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% $BNL;RJ*M}3X(B : $B1i=,LdBj(B 8-2 $B2rEz(B
% $B:n(B  $B@.(B  $B<T(B : g140826 $B?eLn!!MNJe(B 
% $B:n@.G/7nF|(B : /01/12/25
% $BEE;R%a!<%k(B : g140826@mail.ecc.u-tokyo.ac.jp
%
% \mondai{$B:n@.<T(B}{$B:n@.G/7nF|(B}{$BEE;R%a!<%k(B}{$BLdBjHV9f(B}{$BLdBjJ8(B}{$B2rEz(B}
%
\mondai
{g140826 $B?eLn(B $BMNJe(B}
{01/12/25}
{g140826@mail.ecc.u-tokyo.ac.jp}
{8-2}
{2$B<!85$NL58B$K9b$$0f8M$NLdBj$N8GM-CM(B(8.14)$B$G!"(B$a=b$$B$N$H$-$N%(%M%k%.!<8GM-CM$N=L=EEY$,(B
$B#3=E$d#4=E$K$J$k>l9g$,$"$k$+!#$"$k$J$i#1$DNc$r<($;!#(B}
{
(8.14)$B<0(B
\begin{equation}
E_{n\ell} = \frac{\hbar ^2\pi ^2}{2m}\left( {\frac{n^2}{a^2} + \frac{\ell^2}{b^2}} 
\right)
\end{equation}
$B$K(B$a = b$$B$rBeF~$9$k$H!"(B
\begin{equation}
E_{n\ell} = \frac{\hbar ^2\pi ^2}{2m}\left( {\frac{n^2}{a^2} + \frac{\ell^2}{a^2}} 
\right) = \frac{\hbar ^2\pi ^2}{2m}\left( {\frac{n^2 + \ell^2}{a^2}} \right)
\end{equation}
$B$H$J$k$N$G!"(B$n^2 + \ell^2$$B$NCM$NBg>.$G!"%(%M%k%.!<8GM-CM$rI>2A$9$k$3$H$,$G$-$k!#(B
$B$?$@$7!"(B$n,\ell$$B$O$=$l$>$l<+A3?t$G$"$k!#(B

$B$3$3$G!"=L=EEY$,#3$G$"$k$H$O!"$"$kCM(B$M$$B$,0[$J$k(B$(n,\ell)$$B$K$h$C$F(B$M = n^2 + \ell^2$$B$N7A$G(B
$B#3DL$j$KI=$5$l$k$H$$$&$3$H$J$N$G!"Nc$($P!"(B$M = 50$$B$N$H$-$N(B
\begin{equation}
(n,\ell) = (1,7),(7,1),(5,5)
\end{equation}
$B$,5s$2$i$l$k!#F1MM$K=L=EEY$,#4$H$J$k$N$O!"(B$M = 625$$B$N$H$-$N(B
\begin{equation}
(n,\ell) = (20,15),(15,20),(7,24),(24,7)
\end{equation}
$B$,5s$2$i$l$k!#(B
}
