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\makeatletter












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\begin{document}
\pagestyle{empty}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
{\newpage
\clearpage
\samepage \( \alpha =\frac{e^{2}}{\hbar c}\sim \frac{1}{137} \)
}

{\newpage
\clearpage
\samepage \( r_{e}=\frac{e^{2}}{mc^{2}} \)
}

{\newpage
\clearpage
\samepage \( \lambda =\frac{\hbar }{mc} \)
}

{\newpage
\clearpage
\samepage \( a_{0}=\frac{\hbar ^{2}}{me^{2}} \)
}

{\newpage
\clearpage
\samepage \( \frac{\lambda }{2}=\frac{\hbar ^{3}c}{me^{4}} \)
}

{\newpage
\clearpage
\samepage \( \beta \sim \alpha  \)
}

{\newpage
\clearpage
\samepage \( Ry=\frac{e^{2}}{2a_{0}}=13.6eV \)
}

{\newpage
\clearpage
\samepage \( Z^{2}Ry \)
}

{\newpage
\clearpage
\samepage \( \alpha ^{2}Ry \)
}

{\newpage
\clearpage
\samepage \( \frac{m_{e}}{M_{n}}\alpha ^{2}Ry \)
}

{\newpage
\clearpage
\samepage \( E_{n}=(n+\frac{1}{2})\hbar \omega  \)
}

{\newpage
\clearpage
\samepage \( \omega =(\frac{k}{AM})^{\frac{1}{2}} \)
}

{\newpage
\clearpage
\samepage \( \frac{e^{2}}{a^{3}} \)
}

{\newpage
\clearpage
\samepage \( \hbar \omega \sim (\frac{e^{2}\hbar ^{2}}{a^{3}AM})^{\frac{1}{2}}\sim (\frac{m}{AM})^{\frac{1}{2}}(\frac{a_{0}}{a})^{\frac{3}{2}}Ry \)
}

{\newpage
\clearpage
\samepage \( \frac{1}{10}eV \)
}

{\newpage
\clearpage
\samepage \( E_{j}=\frac{j(j+1)\hbar ^{2}}{2I} \)
}

{\newpage
\clearpage
\samepage \( I\sim AMa^{2} \)
}

{\newpage
\clearpage
\samepage \( \frac{\hbar ^{2}}{2I}\simeq (\frac{m}{AM})(\frac{a_{0}}{a})^{2}Ry \)
}

{\newpage
\clearpage
\samepage \( 10^{-3}eV \)
}

{\newpage
\clearpage
\samepage \( P=\frac{2(d'')^{2}}{3c^{3}} \)
}

{\newpage
\clearpage
\samepage \( P=\frac{2e^{2}v'^{2}}{3c^{3}} \)
}

{\newpage
\clearpage
\samepage \( d\sim ea \)
}

{\newpage
\clearpage
\samepage \( A\sim \frac{P}{\hbar \omega }\sim \frac{e^{2}a^{2}\omega ^{3}}{\hbar c^{3}} \)
}

{\newpage
\clearpage
\samepage \( 10^{9}/s \)
}

{\newpage
\clearpage
\samepage \( A\sim 10^{-6}/s \)
}

{\newpage
\clearpage
\samepage \( \frac{A}{\omega }\simeq \frac{e^{6}}{c^{3}\hbar ^{3}}=\alpha ^{3} \)
}


\end{document}
