% <PLAINTEXT>
% $BNL;RJ*M}3X(B $B!'(B $B1i=,LdBj(B 7-2 $B2rEz(B
% $B:n(B  $B@.(B  $B<T(B $B!'(B f9311196 $B?e8M(B $BOB9,(B
% $B:n@.G/7nF|(B $B!'(B /96/02/20
% $BEE;R%a!<%k(B $B!'(B f11196@ced.cas.uec.ac.jp
%
\mondai
{f9311196 $B?e8M(B $BOB9,(B}
{96/02/20}
{f11196@ced.cas.uec.ac.jp}
{7-2}
{
%----$BLdBjJ8(B----%
$ 7.1 $ $B$N7k2L$G(B $ x \rightarrow 1 $ $B$N6K8B$r$H$k$H!"(B
$(7.13) $ $B!"(B$ (7.19) $ $B$N<0$N$=$l$>$l$NF)2a3NN((B $ T $ $B$NCM$,F1$8$K$J$k!#(B
$B$3$N6K8BCM$r(B $ \alpha = 2ma^{2}V_{0} / \hbar^{2} $ $B$rMQ$$$FI=$;!#(B \\
}
{
%----$B2rEzJ8(B---%
$ (7.13) $ $B<0$K$D$$$F9M$($k!#(B$ E < V_{0} $ $B$N$H$-$NF)2a3NN((B $ T $ $B$O!"(B
\begin{equation}
 T  = \displaystyle \frac{4x(1-x)}{\sinh^{2} \sqrt{\alpha(1-x)}+ 4x(1-x)}  
\end{equation}
$B$3$N<0$rJQ7A$9$k$H!"(B\\
\begin{equation}
 T = \displaystyle \frac{4}{A + 4}
\end{equation}
\begin{equation}
 A = \displaystyle \frac{\sinh^{2} \sqrt{\alpha(1-x)}}{x(1-x)} \label{eq:7-2-3}
\end{equation}
$B$H$J$k!#(B$ 1-x = u $ $B$HCV$/$H!"(B $ (7-2-3) $ $B<0$O<!$N$h$&$K$J$k!#(B\\
\begin{equation}
 A = \displaystyle \frac{ \sinh^{2}\sqrt{\alpha u}}{u(1-u)}
\end{equation}
$B$3$3$G!"(B$  u \rightarrow 0 $ $B$N6K8B$r$H$k$H!"(B
$ \displaystyle \lim_{u \rightarrow 0}\sinh^{2}\sqrt{\alpha u} = \alpha u $
$B$h$j!"(B\\
\begin{equation}
\begin{array}{lcl}
 \displaystyle \lim_{u \rightarrow 0} A
& = & \displaystyle \lim_{u \rightarrow 0}\frac{\alpha u}{u(1-u)} \\
& = & \displaystyle \alpha
\end{array}
\end{equation}
$B$H$J$j!"F)2a3NN((B $ T $ $B$O!"(B\\
\begin{equation}
 T = \displaystyle \frac{4}{\alpha +4}
\end{equation}
\\
$B$H$J$k!#F1MM$K!"(B$ (7.19) $ $B<0$K$D$$$F9M$($k!#(B$ E > V_{0} $ 
$B$N$H$-$NF)2a3NN((B $ T $ $B$O!"(B
\begin{equation}
 T  = \displaystyle \frac{4x(x-1)}{\sin^{2} \sqrt{\alpha(x-1)}+ 4x(x-1)}  
\end{equation}
$B$3$N<0$rJQ7A$9$k$H!"(B\\
\begin{equation}
 T = \displaystyle \frac{4}{B + 4}
\end{equation}
\begin{equation}
 B = \displaystyle \frac{\sin^{2} \sqrt{\alpha(x-1)}}{x(x-1)} \label{eq:7-2-9}
\end{equation}
$B$H$J$k!#(B$ x-1 = u $ $B$HCV$/$H!"(B $ (7-2-9) $ $B<0$O<!$N$h$&$K$J$k!#(B\\
\begin{equation}
 B = \displaystyle \frac{ \sin^{2}\sqrt{\alpha u}}{u(u+1)}
\end{equation}
$B$3$3$G!"(B$  u \rightarrow 0 $ $B$N6K8B$r$H$k$H!"(B
$ \displaystyle \lim_{u \rightarrow 0}\sin^{2}\sqrt{\alpha u} = \alpha u $
$B$h$j!"(B\\
\begin{equation}
\begin{array}{lcl}
 \displaystyle \lim_{u \rightarrow 0} B
& = & \displaystyle \lim_{u \rightarrow 0}\frac{\alpha u}{u(u+1)} \\
& = & \displaystyle \alpha
\end{array}
\end{equation}
$B$H$J$j!"F)2a3NN((B $ T $ $B$O!"(B\\
\begin{equation}
 T = \displaystyle \frac{4}{\alpha +4}
\end{equation}
$B$H$J$k!#(B
}
