Journal
PHYSICAL REVIEW A
Volume 67, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.67.022721
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An accidental degeneracy of unbound states gives rise to a double pole in the scattering matrix, a double zero in the Jost function, and a Jordan chain of length 2 of generalized Gamow-Jordan eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound- and resonant-state energy eigenfunctions plus a continuum of scattering wave functions of a complex wave number. In this biorthonormal basis, any operator f(H-r((l))) which is a regular function of the Hamiltonian is represented by a complex matrix that is diagonal except for a Jordan block of rank 2. 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 with the Jordan block in the complex energy representation.
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