% Here we start with the wave function of leftside.m (constant for x < 0.5
% and zero otherwise and then time evolve by including the proper phase
% factors.  At each step in time |psi|^2 is plotted.

nterms = 4; % Number of terms kept in the series.

n = 1:nterms;
c = (1 - cos(pi*0.5*n))*2./(pi*n);

x = 0:0.001:1;

tmax = 2*pi; % This is the maximum time kept because after this the 
             % wave function repeats.

ntime = 100; % number of time steps

for tcounter = 0:ntime,

   t = tcounter*tmax/ntime;
   psi = 0*x;

   for counter = 1:nterms,
      psi = psi + c(counter)*sqrt(2)*sin(pi*counter*x)*exp(-i*counter^2 * t);
   end

   plot(x,abs(psi).^2)
   xlabel('x')
   ylabel('|psi|^2')

pause(0.5);
end