Animate[
Manipulate[
A=1;
m=9.1*10^(-31);
(*Energy=1.6*10^(-19);*)
hbar=6.626*10^(-34);
k=(2*m*Energy/(hbar*hbar))^(1/2);
G=0;
(*alpha=5*10^(-28);*)
beta =m*alpha/(hbar*hbar*k);
SM = {{I*beta,1},{1,I*beta}};
{{B},{F}}=(1/(1-I*beta))*SM.{{A},{G}};
w=Energy/hbar;
w1=hbar*k*k/(2*m);
Plot[{Piecewise[{{Re[Exp[-I*(Energy/hbar)*t](A*Exp[I*((2*m*Energy/(hbar*hbar))^(1/2)*x)]+B*Exp[-I*((2*m*Energy/(hbar*hbar))^(1/2)*x)])],x<0},{Re[F*Exp[I*((2*m*(Energy)/(hbar*hbar))^(1/2)*x-(Energy/hbar)*t)]],x>0}}],Piecewise[{{Im[Exp[-I*(Energy/hbar)*t](A*Exp[I*((2*m*Energy/(hbar*hbar))^(1/2)*x)]+B*Exp[-I*((2*m*Energy/(hbar*hbar))^(1/2)*x)])],x<0},{Im[F*Exp[I*((2*m*(Energy)/(hbar*hbar))^(1/2)*x-(Energy/hbar)*t)]],x>0}}]},{x,-1*10^(-8),1*10^(-8)},PlotRange->{-2,2}]
,{{Energy,2*10^(-19)},1*10^(-19),3*10^(-19),0.1*10^(-19)},{alpha,1*10^(-28),5*10^(-27),1*10^(-28)}],{t,0,1*10^(-13)},AnimationRunning->False]