For every self-adjoint operator $H_{\rm op}$ on a complex [Hilbert space](/page/Hilbert%20Space) $H$, there is a strongly continuous unitary group $(U(t))_{t\in\mathbb R}$ given by \begin{align*} U(t)=e^{-itH_{\rm op}}. \end{align*} Conversely, every strongly continuous unitary group arises in this way from a unique self-adjoint generator.