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Abstract This paper discusses the mean-field limit for the quantum dynamics of N identical bosons in R³ R 3 interacting via a binary potential with Coulomb-type singularity. Our approach is based on the theory of quantum Klimontovich solutions defined in Golse and Paul (Commun Math Phys 369: 1021–1053, 2019). Our first main result is a definition of the interaction nonlinearity in the equation governing the dynamics of quantum Klimontovich solutions for a class of interaction potentials slightly less general than those considered in Kato (Trans Am Math Soc 70: 195–211, 1951). Our second main result is a new operator inequality satisfied by the quantum Klimontovich solution in the case of an interaction potential with Coulomb-type singularity. When evaluated on an initial bosonic pure state, this operator inequality reduces to a Gronwall inequality for a functional introduced in Pickl (Lett Math Phys 97: 151-164, 2011), resulting in a convergence rate estimate for the quantum mean-field limit leading to the time-dependent Hartree equation.
Porat et al. (Sat,) studied this question.