Degeneracy of Resonances, Jordan Blocks, and Gamow–Jordan Eigenfunctions

Abstract

We show that a degeneracy of resonances is associated with a second rank pole in the scattering matrix and a Jordan chain of generalized eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in complex resonance energy eigenfunctions. In this biorthonormal basis, any operator f(H r \(\overline B\) which is a regular function of the Hamiltonian is represented by a nondiagonal complex matrix with a Jordan block of rank 2.