Consider a general quantum mechanical system. This system has the Hamiltonian H 0 . Let the initial state of the system be the pure state | n ⟩ ⟩ . If we now add a time-dependent perturbation to this Hamiltonian, say H ′ ( t ) , the full Hamiltonian is H ( t ) = H 0 + H ′ ( t ) and hence the system will evolve in time under the full Hamiltonian. In this section, we will see how time evolution actually works in quantum mechanics.