Let | ψ ψ S ( t ) ⟩ ⟩ = e − − i H S t / ℏ ℏ | ψ ψ ( 0 ) ⟩ ⟩ be the time-dependent state vector in the Schrödinger picture. A state vector in the interaction picture, | ψ ψ I ( t ) ⟩ ⟩ , is defined with an additional time-dependent unitary transformation.