Consider a system whose initial state ∣ψ(0)⟩ and Hamiltonian are given by
∣ψ(0)⟩=51304,H=300005050.
(a) If a measurement of the energy is carried out, what values would 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?