Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator

Cariñena, J.F. (Universidad de Zaragoza) ; Plyushchay, M.S.

Resumen: Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp(1|2) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via nonphysical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.

Idioma: Inglés

DOI: 10.1103/PhysRevD.94.105022

Año: 2016

Publicado en: PHYSICAL REVIEW. D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY 94, 10 (2016), 105022 [11 pp]
ISSN: 1550-7998

Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-1
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2015-64166-C2-1

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Física Teórica (Departamento de Física Teórica)