Metastable states in strongly coupled quantum systems with continuous spectra

Abstract

The problem of constructing metastable states in strongly coupled quantum systems whose spectra are continuous is treated within the context of the general perturbation method developed by Van Hove. The state is constructed in terms of the unperturbed states and its metastable character is proved without explicitly introducing the perturbed stationary states. An interesting feature of the result is that the construction of the state requires the use of a complex number, the real part of which is equal to the energy of the state while its imaginary part is juch larger than the line width of the state. The general result is applied to the Fermi gas and the Lee model. In the latter case it reduces to the result previously obtained by Glaser and Källén.