%
% $BNL;RJ*M}3X(B : $B1i=,LdBj(B 6-2 $B2rEz(B
% $B%U%"%$%kL>(B : /home/edu/a-94e/y9410205/tex/quantum_physics/Q6-2.tex
% $B:n(B  $B@.(B  $B<T(B : y9410205 Yuzri Mohd Yusoff
% $B:n@.G/7nF|(B : /96/1/15
% $BEE;R%a!<%k(B : y9410205@edu.uec.ac.jp
%
\mondai
{y9410205 Yuzri Mohd Yusoff}
{96/1/15}
{y9410205@edu.uec.ac.jp}
{6-2}
{
%**********     $BLdBjJ,(B  ***************%
$B<!$NGH$NJ,;64X78$N72B.EY(B, $B0LAjB.EY$r(B $k$ $B$N4X?t$H$7$FI=$;!#(B 
\begin{eqnarray}
(a)\hspace{2mm} \omega(k)=\omega_oka, & (b)\hspace{2mm} \omega(k)=\omega_o(ka)^n, & (c)\hspace{2mm} \omega(k)=\omega_o\sin(ka) \nonumber
\end{eqnarray}
}
{
%**********  $B2sEz(B ****************%
(a)$B72B.EY(B
\[
v_g  =  \frac{\partial\omega}{\partial k} 
     =  \omega_oa
\]
$B0LAjB.EY(B
\[
v_p  =  \frac{\omega}{k} 
     =  \frac{\omega_oka}{k} = \omega_oa
\]
(b)$B72B.EY(B
\[
  v_g  =  \frac{\partial\omega}{\partial k} 
       =  \frac{\partial}{\partial k}\omega_ok^na^n  
       =  n\omega_ok^{n-1}a^n 
\]
$B0LAjB.EY(B
\[
  v_p  =  \frac{\omega}{k} 
       =  \frac{\omega_ok^na^n}{k}  
       =  \omega_ok^{n-1}a^n 
\]

(c)$B72B.EY(B
\[
  v_g  =  \frac{\partial\omega}{\partial k} 
       =  \frac{\partial}{\partial k}\omega_o\sin(ka)
       =  \omega_o\cos(ka)a
       =  \omega_oa\cos(ka)
\]
$B0LAjB.EY(B
\[
  v_p  =  \frac{\omega}{k}
       =  \frac{\omega_o\sin(ka)}{k}
\]
%********* $B2rEz=*(B *************%
}
