English

Existence of a Unique Local Solution to the Many-body Maxwell-Schr\"odinger Initial Value Problem

Mathematical Physics 2014-02-18 v1 math.MP

Abstract

We study the many-body problem of charged particles interacting with their self-generated electromagnetic field. We model the dynamics of the particles by the many-body Maxwell-Schr\"odinger system, where the particles are treated quantum mechanically and the electromagnetic field is a classical quantity. We prove the existence of a unique local in time solution to this nonlinear initial value problem using a contraction mapping argument.

Keywords

Cite

@article{arxiv.1402.3680,
  title  = {Existence of a Unique Local Solution to the Many-body Maxwell-Schr\"odinger Initial Value Problem},
  author = {Kim Petersen},
  journal= {arXiv preprint arXiv:1402.3680},
  year   = {2014}
}