {lyxcode}
{\list{}{
\rightmargin\leftmargin
\raggedright
\itemsep 0pt
\parsep 0pt
\ttfamily
}\item[]
}
{\endlist}

\newcommand {\lyxlabel}[1]{#1 \hfill}

\newenvironment {lyxlist}[1]
{\begin{list}{}
{\settowidth{\labelwidth}{#1}
\setlength{\leftmargin}{\labelwidth}
\addtolength{\leftmargin}{\labelsep}
\renewcommand  {\makelabel}{\lyxlabel}}}
{\end{list}}

\newcommand {\lyxletterstyle}{
\setlength\parskip{0.7em}
\setlength\parindent{0pt}
}

\newcommand {\lyxaddress}[1]{
\par {\raggedright #1 
\vspace{1.4em}
\noindent\par}
}

\newcommand {\lyxrightaddress}[1]{
\par {\raggedleft \begin{tabular}{l}\ignorespaces
#1
\end{tabular}
\vspace{1.4em}
\par}
}

\newcommand {\lyxformula}[1]{
\begin{eqnarray*}
#1
\end{eqnarray*}
}

\newcommand {\lyxnumberedformula}[1]{
\begin{eqnarray}
#1
\end{eqnarray}
}

\makeatother
\newenvironment{tex2html_wrap}{}{}
\newwrite\lthtmlwrite
\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}%
\newbox\sizebox
\begin{document}
\pagestyle{empty}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
{\newpage
\clearpage
\samepage \( <r_{i}|qU(r_{j})|r_{i}'>=qU(r_{j})\delta (r_{i}-r_{i}') \)
}

{\newpage
\clearpage
\samepage \( \nabla ^{2}U(r)=0 \)
}

{\newpage
\clearpage
\samepage \( qU(r_{i})=\sum _{l=0}^{\infty }\sum _{m=-l}^{l}c_{lm}f_{lm}(r)Y_{lm}(\widehat{r}) \)
}

{\newpage
\clearpage
\samepage \( Y_{lm}(\widehat{r}) \)
}

{\newpage
\clearpage
\samepage \( Q_{m}^{(l)}(r_{i})=q\sqrt{\frac{4\pi }{2l+1}}r^{l}Y_{lm}(\widehat{r}) \)
}

{\newpage
\clearpage
\samepage \( Q_{0}^{(0)}=Q+total \)
}

{\newpage
\clearpage
\samepage \( Q^{(1)}_{i}=Q_{1}^{(1)}|11>+Q_{0}^{(1)}|10>+Q_{-1}^{(1)}|1-1>=D_{i} \)
}

{\newpage
\clearpage
\samepage \( \nabla ^{2}U(r)=4\pi \rho (r_{i}) \)
}

{\newpage
\clearpage
\samepage \( r^{l}\rightarrow j_{l}(r) \)
}

{\newpage
\clearpage
\samepage \( \begin{array}{cccc}
Identify & l=0 & l=1 & l=2\\ 
c_{lm} & U_{o} & c_{l\pm 1,0}\rightarrow \nabla ^{i}U=-E^{i} & c_{2m}\\ 
Q^{(0)} & \sum q_{n}=Q_{tot} & Q_{\pm 1,0}^{(1)}\rightarrow \sum _{n}q_{n}r_{n}^{i}=D^{i} & Q_{m}^{(2)}\\ 
qU & Q_{tot}U_{0} & -qE_{i}r^{i}=-E_{i}D^{i} & c_{2m}Q_{m}^{(2)}
\end{array}
 \)
}

{\newpage
\clearpage
\samepage \( c_{2m}Q_{m}^{(2)}=\frac{1}{2}\sum _{ij}\nabla ^{i}\nabla ^{j}U|_{r=0}\sum _{n=1}^{N}q_{n}x_{n}^{i}x_{n}^{j} \)
}

{\newpage
\clearpage
\samepage \( Q_{ij}=Q_{ji}=3x_{i}x_{j}-r^{2}\delta _{ij} \)
}

{\newpage
\clearpage
\samepage \( c_{lm}\rightarrow 0 \)
}

{\newpage
\clearpage
\samepage \(>\)
}

{\newpage
\clearpage
\samepage \( <Q_{m}^{(l)}>=0 \)
}

{\newpage
\clearpage
\samepage \(<\)
}

{\newpage
\clearpage
\samepage \( <Q>=0 \)
}


\end{document}
