%% ================ 2.2 ====================
V = @(x) 0;

L = 1;
alpha = 0;
beta = 0;
N = 499;

x = zeros(1,N);
for i = 1:N
    x(i) = (i*L)/(N+1);
end

vec = V(x);

[vector, lambda] = schroedinger(vec, alpha, beta, L, N);

%% plot error
for i = 3:N
    [vector,lamda]=schroedinger(vec,alpha,beta,L,i);
    for k = 1:3
        error(k,i-2) = norm(lamda(k)+(k*pi)^2);
    end
end

figure
loglog(error(1,:),'r')
hold on
loglog(error(2,:),'b')
loglog(error(3,:),'g')
grid on

%% nonzero
%V = @(x) 0;
%V = @(x) 700 * (1/2 - abs(x-1/2));
V = @(x) 800 * (sin(pi*x)).^2;

L = 1;
alpha = 0;
beta = 0;
N = 499;

x = zeros(1,N);
for i = 1:N
    x(i) = (i*L)/(N+1);
end

vec = V(x);

[lambda, u, normu] = schroedinger(vec, alpha, beta, L, N);

%plot wave function
figure
plot(x, u)

%plot probability density

% nor = zeros(N,1);
% for i = 1:N
%     nor(i) = norm(u(i))^2;
% end

figure
plot(x, normu);