Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix

Details Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix Jordan blocks and Gamow-Jordan eigenfunctions associated to a double pole of the S-matrix

2002-04-15

arxiv.org/abs/quant-ph/0204084v1

Phys.Rev.A67:022721,2003

Physics

Quantum Physics

Latex, 21 pages, 1 embedded eps figure, packages amsmath, graphicx

Scientific paper

10.1103/PhysRevA.67.022721

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.

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