Let $(U_t)_{t\in\mathbb R}$ be a strongly continuous one parameter unitary group on a complex [Hilbert space](/page/Hilbert%20Space) $H$. There exists a unique self-adjoint operator $A$ such that \begin{align*} U_t=e^{-itA} \end{align*} for all $t\in\mathbb R$, where $e^{-itA}$ is defined by the [Borel functional calculus](/theorems/2696) for the self-adjoint operator $A:D(A)\subset H\to H$.