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


\makeatletter












\makeatother


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

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\global\@topnum\z@
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}

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{#1 \vspace{1ex} \hrule width \columnwidth \vspace{1ex}}
}

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{
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\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 \( H_{0} \)
}

{\newpage
\clearpage
\samepage \( E=E_{0}=\hbar \omega _{0} \)
}

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

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

{\newpage
\clearpage
\samepage \( H_{0}=E_{0}|+><+|+E_{0}|-><-| \)
}

{\newpage
\clearpage
\samepage \( H_{0}=(E_{0}+(K=g_{e}\frac{|\mu _{e}|}{2}B_{0}))|+><+|+(E_{0}-K)|-><-| \)
}

{\newpage
\clearpage
\samepage \( |g\mu |=\hbar \omega _{12} \)
}

{\newpage
\clearpage
\samepage \( H'(t)=C(cos(\omega t)-isin(\omega t))|+><-|+C(cos(\omega t)+isin(\omega t))|-><+| \)
}

{\newpage
\clearpage
\samepage \( C=\frac{|g\mu |}{2}B_{1} \)
}

{\newpage
\clearpage
\samepage \( i\hbar (b_{-}'(t)|->+b_{+}'(t)|+>=Ce^{-i(\omega -\omega _{12})t}|+><-|+Ce^{i(\omega -\omega _{12})t}|-><+| \)
}

{\newpage
\clearpage
\samepage \( b_{-}=1 \)
}

{\newpage
\clearpage
\samepage \( b_{1}(t)=-2\iota C\frac{1}{\hbar (\omega -\omega _{12})}e^{-i(\omega -\omega _{12})t/2}sin((\omega -\omega _{12})t/2) \)
}

{\newpage
\clearpage
\samepage \( \frac{4C^{2}}{\hbar ^{2}(\omega -\omega _{12})^{2}}sin^{2}(\frac{\omega -\omega _{12}}{2}t) \)
}

{\newpage
\clearpage
\samepage \( sin^{2} \)
}

{\newpage
\clearpage
\samepage \( C^{2}t^{2}\frac{1}{\hbar ^{2}} \)
}

{\newpage
\clearpage
\samepage \( b_{i}(t)=c_{i}(t)e^{\mp (\omega -\omega _{12})t/2} \)
}

{\newpage
\clearpage
\samepage \( i\hbar c_{i}'=\mp (\delta =\frac{\omega -\omega _{12}}{2})c_{i}+C\epsilon _{ij}c_{j} \)
}

{\newpage
\clearpage
\samepage \( \lambda =\pm \hbar \sqrt{\frac{C^{2}}{\hbar ^{2}}+\delta ^{2}} \)
}

{\newpage
\clearpage
\samepage \( |\lambda _{+}>=cos(\theta )|+>+sin(\theta )|-> \)
}

{\newpage
\clearpage
\samepage \( |\lambda _{-}> \)
}

{\newpage
\clearpage
\samepage \( \theta =\frac{1}{2}atan(\frac{-C}{\hbar \delta }) \)
}

{\newpage
\clearpage
\samepage \( sin(\theta )cos(\theta )(e^{-i\lambda t/\hbar }-e^{i\lambda t/\hbar })e^{-i(\omega _{0}+\omega /2)t}|+> \)
}

{\newpage
\clearpage
\samepage \( +(sin^{2}(\theta )e^{-i\lambda t/\hbar }-cos^{2}(\theta )e^{i\lambda t/\hbar })e^{-i(\omega _{0}-\omega /2)t}|-> \)
}

{\newpage
\clearpage
\samepage \( P_{1}=\frac{\frac{C^{2}}{\hbar ^{2}}}{\frac{C^{2}}{\hbar ^{2}}+(\frac{w-w_{12}}{2})^{2}}sin^{2}(t\sqrt{\frac{C^{2}}{\hbar ^{2}}+(\frac{w-w_{12}}{2})^{2}}) \)
}


\end{document}
