Let $d \ge 1$ and let $u_{\mathrm{in}} \in L^1(\mathbb{R}^d)$. The solution $u(t) = e^{it\Delta}u_{\mathrm{in}}$ of the free Schrödinger equation $i\partial_t u + \Delta u = 0$ satisfies
\begin{align*} \|e^{it\Delta}u_{\mathrm{in}}\|_{L^\infty(\mathbb{R}^d)} \le \frac{C_d}{|t|^{d/2}}\|u_{\mathrm{in}}\|_{L^1(\mathbb{R}^d)}, \qquad t \ne 0, \end{align*}
where $C_d = (4\pi)^{-d/2}$.