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Title: Superintegrable quantum u(3) systems and higher rank factorizations

Abstract

A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant intertwining operators we arrive at a so(6) dynamical algebra and its Hamiltonian hierarchies. We pay attention to those associated to certain unitary irreducible representations that can be displayed by means of three-dimensional polyhedral lattices. We also discuss the role of superpotentials in this new context.

Authors:
; ;  [1]
  1. Departamento de Matematica Aplicada, Universidad de Valladolid, E-47011 Valladolid (Spain)
Publication Date:
OSTI Identifier:
20768767
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 47; Journal Issue: 4; Other Information: DOI: 10.1063/1.2191360; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; FACTORIZATION; HAMILTONIANS; IRREDUCIBLE REPRESENTATIONS; ONE-DIMENSIONAL CALCULATIONS; QUANTUM MECHANICS; SO-6 GROUPS; SURFACES; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS; U-3 GROUPS

Citation Formats

Calzada, J A, Negro, J, Olmo, M.A. del, and Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47005 Valladolid. Superintegrable quantum u(3) systems and higher rank factorizations. United States: N. p., 2006. Web. doi:10.1063/1.2191360.
Calzada, J A, Negro, J, Olmo, M.A. del, & Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47005 Valladolid. Superintegrable quantum u(3) systems and higher rank factorizations. United States. https://doi.org/10.1063/1.2191360
Calzada, J A, Negro, J, Olmo, M.A. del, and Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47005 Valladolid. 2006. "Superintegrable quantum u(3) systems and higher rank factorizations". United States. https://doi.org/10.1063/1.2191360.
@article{osti_20768767,
title = {Superintegrable quantum u(3) systems and higher rank factorizations},
author = {Calzada, J A and Negro, J and Olmo, M.A. del and Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47005 Valladolid},
abstractNote = {A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant intertwining operators we arrive at a so(6) dynamical algebra and its Hamiltonian hierarchies. We pay attention to those associated to certain unitary irreducible representations that can be displayed by means of three-dimensional polyhedral lattices. We also discuss the role of superpotentials in this new context.},
doi = {10.1063/1.2191360},
url = {https://www.osti.gov/biblio/20768767}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 4,
volume = 47,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}