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

Cariñena Marzo, José Fernando; Plyushchay, M. S.

doi:10.1103/PhysRevD.94.105022

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

Cariñena Marzo, José Fernando (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: Article (Published version)
Área (Departamento): Física Teórica (Departamento de Física Teórica)
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Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator