标题： 一维麦克斯韦-薛定谔方程的束缚态 显示英文标题

标题： Bound States of the One-Dimensional Maxwell--Schrödinger Equations

摘要： 我们证明了一维空间中麦克斯韦-薛定谔方程组存在一个基态，该基态描述了在固定电荷影响下一定量的自由电荷。 对于一种情况（自由电荷和固定电荷相等，即中性原子），我们引入了一种新的四次巴拿赫空间，在该空间中哈密顿量自然具有强制性。 我们还表明，对于点电荷，对于任何使得基态存在的电荷比，基态都是对称且递减的。 显示英文摘要

摘要： 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.