% Matlab file to produce movies of time evolution for problems 2.a. and b.
% in homework assignment 5.

npts = 500;	% The actual number of points in one more than this.
nterms = 20;
x = (0:npts)/npts;
n = (1:nterms)';
ratioenergies = (n.*n)';
angle = pi*n*x;
basis = sqrt(2)*sin(angle);

coefstep = 2*(1 - cos(pi*(n')/2))./(pi*(n'));

figure(1)
time = 0:0.001:1;
for counter = 1:length(time),
coefstepn = coefstep.*exp(-i*ratioenergies*2*pi*time(counter));
psin = coefstepn*basis;
plot(x,abs(psin).^2)
axis([0 1 0 5])
title('Homework 5, Problem 2.a.')
pause(0.1)
end

figure(2)
time = 0:0.01:1;
for counter = 1:length(time),
densn = 0.5*(basis(1,:).^2 + basis(2,:).^2 + 2*cos(2*pi*time(counter))*basis(1,:).*basis(2,:));
plot(x,densn)
axis([0 1 0 5])
title('Homework 5, Problem 2.b.')
pause(0.1)
end