3. The states of a two-state system are represented by the orthogonal kets, |1) and 2). In

this basis, the Hamiltonian for the system may be written as

(a) (10 points) Are [1) and 2) eigenstates of Ĥ? If so, what are their eigenenergies?

If not, then express the eigenstates of Ĥ in terms of |1) and 2).

(b) (5 points) Write down the time-dependent Schrödinger equation for this system.

(c) (15 points) The system initially is in the state (0)) = (1) + |2)) at time t = 0.

At a later time, t, it is in another superposition, (t))