%<PLAINTEXT>
%$BNL;RJ*M}3X!!(B:$B!!1i=,LdBj(B10-4$B2rEz(B
%$B:n@.<T!!(B    :$B!!(B250237G$B!!J?Ln2m5,(B
%$B:n@.G/7nF|!!(B:  2002/12/1
%$BEE;R%a!<%k!!(B:$B!!(Bg250237@mail.ecc.u-tokyo.ac.jp
 \mondai {250237G$B!!J?Ln2m5,(B}
{2002/12/17}
{g250237@mail.ecc.u-tokyo.ac.jp}
{10-4} {$B@5(B6$B3Q7A$NC:AG%/%i%9%?!<$G!"86;R(B2$B$N&R50F;(B$\varphi_{i}(i=1,2,3)$$B$K$*$1(B
$B$k:.@.50F;$N(B$2s,2p_x,2p_y$$B86;R50F;$N78?t$r5a$a$h!#(B}
{
$B652J=q(Bp.131$B$N?^(B10.5$B$K$*$$$F9M$($k!#(B$sp^2$$B:.@.50F;$K$*$$$F$O!"(B3$B$D$N&R7k9g$N$?(B
$B$a$N50F;$,$G$-!"&R7k9g$N%(%M%k%.!<$,:G$bF@$i$l$k$h$&$K!"50F;$O86;R$,?-$S$kJ}(B
$B8~$K:n$i$l$k$N$G!"86;R(B2$B$G$O(B1$BHVL\$H(B3$BHVL\$NJ}8~$K?-$S$k50F;$,:n$i$l$k!#=>$C(B
$B$F!"86;R$N50F;$,5,3JD>8r2=$9$k>r7o$r9MN8$KF~$l!"86;R(B2$B$N(B$sp^2$$B50F;$O!"<!$NGH(B
$BF04X?t$N7A$GI=$5$l$k!#(B
\begin{eqnarray}
\varphi_1 &=& C_1|2s >-\sqrt{1-{C_1}^2}|2p_x > $B!!(B\nonumber \\
\varphi_2 &=& C_2|2s>+\sqrt{1-{C_2}^2} \displaystyle{\left( \frac{1}{2}|2p_x
>+\frac{\sqrt3}{2}|2p_y > \right)}  \nonumber \\
\varphi_3 &=& C_3|2s >+C_4|2p_x >+C_5|2p_y >
\end{eqnarray}
$B$3$3$G!"GHF04X?t$N5,3JD>8r2=>r7o(B$<\varphi_i|\varphi_j> = \delta_{ij} $$B$H%f%K(B
$B%?%j!<$J4X78(B$|\varphi_1|^2+$ ${\displaystyle{|\varphi_2|^2+|\varphi_3|^2 =
\left|  |2s > \right|^2+\left|  |2p_x > \right|^2+ \left|  |2p_y >
\right|^2}}$$B$h$j!"(B

\[
 \left.
\begin{array}{l}
\displaystyle{C_1 C_2 -\frac{1}{2}\sqrt{1-C_1^2}\sqrt{1-C_2^2}=0} \\
\displaystyle{C_1 C_3 - \sqrt{1-C_1^2}C_4=0} \\
\displaystyle{C_2 C_3 +
\frac{1}{2}C_4\sqrt{1-C_2^2}+\frac{\sqrt3}{2}\sqrt{1-C_2^2}C_5=0} \\
\displaystyle{C_1^2+C_2^2+C_3^2=1} \\
\displaystyle{(1-C_1^2)+\frac{(1-C_2^2)}{4}+C_4^2=1} \\
\displaystyle{\frac{3(1-C_2^2)}{4}+C_5^2=1}
 \end{array}
\right.
\]
$B$3$l$r2r$/$H(B${\displaystyle{C_1=
C_2=C_3=\frac{1}{\sqrt3},C_4=\frac{1}{\sqrt6},C_5=-\frac{1}{\sqrt2}}}$$B$H$J(B
$B$k!#(B
}

