Double resonances and Jordan block spectra

Metastable states are associated with discrete complex eigenvalues of the Hamiltonian in the analytically continued spaces of quantum mechanics formulated in dual spaces. The necessary modifications when two resonances approach each other and coincide are discussed and illustrated in some exactly soluble models. The Hamiltonian no longer can be diagonalized completely but can be reduced to a Jordan block form. The duals are identified and a resolution of unity established. Some remarks are made about secular terms in the survival amplitude.