function [lambda, u, normu] = schroedinger(v, alpha, beta, L ,N)
   %Create Toeplitz
   sub = ones(N-1,1);
   main = -2* ones(N,1);
   toeplitz = diag(sub,-1) + diag(main, 0) + diag(sub,1);
   deltax = L/(N+1);

   schroed = (1/deltax^2) * toeplitz  -eye(N)*v';

   %Calculate lambda
   lam = eig(schroed);
   m = length(lam);
   lambda = lam((m-8):m);

   %Calculate u
   u = (schroed)\ lam;

   nor = zeros(N,1);
   for i = 1:N
       nor(i) = norm(u(i));
   end
   u = nor;


   normu = abs(u).^2;% -lam;
   %u = u - lam;


end