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arXiv · 1608.02637

Bound States of the One-Dimensional Maxwell--Schr\"odinger Equations

Richard Chapling
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Abstract

We prove the existence of a ground state of the Maxwell--Schr\"odinger equations in one spatial dimension, describing a specified amount of free charge under the influence of a fixed charge. For one case (equal free and fixed charge, i.e., a neutral atom), we introduce a new type of quartic Banach space, in which the Hamiltonian is naturally coercive. We also show that for a point charge, for any ratio of charge such that the ground state exists, it is symmetric and decreasing.

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Richard Chapling. 2016-08-08. Bound States of the One-Dimensional Maxwell--Schr\"odinger Equations. https://arxiv.org/abs/1608.02637

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