L=3;W=3;
H=kron(eye(L),diag(ones(1,W-1),1)+diag(ones(1,W-1),-1))+...
  kron(diag(ones(1,L-1),1)+diag(ones(1,L-1),-1),eye(W));
psi=zeros(L*W,1);psi(1)=1;
pos=2;
tv=[0];Nv=[abs(psi(pos)).^2]; dt=0.1; U=expm(-1i*H*dt);
for run=1:10/dt
    tv=[tv;tv(end)+dt];
    psi=U*psi;
    Nv=[Nv;abs(psi(pos)).^2];
    figure(1),plot(tv,Nv),drawnow
end