3. The following boundary value problem is used in quantum mechanics to describe 7r electrons in conjugated linear molecules: _ (MW) (13:2 where a: is position, L is the length of the molecule. = 12%(2); 2M0) = ML) = 0 (3) a) Show that the eigenvalues are discrete. b) Find the eigenfunctions. c) Show that any two eigenfunctions, 1/)\"(w) and 1pm($), satisfy: fownawmam = {