(f) Consider the x-component of the spin angular momentum operator for S 1/2 particles 力101 2 (i) Find the eigenvalues and normalised eigenvectors of S*. (4 marks) (ii) Do these eigenvectors form a basis for the Hilbert space of S 1/2 spins (i.e., is this set of eigenvectors complete and orthonormal)? (4 marks) (ii) Construct the matrix U formed from the normalized eigenvectors of S”. Verify that U is unitary and show that it satisfies the relation 시 0 What are the values λ1 and λ2? (4 marks)