%<PLAINTEXT>
% 
% $BNL;RJ*M}3X(B : $B1i=,LdBj(B 11-1 $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 $BMNJe(B}
{01/12/25}
{g140826@mail.ecc.u-tokyo.ac.jp}
{11-1}
{
2$B<!85$N@5J}3J;R(B($B@5J}7A$rC10LK&$H$9$k3J;R(B)$B$N4pK\3J;R%Y%/%H%k$r!"(B
$\vec {a}_1=(a,0) ,\vec {a}_2=(0,a)$$B$H$*$/$3$H$,$G$-$k!#(B
$B$3$N$H$-5U3J;R%Y%/%H%k(B$\vec {b}_1 ,\vec {b}_2$$B$r5a$a$h!#(B
$B%V%j%k%"%sNN0h$r<($;!#$^$?!"%(%M%k%.!<%P%s%I$rI=<($9$k$H$9$l$P!"(B
$B$I$NBP>N@~$K$=$C$FIA$1$PNI$$$+!#(B
}
{
$B5U3J;R%Y%/%H%k(B$\vec {b}_1 ,\vec {b}_2 $$B$r(B
\begin{equation}
\vec {b}_1 = \left( {{\begin{array}{*{20}c}
 {b_{1x} } \hfill \\
 {b_{1y} } \hfill \\
\end{array} }} \right)
\end{equation}
\begin{equation}
\vec {b}_2 = \left( {{\begin{array}{*{20}c}
 {b_{2x} } \hfill \\
 {b_{2y} } \hfill \\
\end{array} }} \right)
\end{equation}
$B$H$*$/!#(B$\vec {a}_1 ,\vec {a}_2 ,\vec {b}_1 ,\vec {b}_2 $$B$r(B(11.7)$B<0(B
\begin{equation}
\vec {a}_i \cdot \vec {b}_j = 2\pi \delta _{ij} 
\end{equation}
$B$KBeF~$9$k$H!"(B
\begin{equation}
\vec {a}_1 \cdot \vec {b}_1 = a b_{1x} = 2\pi 
\end{equation}
\begin{equation}
\vec {a}_1 \cdot \vec {b}_2 = a b_{2x} = 0
\end{equation}
\begin{equation}
\vec {a}_2 \cdot \vec {b}_1 = a b_{1y} = 0
\end{equation}
\begin{equation}
\vec {a}_2 \cdot \vec {b}_2 = a b_{2y} = 2\pi 
\end{equation}
$B$H$J$j!"$3$l$r2r$$$F!"(B
\begin{equation}
b_{1x} = \frac{2\pi }{a}
\end{equation}
\begin{equation}
b_{1y} = 0
\end{equation}
\begin{equation}
b_{2x} = 0
\end{equation}
\begin{equation}
b_{2y} = \frac{2\pi }{a}
\end{equation}
$B$,F@$i$l$k!#8N$K5U3J;R%Y%/%H%k(B$\vec {b}_1 ,\vec {b}_2 $$B$O!"(B
\begin{equation}
\vec {b}_1 = \frac{2\pi }{a}\left( {{\begin{array}{*{20}c}
 1 \hfill \\
 0 \hfill \\
\end{array} }} \right)
\end{equation}
\begin{equation}
\vec {b}_2 = \frac{2\pi }{a}\left( {{\begin{array}{*{20}c}
 0 \hfill \\
 1 \hfill \\
\end{array} }} \right)
\end{equation}
$B$H$J$k!#%V%j%k%"%sNN0h$O!"(B$\vec {b}_1 ,\vec {b}_2 $
$B$GD%$i$l$k@5J}7A$G$"$k!#(B
$B$^$?!"%(%M%k%.!<%P%s%I$rI=<($9$k$K$O!"$=$N@5J}7A$ND:E@$N$R$H$D$r(BX$B!"(B
$BCf?4$r(B$\Gamma $$B!"(BX$B$r4^$`JU$NCf?4$N$R$H$D$r(BM$B$H$7$?$H$-!"(BX
$ \to \Gamma  \to $M$ \to $X$B$N=g$KIA$1$P$h$$!#(B
}
