RESONANCES, METASTABLE STATES AND EXPONENTIAL DECAY LAWS IN PERTURBATION-THEORY

Resonances which appear as perturbed bound states are discussed in the framework of Balslev-Combes theory. The corresponding metastable states are constructed using the formal perturbation expansion to order N-1 for the (nonexistent) perturbed bound states. They are shown to have exponential decay in time governed by the complex resonance energies, up to a background of order 2 N in the perturbation parameter. The results apply in lowest order N=1 to the perturbation of bound states embedded in the continuum and in arbitrary order to cases like the Stark effect. © 1990 Springer-Verlag.