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Title: The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.
Authors:
 [1] ;  [2]
  1. Department of Mathematics, St. Petersburg State University of Telecommunications, 191186, Moika 61, St. Petersburg (Russian Federation)
  2. Department of Natural Sciences, Institute of Defense Technical Engineering (VITI), 191123, Zacharievskaya 22, St. Petersburg (Russian Federation)
Publication Date:
OSTI Identifier:
22305864
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; HILBERT SPACE; IRREDUCIBLE REPRESENTATIONS; LIE GROUPS; OSCILLATORS; TWO-DIMENSIONAL CALCULATIONS