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

Journal Article · Sat Feb 01 04:00:00 EST 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.022721· OSTI ID:20633733

Hernandez, E; Mondragon, A ^[1]; Jauregui, A ^[2]

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1. Instituto de Fisica, UNAM, Apartado Postal 20-364, 01000 Mexico D.F. (Mexico)
2. Departamento de Fisica, Universidad de Sonora, Apartado Postal 1626, Hermosillo, Sonora (Mexico)

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 Schroedinger 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{sub r}{sup (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.

• OSTI ID: 20633733
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 67; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGEBRA
EIGENFUNCTIONS
EIGENVALUES
ENERGY LEVELS
EVOLUTION
GREEN FUNCTION
HAMILTONIANS
JOST FUNCTION
S MATRIX
SCATTERING
SCHROEDINGER EQUATION
WAVE FUNCTIONS