Alternatively, by Stone's theorem one can state that there is a strongly continuous one-parameter unitary map U (t) : H → H such that | ψ ψ ( t + s ) ⟩ = U ( t ) | ψ ψ ( s ) ⟩ for all times s, t. The existence of a self-adjoint Hamiltonian H such that U ( t ) = e − − ( i / ℏ ℏ ) t H is a consequence of Stone's theorem on one-parameter unitary groups. It is assumed that H does not depend on time and that the perturbation starts at t 0 = 0 ; otherwise one must use the Dyson series, formally written as U ( t ) = T [ exp ⁡ ⁡ ( − − i ℏ ℏ ∫ ∫ t 0 t d t ′ H ( t ′ ) ) ] , where T is Dyson's time-ordering symbol.