Work

Bound states in the continuum and time evolution of the generalized eigenfunctions

Year: 2018

Type: article

Abstract: We study the Jost solutions for the scattering problem of a von Neumann-Wigner type potential, constructed by means of a two times iterated and completely degenerated Darboux transformation. We show that for a particular energy the unnormalizedJost solutions coalesce to give rise to a Jordan cycle of rank two. Performing a pole decomposition of the normalized Jost solutions we find the generalized eigenfunctions: one is a normalizable function corresponding to the bound state in the continuum and the other is a bounded, non-normalizable function. We obtain the time evolution of these functions as pseudo-unitary, characteristic of a pseudo-Hermitian system.

Source: Revista Mexicana de Física

DOI: 10.31349/revmexfis.64.464

Authors: David Lohr, Enriqueta Hernandez, Antonio Jauregui, Alfonso Mondragon

Institutions: Universidad Nacional Autónoma de México, Universidad de Sonora

Language: English

Topic: Quantum Mechanics and Non-Hermitian Physics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W2889200111

FWCI: 0.116

Cites:

Cited by: 4

Related to: 10