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

被引：4

作者：

Lohr, D. ^{[1
]}

Hernandez, E. ^{[1
]}

Jauregui, A. ^{[2
]}

Mondragon, A. ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Fis, Apartado Postal 20-364, Mexico City 01000, DF, Mexico

[2] Univ Sonora, Dept Fis, Apartado Postal 106, Hermosillo, Sonora, Mexico

来源：

REVISTA MEXICANA DE FISICA | 2018年 / 64卷 / 05期

关键词：

Bound states in the continuum; Darboux transformations; Jordan chain; SUPERSYMMETRIC QUANTUM-MECHANICS; POTENTIALS; BEHAVIOR;

D O I：

10.31349/RevMexFis.64.464

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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. An explicit calculation of the cross section as a function of the wave number k reveals no sign of the bound state in the continuum.

引用

页码：464 / 471

页数：8

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