function [xtU] = pot(n,xmin,xmax,potent,B,s,T,wrap)

% parameters ..........
dt = .0001;   %time step
k = 10;        %wave number
c = 2;          %width
% .................

dx = (xmax-xmin)/n;
x = xmin + (1:n)'*dx;           %x is col vector

V = zeros(1,n);

if potent == 0;                 %no potential. potent = 0
    x0 = 2;
else
   if potent == 1;
       for a = floor(5*n/12):floor(7*n/12)
           x0 = xmin + 5*n/8*dx + 3;       %displacement
           V(a) = s;
       end
   else
       %x0 = 0;
       %V = s*x.^2;
   end
end

a = -1/(dx)^2 - V/2;
b = 1/(2*dx^2);

% creation of K the sparse matrix
D = sparse(1:n,1:n,a,n,n);
E = sparse(2:n,1:n-1,b*ones(1,n-1),n,n);
E(1,n) = wrap*b;
K = E+D+E';

U = c*sech(c*(x-x0)).*exp(-1i*k*x);
I = speye(n,n);           % keeps everything sparse 
t = 0;

%using CN scheme in paper...
Uold = U;
Unew = zeros(n,1);
modT = 10;
xtU = zeros(n,(T + modT*dt)/(modT*dt));     %records U as time goes on

while t < T
  if (mod(floor(t/dt),modT)==0)
    plot(x, [U.*conj(U) real(U) imag(U)], x, V);
    axis([xmin xmax -1 5]);
    text(1,1, sprintf('t=%g, prob=%g', t, dx*dot(U,U)));
    drawnow;
  end
    xtU(:,floor(t/(modT*dt) + 1)) = U.*conj(U);
    Unew = (I - 1i*dt*K)\((I + 1i*dt*K)*U - B*1i*dt*(3/2*conj(U).*U.*U - 1/2*conj(Uold).*Uold.*Uold));
    Uold = U;
    U = Unew;
    t = t + dt;
end