In this paper, we define a quantum analogue of the notion of empirical measure in the classical mechanics of $N$-particle systems. We establish an equation governing the evolution of our quantum analogue of the $N$-particle empirical measure, and we prove that this equation contains the Hartree equation as a special case. Our main application of this new notion to the mean-field limit of the $N$-particle Schrödinger equation is an $O(1/\sqrt{N})$ convergence rate in some appropriate dual Sobolev norm for the Wigner transform of the single-particle marginal of the $N$-particle density operator, uniform in $\hbar\in(0,1]$ (where $\hbar$ is the Planck constant) provided that $V$ and $(−∆)^{3+d/2}V$ have integrable Fourier transforms.