0 E 2. The Hamiltonian for a three-level system is 0 0 0 where is positively real. E 0 0. a) What are the three eigenenergies and their corresponding eigenstates? (6 pts) b) If the system is initially in 1 time t? (2 pts) what is the probability for the system to remain in the same state after some c) If the system is initially in (0), what state is the system in at time t? (2 pts) Q2 2a) The eigenenergies are: 1 = 0, = -e and + -e, with corresponding eigenvectors: 2b) Probability is 1. 2c) 1 [vo) |v_) (+al 1 |S (t)) = = (eiet/h |v+) + eiet/h |\v_)). 2