Consider a system which is initially in a state ∣ψ(0)⟩ and having a Hamiltonian H^, where
∣ψ(0)⟩=4−i−2+5i3+2i,H=210i0−i33030.
(a) If a measurement of H is carried out, what values will we obtain and with what probabilities?
(b) Find the state of the system at a later time t; you may need to expand ∣ψ(0)⟩ in terms of the eigenvectors of H.
(c) Find the total energy of the system at time t=0 and any later time t; are these values different?
(d) Does H^ form a complete set of commuting operators?