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An accidental degeneracy of resonances gives rise to a double pole in thescattering matrix, a double zero in the Jost function and a Jordan chain oflength two of generalized Gamow-Jordan eigenfunctions of the radialSchroedinger equation. The generalized Gamow-Jordan eigenfunctions are basiselements of an expansion in bound and resonant energy eigenfunctions plus acontinuum of scattering wave functions of complex wave number. In thisbiorthonormal basis, any operator which is a regular function of theHamiltonian is represented by a complex matrix which is diagonal except for aJordan block of rank two. The occurrence of a double pole in the Green'sfunction, as well as the non-exponential time evolution of the Gamow-Jordangeneralized eigenfunctions are associated to the Jordan block in the complexenergy representation.Comment: Latex, 21 pages, 1 embedded eps figure, packages amsmath, graphic

Jordan blocks and Gamow-Jordan eigenfunctions associated with a degeneracy of unbound states