% <PLAINTEXT>
% $BNL;RJ*M}3X(B $B!'(B $B1i=,LdBj(B 6-4 $B2rEz(B
% $B:n(B $B@.(B $B<T(B $B!'(B f9311196 $B?e8M(B $BOB9,(B
% $B=$@5<T(B : 240423G $B:4F#?.M5(B
% $B:n@.G/7nF|(B $B!'(B /96/02/20
% $B=$@5G/7nF|(B $B!'(B /02/11/28 
% $BEE;R%a!<%k(B $B!'(B f11196@ced.cas.uec.ac.jp
% $B=$@5<TEE;R%a!<%k(B : g240423@mail.ecc.u-tokyo.ac.jp
%
\mondai
{f9311196 $B?e8M(B $BOB9,(B}
{96/02/20}
{f11196@ced.cas.uec.ac.jp}
{6-4}
{
%----$BLdBjJ8(B----%
$B<0(B $ (6.23) $$B$r(B $BMQ$$$F!"<!$N%O%_%k%H%K%"%s$N1?F0J}Dx<0$r5a$a$h!#(B\\
\[ \begin{array}{lcl}
\displaystyle {\rm (a)} \hspace{2mm} H = \frac{p^{2}}{2m} +
\frac{k}{2}x^2, &
\displaystyle {\rm (b)} \hspace{2mm} H = \frac{p^{2}}{2m}, &
\displaystyle {\rm (c)} \hspace{2mm} H = \frac{p^{2}}{2m}
+ V_{0} \cos \left( \frac{x}{a} \right)
\end{array} \]
}
{
%----$B2rEzJ8(B---%
\[ \begin{array}{lcl}
\displaystyle \dot{p}
& = & \displaystyle -\frac{i}{\hbar}[p,H] \\
& = & \displaystyle -\frac{i}{\hbar}(pH-Hp) \\
& = & \displaystyle
-\frac{i}{\hbar}\left(-i\hbar\frac{d}{dx}H+Hp-Hp\right) \\
& = & \displaystyle -\frac{i}{\hbar}\left(-i\hbar\frac{d}{dx}H\right) \\
& = & \displaystyle -\frac{d}{dx}H
\end{array} \]
$B$rMQ$$$F2r$/!#(B\\
$ {\rm (a)} $
\[ \begin{array}{lcl}
\displaystyle \dot{p}
& = & \displaystyle -\frac{d}{dx}
\left(\frac{p^{2}}{2m}+\frac{k}{2}x^{2}\right) \\
& = & \displaystyle -\left(0+\frac{2k}{2}x\right) \\
& = & \displaystyle -kx
\end{array} \]
\\
$ {\rm (b)} $
\[ \begin{array}{lcl}
\displaystyle \dot{p}
& = & \displaystyle -\frac{d}{dx}\left(\frac{p^{2}}{2m}\right) \\
& = & 0
\end{array} \]
\\
$ {\rm (c)} $
\[ \begin{array}{lcl}
\displaystyle \dot{p}
& = & \displaystyle -\frac{d}{dx}
\left(\frac{p^{2}}{2m}+V_{0}\cos(\frac{x}{a})\right) \\
& = & \displaystyle 0+\frac{V_{0}}{a}\sin\left(\frac{x}{a}\right) \\
& = & \displaystyle \frac{V_{0}}{a}\sin(\frac{x}{a})
\end{array} \]
}




