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 Schrödinger 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.
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Hernández, E., Jáuregui, A. & Mondragón, A. Degeneracy of Resonances, Jordan Blocks, and Gamow-Jordan Eigenfunctions. International Journal of Theoretical Physics 42, 2167–2190 (2003). https://doi.org/10.1023/B:IJTP.0000005953.43759.c7
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DOI: https://doi.org/10.1023/B:IJTP.0000005953.43759.c7