Let $H_0=-\frac{\hbar^2}{2m}\Delta$ on $L^2(\mathbb R^3)$ and let $V \in C_c^\infty(\mathbb R^3;\mathbb R)$. Then the wave operators $\Omega_\pm$ exist. Their ranges are contained in the absolutely continuous spectral subspace $\mathcal H_{\mathrm{ac}}(H)=P_{\mathrm{ac}}(H)L^2(\mathbb R^3)$. The scattering subspace is \begin{align*} \mathcal H_{\mathrm{scatt}}(H)=\operatorname{Range}(\Omega_-)+\operatorname{Range}(\Omega_+)\subseteq \mathcal H_{\mathrm{ac}}(H), \end{align*} and on this subspace the wave operators implement the comparison between free and interacting dynamics.