where H is the Hamiltonian of the system, ⟨ ⟨ A B ⟩ ⟩ t c = ⟨ ⟨ A B ⟩ ⟩ t − − ⟨ ⟨ A ⟩ ⟩ t ⟨ ⟨ B ⟩ ⟩ t are connected averages, and the quantum expectation values are taken over the time-dependent variational wave function, i.e., ⟨ ⟨ ⋯ ⋯ ⟩ ⟩ t ≡ ≡ ⟨ ⟨ Ψ Ψ ( t ) | ⋯ ⋯ | Ψ Ψ ( t ) ⟩ ⟩ .