Jordan blocks and Gamow-Jordan eigenfunctions associated to a double   pole of the S-matrix
  An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schroedinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wave functions of complex wave number. In this biorthonormal basis, any operator which is a regular function of the Hamiltonian is represented by a complex matrix which is diagonal except for a Jordan block of rank two. The occurrence of a double pole in the Green's function, as well as the non-exponential time evolution of the Gamow-Jordan generalized eigenfunctions are associated to the Jordan block in the complex energy representation. 
E. Hernandez (1), A. Jauregui (2) and A. Mondragon (1) ((1)Instituto   de Fisica, UNAM. Mexico, (2) Depto. de Fisica, U. de ...