(20 points) A simple model for the ammonia molecule NH3 is as follows. The three H nuclei are in a plane and the N nucleus is at some fixed clistance either above (labelled as A ) or below (B) the plane of the H nuclei. Here A and B are two orthogonal, normalized kets. The Hamiltonian of the molecule H=E0[AA+BB]+[AB+BA]. (a) Find the eigenvalues of H and the corresponding eigenkets in terms of A and B. (b) Initially, at t=0, the N nucleus is above the H plane, i.e. the molecule is in state A. What is the probability for observing the N nucleus below the H plane at time t=/2