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

D.S. Lohr-Robles | Zendy; E. Hernández | Zendy; A. Jáuregui | Zendy; Alfonso Mondragón | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

D.S. Lohr-Robles,

E. Hernández,

A. Jáuregui,

Alfonso Mondragón

Publication year - 2018

Publication title -

revista mexicana de física

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.181

H-Index - 25

eISSN - 2683-2224

pISSN - 0035-001X

DOI - 10.31349/revmexfis.64.464

Subject(s) - eigenfunction , bound state , hermitian matrix , mathematical physics , bounded function , physics , time evolution , eigenvalues and eigenvectors , unitary state , iterated function , semiclassical physics , function (biology) , quantum mechanics , pure mathematics , mathematics , mathematical analysis , quantum , law , evolutionary biology , political science , biology

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 unnormalized Jost 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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research