Non-standard quantum algebras and infinite-dimensional PT-symmetric systems
Year: 2025
Type: article
Abstract: In this work, we introduce a PT -symmetric infinite-dimensional representation of the U z ( s l ( 2 , R ) ) Hopf algebra, and we analyse a multiparametric family of Hamiltonians constructed from such representation of the generators of this non-standard quantum algebra. It is shown that all these Hamiltonians can be mapped to equivalent systems endowed with a position-dependent mass. From the latter presentation, it is shown how appropriate point canonical transformations can be further defined in order to transform them into Hamiltonians with constant-mass over suitable domains. By following this approach, the bound-state spectrum and the corresponding eigenfunctions of the initial PT -symmetric Hamiltonians can be determined. It is worth stressing that a relevant feature of some of the new U z ( s l ( 2 , R ) ) systems here presented is found to be their connection with double-well and Pöschl-Teller potentials. In fact, as an application we present a particular Hamiltonian that can be expressed as an effective double-well trigonometric potential, which is commonly used to model several relevant systems in molecular physics.
Institutions: Universidad de Burgos, Universidad Nacional de La Plata
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415530342