不稳定多能级系统的边界态本征能
Bound-state eigenenergy outside and inside the continuum for unstable multilevel systems
摘要：
基于描述离散能级与连续谱耦合的N能级Friedrichs模型，研究了不稳定多能级系统的束缚态特征值问题.它示出的束缚态本征能总是存在于每个位于连续体之外的离散能级之下。进一步地，通过逐渐加强耦合，连续谱中每个分立能级对应的本征能最终显现出来。另一方面，证明了在弱但有限的耦合制度，每个形状因子，确定之间的某些特定的水平和连续的过渡不消失，在该能级内的连续的本征能量的情况下。并将其应用于氢原子与电磁场相互作用的自发发射过程。
英文摘要：
The eigenvalue problem for the dressed bound-state of unstable multilevel systems is examined both outside and inside the continuum, based on the N-level Friedrichs model which describes the couplings between the discrete levels and the continuous spectrum. It is shown that a bound-state eigenenergy always exists below each of the discrete levels that lie outside the continuum. Furthermore, by strengthening the couplings gradually, the eigenenergy corresponding to each of the discrete levels inside the continuum finally emerges. On the other hand, the absence of the eigenenergy inside the continuum is proved in weak but finite coupling regimes, provided that each of the form factors that determine the transition between some definite level and the continuum does not vanish at that energy level. An application to the spontaneous emission process for the hydrogen atom interacting with the electromagnetic field is demonstrated.
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