chi_vs_phi_comparison.m

theta = pi/2;
mu = 0;
alpha = 1;
k = 25;
omega = 25;
time = 2;
N = 1;
mesh = .01;
step = 1/mesh;
L = 1;

times = (0:mesh:time)+1e-6;
space = (mu-2:mesh:mu+2);

for t = 1:length(times)
    psiFrame = NaN(size(space));
    chiSumFrame = NaN(size(space));
    transportFrame = NaN(size(space));
    chiFrame = NaN(size(space));
    
    for i = 1:length(space)
        psi = psiPlus(times(t),space(i),theta,alpha,k,mu,omega,step,L);
        phi = phiPlus(times(t),space(i),theta,alpha,k,mu,omega,step);
        transport = -phiPlus(times(t)-L+space(i),L,theta,alpha,k,mu,omega,step);

        psiFrame(i) = abs(psi).^2;
        chiSumFrame(i) = abs(psi-phi-transport).^2;
        transportFrame(i) = abs(transport).^2;
        chiFrame(i) = abs(psi-phi).^2;
    end
    hold on
    plot(space,psiFrame)
    plot(space,chiSumFrame)
    plot(space,transportFrame)
    plot(space,chiFrame)
    xlim([space(1) space(length(space))])
    ylim([0 .4])
    xlabel('position')
    legend({'psi','chiSum','transport','chi'},'Location','southwest');
    M(t) = getframe;
    hold off
    clf
end