Mutual transformation among bound, virtual and resonance states in one-dimensional rectangular potentials

2008/10/19 by M. Kawasaki, Kawasaki, M., T. Maehara +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #quant-ph

paper · pdf · doi:10.48550/arxiv.0810.3368

12 pages, 2 Fig's (each has 6 figures)

arxiv created 2008/10/19 · openalex publication_date 2008/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A detailed analysis has been made by R.Zavin and N.Moiseyev(2004 J. Phys. A: Math, Gen, 37 4619) for the change of bound states into resonance states via coalescence of virtual states in a one-dimensional symmetric rectangular attractive potential as it becomes shallow, with convergent wave functions of virtual and resonance states by the complex scaling method. As a complement to such an analysis, we discuss some global features of the pole spectrum of the S-matrix by using a complex extension of the real potential V^(real) to e^iαV^(real) with a real phase α. We show the structures of trajectories of poles developed for the change of α in the complex momentum plane, which is useful to understand the mutual transformation among the bound, virtual and resonance states.

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