hello
let's fix it
1/ had to remove the trailing end - there's simply no reason to have an "end" at the end of your code - probably a copy paste mistake.
2/ add the init of missing variable l (copy pasted from your other post Script has no errors, but no plot is given - MATLAB Answers - MATLAB Central (mathworks.com) ) - please put the correct value and definition if I'm wrong here
3/ corrected Theta computation - I believe there is no idx indexing involved in this code - or it's not defined on your side - i simply assumed you wanted to plot the entire array of eigenvalues vs theta.
% I added following lines
l = 1; % angular momentum quantum number
% Discretization parameters
theta_min = 0;
theta_max = pi;
M = 100; % Number of grid points
theta = linspace(theta_min, theta_max, M);
dtheta = theta(2) - theta(1);
% Initialize the Theta(theta) vector
Theta = zeros(M, 1);
% Set up the finite difference matrix
B = zeros(M, M);
for j = 3:M-2
B(j, j-2) = -1 / (2 * dtheta^3);
B(j, j-1) = 2 / (dtheta^3);
B(j, j) = -2 / (dtheta^3) + l * (l + 1);
B(j, j+1) = 2 / (dtheta^3);
B(j, j+2) = -1 / (2 * dtheta^3);
end
% Apply boundary conditions (example: Theta(0) = 0 and Theta(pi) = 0)
B(1,1) = 1;
B(M,M) = 1;
% Solve the eigenvalue problem
[~, D_theta] = eig(B);
% The eigenvalues are the diagonal elements of D_theta
eigenvalues_theta = diag(D_theta);
% The solution Theta(theta) corresponds to the eigenvector with the desired eigenvalue
%Theta = eig(:, idx); % NO !! eig is a function not a variable
% Theta = eigenvalues_theta(:, idx); % maybe but where is defined idx ??
Theta = eigenvalues_theta; % my 2 cents , just to make the code work here
% Plot the solution
plot(theta, Theta);
xlabel('theta');
ylabel('Theta(theta)');
title('Angular Wavefunction');
