Let $(U(a))_{a\in\mathbb R}$ and $(V(b))_{b\in\mathbb R}$ be strongly continuous one-parameter unitary groups on a separable [Hilbert space](/page/Hilbert%20Space) $H$ satisfying \begin{align*} U(a)V(b)=e^{iab\lambda}V(b)U(a) \end{align*} for all $a,b\in\mathbb R$, where $\lambda\in\mathbb R\setminus\{0\}$ is the fixed central character. If the representation is irreducible, then it is unitarily equivalent to the Schrödinger representation on $L^2(\mathbb R)$ with the same parameter $\lambda$; in physical units, $\lambda$ is identified with the Planck parameter after the chosen normalization of $Q$ and $P$.