Juerg Froehlich, Antti Knowles, Simon Schwarz
On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
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ABSTRACT. In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of ``observables'', thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a ``semi-classical'' limit.