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\begin{center}
$BNL;RNO3X#21i=,(B No.7 (01/6/14)
\end{center}
\bigskip
\begin{enumerate}

\item
 $B#3=`0L7O$N%O%_%k%H%K%"%s9TNs(B
 \begin{eqnarray*}
  \left(\matrix{E^{(0)}_1 & 0 & \lambda a \cr 
 0 & E^{(0)}_1 & \lambda b \cr 
\lambda a^* & \lambda b^* & E^{(0)}_2}
 \right)
 \end{eqnarray*}
 $B$r9M$($k(B($\lambda$ $B$O<B?t(B)$B!#@]F0$N$J$$LdBj(B $(\lambda =0)$
 $B$KBP$9$k%(%M%k%.!<8GM-CM$K=LB`$,$"$k$3$H$KCm0U$7$F0J2<(B
$B$NLd$$$KEz$($h!#(B
 \begin{enumerate}
 \item
  $B%O%_%k%H%K%"%s$r87L)$KBP3Q2=$7!"%(%M%k%.!<8GM-CM(B$E_1, 
E_2,E_3$$B$r5a$a$h!#(B
  \label{EXACT}
 \item
  $\lambda^2 (|a|^2 + |b|^2) \ll |E^{(0)}_1-E^{(0)}_2|^2$$B$r2>Dj$7$F!"(B
$BF1$8LdBj$r@]F0O@$rMQ$$$F2r$-!"%(%M%k%.!<8GM-CM$r#2<!(B
  $B$^$G5a$a$h!#(B
  \label{APPROX}
 \item
  \ref{APPROX}$B$N7k2L$r(B\ref{EXACT}$B$G5a$a$?87L)$J7k2L$HHf3S$;$h!#(B
 \end{enumerate}


\item $B%/!<%m%s%]%F%s%7%c%k$G5-=R$5$l$k?eAG86;R$r9M$($k!#(B
 \begin{enumerate}
 \item $B<gNL;R?t(B$n=2$$B$N>uBV$N=LB`$NMM;R$r<($;!#(B
 \item $B$3$N7O$K0lMM$J(Bz$BJ}8~$NEE>l(B$E$$B$r$+$1$k$H%]%F%s%7%c%k$H$7$F(B
       $V_E=-ezE$$B$,%O%_%k%H%K%"%s$KIU$12C$o$k!#(B
       $n=2$$B$N>uBV$N6u4V$G$N(B$V_E$$B$N9TNsMWAG$r5a$a$h!#(B
 \item $V_E$$B$K$h$k@]F0$G$I$N$h$&$K(B$n=2$$B$N>uBV$N=LB`$,$H$1$k$+(B
       $B<($;!#(B(Stark$B8z2L(B)
 \item $B<B:]$N?eAG86;R$G$O(B$2s$$B!"(B$2p$$B$N>uBV$O%/!<%m%s%]%F%s%7%c%k0J30$N(B
       $B8z2L$K$h$j=LB`$7$F$$$J$$!#>e$N7W;;$O$I$N$h$&$J$H$-$KE,MQ$G$-$k$+!#(B
 \end{enumerate}

\item $B%O%_%k%H%K%"%s$,(B
      \[
        H_0=\frac{p_x^2}{2m}+\frac{p_y^2}{2m}+\frac{m\omega^2}{2}(x^2+y^2)
      \]
      $B$GM?$($i$l$k(B2$B<!85$NEyJ}D4OB?6F0;R$r9M$($k!#(B
 \begin{enumerate}
 \item $BDc$$J}$+$i(B3$BHVL\$^$G$N>uBV$N%(%M%k%.!<$r5a$a$h!#=LB`$OB8:_$9$k$+!#(B
 \item $B<!$K@]F0(B\ $V=\delta m\omega^2xy$\ $B$r$+$1$?$H$9$k!#(B
       $B$?$@$7$3$3$G(B\ $\delta$\ $B$O(B1$B$h$j$:$C$H>.$5$$L5<!85$N<B?t$H$9$k!#(B
       $B>e$G5a$a$?(B3$B$D$N>uBV$N$=$l$>$l$KBP$7$F!"@]F0$N(B1$B<!$NJd@5$r2C$($?(B
       $B%(%M%k%.!<$r5a$a$h!#(B
 \item $B%O%_%k%H%K%"%s$,(B\ $H_0+V$\ $B$GM?$($i$l$k7O$O<B$O87L)$K2r$1$k!#(B
       $B>e$N(B3$B$D$N>uBV$KBP1~$9$k87L)$J%(%M%k%.!<8GM-CM$r5a$a!">e$N7k2L$H(B
       $BHf3S$;$h!#(B($B%R%s%H!'A4%O%_%k%H%K%"%s$O(B$x$$B$H(B$y$$B$NF~$l$+$($KBP$7$F(B
       $BITJQ$G$"$k!#(B)
 \end{enumerate}

\end{enumerate}
\end{document}


