delt = .01;
endt = input('End time?');
mindelx = input('What is the smallest delta x you wish to test for?');
maxdelx = input('What is the largest?');
deldelx = input('What is the spacing between delta Xes?');
delx = [.001 mindelx:deldelx:maxdelx];
delxmesh = size(delx,2);
m = 1;
figure
while m<delxmesh+1;
t = 0:delt:endt;
tmesh=size(t,2);
a = 5.1;
x = -a:delx(m):a;
s = 10;
spread = 0;

k = s:(spread+s);
vr = .6;
xmesh = size(x,2);
j = 1:xmesh;
p = 1:xmesh;
ymin = -1;
ymax = 1;
d = ones(1,xmesh);
e = ones(xmesh,1);
pot = x.^2;
e = ones(xmesh,1);
K = spdiags([-e (2+(delx(m)^2)*pot').*e -e], -1:1, xmesh, xmesh);
c=delt/delx(m)^2;
sigma=.3;
K(xmesh,1) = -1;
K(1,xmesh) = -1;
A = zeros(xmesh,(spread+1));
nv = ones((spread+1),1);
fc = zeros((spread+1),1);

    
    n=1;
    u = (2/(pi*sigma^2))^.25.*exp(-(x).^2/(sigma^2)).*(exp(i*(k+vr).*x)+exp(i*(k-vr).*x));

    while n<tmesh;
    y = (abs(u)).^2;
    subplot(3,1,1); plot(x,[real(u); imag(u)])
    axis([-a a ymin ymax])
    set(gca,'xtick',[-10:2:10])
    subplot(3,1,2); plot(x,y)
    set(gca,'xtick',[-10:2:10])
    axis([-a a 0 2*ymax])
    u = ((speye(xmesh) + .5i*c.*K)*((speye(xmesh) - .5i*c.*K)\(u')))';
    n = n + 1;
    text(0,1.5,sprintf('t=%g',t(n)));
    drawnow
end
q = 1:delxmesh;
q(m)=sum(u);
m = m+1;
pause
end
hold on
subplot(3,1,3); plot(delx,q)