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

David Lohr, Enriqueta Hernandez, Antonio Jauregui, Alfonso Mondragon

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.

Keywords


Bound states in the continuum; Darboux transformations; Jordan chain

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DOI: https://doi.org/10.31349/RevMexFis.64.464

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Revista Mexicana de Física

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