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arXiv · 1402.3680

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

Kim Petersen
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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.

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Kim Petersen. 2014-02-15. Existence of a Unique Local Solution to the Many-body Maxwell-Schr\"odinger Initial Value Problem. https://arxiv.org/abs/1402.3680

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