氢原子Stark哈密顿量共振团簇的半经典Szego极限
Semiclassical Szego limit of resonance clusters for the hydrogen atom Stark Hamiltonian
摘要：
研究了弱场极限下氢原子与斯塔克电场作用下的共振团簇的加权平均。我们证明了共振团簇的半经典的Synth型定理，表明共振位移的极限分布集中在对应于氢原子哈密顿量的重标本征值的经典能量表面上。这一结果扩展了本征值集群的Synth型结果共振集群。本文的工作有两个新的特点：第一，对共振团簇的研究需要使用非自伴算符;第二，Stark微扰是无界的，因此可以利用氢原子本征值对应的相干态的局域化性质来控制Stark微扰。
英文摘要：
We study the weighted averages of resonance clusters for the hydrogen atom with a Stark electric field in the weak field limit. We prove a semiclassical Szego-type theorem for resonance clusters showing that the limiting distribution of the resonance shifts concentrates on the classical energy surface corresponding to a rescaled eigenvalue of the hydrogen atom Hamiltonian. This result extends Szego-type results on eigenvalue clusters to resonance clusters. There are two new features in this work: first, the study of resonance clusters requires the use of non self-adjoint operators, and second, the Stark perturbation is unbounded so control of the perturbation is achieved using localization properties of coherent states corresponding to hydrogen atom eigenvalues.
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