Abstract
We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter β. When β=0, there is an eigenstate ψ0; when β ≠ 0, ψ0 ‘dissolves’ into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.
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This work was partially supported by NSF Grant DMS-8922941