% <PLAINTEXT>
%
% $BNL;RJ*M}3X(B $B!'(B $B1i=,LdBj(B 7-7 $B2rEz(B
% $B:n(B  $B@.(B  $B<T(B $B!'(B 240916J $B9b>k(B $B=E9((B
% $B=$!!@5!!<T(B $B!'(B 241025B $B;32<!!??(B
% $B:n@.G/7nF|(B $B!'(B /02/10/22
% $B=$@5G/7nF|(B $B!'(B /02/12/19
% $BEE;R%a!<%k(B $B!'(B g240916@mail.ecc.u-tokyo.ac.jp
% $B=$@5<TEE;R%a!<%k(B $B!'(B g241025@mail.ecc.u-tokyo.ac.jp
%
% \mondai{$B:n@.<T(B}{$B:n@.G/7nF|(B}{$BEE;R%a!<%k(B}{$BLdBjHV9f(B}{$BLdBjJ8(B}{$B2rEz(B}
%
\mondai
{241025B $B;32<!!??(B}
{/02/12/19}
{g241025@mail.ecc.u-tokyo.ac.jp}
{7-7}
{
%----$BLdBjJ8(B----%
$B%]%F%s%7%c%k(B$V(x)$$B$,BP>N$G6v4X?t$N>l9g(B$(V(-x)=V(x))$$B!"B+G{>uBV$NG$0U$NGHF04X?t$O6v4X?t$J$k$"$kGHF04X?t$H4q4X?t$J$k$"$kGHF04X?t$H$NOB$G$"$k!#$3$N>l9gE>Aw9TNs$O!"(B$x>0$B!J$^$?$O(Bx<0$B!K(B$$B$NItJ,$@$19M$($l$PNI$$$3$H$r@bL@$;$h!#(B
}
{
%----$B2rEzJ8(B---%
$B$I$s$JGHF04X?t$b6vGHF04X?t$H4qGHF04X?t$NOB$KJ,2r$5$l$k$3$H$,(B\(V(-x)=V(x)\)$B$+$i$o$+$k!#$b$7$=$N6vGHF04X?t$H4qGHF04X?t$,Dj?tG\$r$N$>$$$F0l0U$KDj$^$k$J$i$P!"G$0U$NGHF04X?t$rM?$($kI=<0(B\(\varphi=a\varphi_1+b\varphi_2\)(\(\varphi_1\)$B$O6v4X?t$G(B\(\varphi_2\)$B$O4q4X?t!"(B$a,b$$B$O5,3J2=>r7o$rK~$?$9$h$&$KA*$P$l$?Dj?t(B)$B$rF@$k$3$H$K$J$k!#6v4X?t$K$7$F$b4q4X?t$K$7$F$b!"(B$0<x$$B$K$*$1$k5sF0$,M?$($i$l$l$P$8$e$&$V$s$G$"$k!#$h$C$F!"GHF04X?t$r6v4X?t$^$?$O4q4X?t$G$"$k$H2>Dj$7!"$=$l$i$,(B$0\leq x$$B$K$*$$$FDj?tG\$r$N$>$-0l0U$KDj$^$k$3$H$r<($9!#(B\\
$BNN0h(B\(0<x\)$B$K$*$1$k%]%F%s%7%c%k$r3,CJ>u$K6a;w$7$F!"(B$-x_0<x<x_0$$B$K$*$$$F$O(B$V(x)=V_0$$B!"(B\(x_{n-1}<x<x_n\;n=1,2,\cdots\)$B$K$*$$$F$O(B$V(x)=V_n$$B$G0lDj$H$9$k!#GHF04X?t$O(B$k_n=\left.\sqrt{2m(E-V_n)}\right/\hbar$$B$rMQ$$$F!"(B
\begin{displaymath} 
\varphi_0(x)=A_0e^{ik_0x}+B_0e^{-ik_0x}\;(-x_0<x<x_0)
\end{displaymath} 
\begin{displaymath} 
\varphi_n(x)=A_ne^{ik_nx}+B_ne^{-ik_nx}\;(x_{n-1}<x<x_n)
\end{displaymath} 
$B$H$J$k!#GHF04X?t$,6v4X?t$J$i$P!"86E@$N<~$j$N(B$-x_0<x<x_0$$B$G$9$G$K6v4X?t$G$J$1$l$P$J$i$J$$$N$G(B$A_0=B_0$$B$H$J$j!"4q4X?t$J$i$PF1MM$K$7$F(B$A_0=-B_0$$B$H$J$k!#(B$x=x_n$$B$K$*$1$k6-3&>r7o$O(B
\begin{displaymath}
M_n(x)=\left( \begin{array}{cc} 
	 e^{ik_nx} & e^{-ik_nx} \\
	 ik_ne^{ik_nx} & -ik_ne^{-ik_nx} 
\end{array} \right)
\end{displaymath}
$B$H$7$F!"(B
\begin{displaymath}
M_n(x_n)\left( \begin{array}{c} 
	 A_n  \\
	 B_n
\end{array}\right)
=M_{n+1}(x_n)\left( \begin{array}{c} 
	 A_{n+1}  \\
	 B_{n+1}
\end{array}\right) 
\end{displaymath}
$B$H=q$+$l$k!#(B$J_n(x)=M_{n+1}(x)^{-1}M_n(x)$$B$H$7$F!"(B
\begin{eqnarray*}
\left(\begin{array}{c} 
	 A_n\\
	 B_n
\end{array}\right) 
&=&J_{n-1}(x_{n-1})\left( \begin{array}{c} 
	 A_{n-1}\\
	 B_{n-1}
\end{array}\right)\\
&=&J_{n-1}(x_{n-1})J_{n-2}(x_{n-2})\cdots J_0(x_0)\left(\begin{array}{c} 
	 A_0 \\
	 B_0
\end{array}\right)
\end{eqnarray*}
$B$O$8$a$K(B$B_0=A_0$$B$^$?$O(B$B_0=-A_0$$B$r2>Dj$7$F$$$?$+$i!"$3$l$O$9$Y$F$N(B$A_n,B_n$$B$,(B$A_0$$B$NDj?tG\$H$7$FDj$^$k$3$H$r<($7$F$$$k!#$D$^$j!"6v4X?t$^$?$O4q4X?t$G$"$k$h$&$JGHF04X?t$ODj?tG\$r$N$>$$$F0l0U$KDj$^$k!#:#9M$($F$$$k%]%F%s%7%c%k$K$*$1$k!"G$0U$NGHF04X?t$O$3$l$i$+$iDj?tG\$HOB$K$h$C$F@8@.$5$l$k!#(B
}
