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

David Lohr, Enriqueta Hernandez, Antonio Jauregui, Alfonso Mondragon


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.


Bound states in the continuum; Darboux transformations; Jordan chain

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Revista Mexicana de Física

ISSN: 0035-001X

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