% Define constants and variables
n = 3;
Lx = 1;
hbar = 1;
m = 1;
k = @(n) n*pi/Lx;
w = hbar*k(n)^2/2*m;
A = sqrt(2/Lx);
x = linspace(0,Lx,200);
t = linspace(0,10,500);

% Define the position and time functions
psi = @(x,n) A.*sin(k(n)*x);
phi = @(t) exp(-1i.*w.*t);

% Make a .gif of the plots
filename = '1DParticle.gif';
for m = 1:3:length(t)
 plot(x, real(psi(x,n)*phi(t(m))))
 xlim([0 1])
 ylim([-1.5 1.5])
 title('$\psi(x)$ for $n = 3$','interpreter','latex')
 drawnow
 frame = getframe(1);
 im = frame2im(frame);
 [Q,map] = rgb2ind(im,256);
 if m == 1;
 imwrite(Q,map,filename,'gif','LoopCount',Inf,'DelayTime',1);
 else
 imwrite(Q,map,filename,'gif','WriteMode','append','DelayTime',1);
 end
end