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Journal of Mathematical Physics

Dynamics of a multilevel Wigner-Weisskopf atom

E. B. Davies

Published Dec 1, 1974• 40 citations
Publisher

Abstract

We study the dynamics of an atom with a finite number of discrete energy levels weakly coupled to a continuum of energy levels, showing that any bound state undergoes a decay into the continuum which, in the limit as the coupling constant goes to zero, becomes rigorously exponential.
DOI
10.1063/1.1666578

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The eigenvalue problem for the dressed bound state of unstable multilevel systems is examined both outside and inside the continuum, based on the NNN-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.