On the Eigenvalues of some non-Hermitian oscillators

We consider a class of one-dimensional non-Hermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between the strong-coupling expansions for the eigenvalues of those o...

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Detalles Bibliográficos
Autores principales: Fernández, Francisco Marcelo, García, Javier
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2013
Materias:
Física
Resonances
PT-symmetry
Non-hermitian
Quantum mechanics
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/101472
https://ri.conicet.gov.ar/11336/5051
http://iopscience.iop.org/1751-8121/46/19/195301
http://arxiv.org/abs/1301.1676
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-101472
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Resonances
PT-symmetry
Non-hermitian
Quantum mechanics
spellingShingle Física
Resonances
PT-symmetry
Non-hermitian
Quantum mechanics
Fernández, Francisco Marcelo
García, Javier
On the Eigenvalues of some non-Hermitian oscillators
topic_facet Física
Resonances
PT-symmetry
Non-hermitian
Quantum mechanics
description We consider a class of one-dimensional non-Hermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between the strong-coupling expansions for the eigenvalues of those oscillators. A comparison of the results of the complex rotation and the Riccati–Padé methods reveals that the optimal rotation angle converts the oscillator into either a PT-symmetric or a Hermitian one. In addition to the real positive eigenvalues, the PT-symmetric oscillators exhibit real positive resonances under different boundary conditions. These can be calculated by means of the straightforward diagonalization method. The Riccati–Padé method yields not only the resonances of the non-Hermitian oscillators but also the eigenvalues of the PT-symmetric ones.
format Articulo
Preprint
author Fernández, Francisco Marcelo
García, Javier
author_facet Fernández, Francisco Marcelo
García, Javier
author_sort Fernández, Francisco Marcelo
title On the Eigenvalues of some non-Hermitian oscillators
title_short On the Eigenvalues of some non-Hermitian oscillators
title_full On the Eigenvalues of some non-Hermitian oscillators
title_fullStr On the Eigenvalues of some non-Hermitian oscillators
title_full_unstemmed On the Eigenvalues of some non-Hermitian oscillators
title_sort on the eigenvalues of some non-hermitian oscillators
publishDate 2013
url http://sedici.unlp.edu.ar/handle/10915/101472
https://ri.conicet.gov.ar/11336/5051
http://iopscience.iop.org/1751-8121/46/19/195301
http://arxiv.org/abs/1301.1676
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