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Deformed su (1,1) algebra as a model for quantum oscillators

Elchin Jafarov UGent, Nedialka Stoilova UGent and Joris Van der Jeugt UGent (2012) SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 8.
abstract
The Lie algebra su(1, 1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1, 1) can be extended to representations of this deformed algebra su (1, 1)(gamma). Just as the positive discrete series representations of su(1, 1) can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su (1, 1)(gamma) can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Meixner-Pollaczek polynomial, continuous dual Hahn polynomial, oscillator model, deformed algebra su(1_1), FINITE 2-DIMENSIONAL OSCILLATOR, GROUP THEORETIC INTERPRETATIONS, ORTHOGONAL POLYNOMIALS, REPRESENTATIONS, OPERATORS, LIE
journal title
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
Symmetry Integr. Geom.
volume
8
article number
025
pages
15 pages
Web of Science type
Article
Web of Science id
000303998000001
JCR category
PHYSICS, MATHEMATICAL
JCR impact factor
1.243 (2012)
JCR rank
25/55 (2012)
JCR quartile
2 (2012)
ISSN
1815-0659
DOI
10.3842/SIGMA.2012.025
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2137364
handle
http://hdl.handle.net/1854/LU-2137364
date created
2012-06-08 13:49:14
date last changed
2017-05-02 08:22:06
@article{2137364,
  abstract     = {The Lie algebra su(1, 1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1, 1) can be extended to representations of this deformed algebra su (1, 1)(gamma). Just as the positive discrete series representations of su(1, 1) can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su (1, 1)(gamma) can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models.},
  articleno    = {025},
  author       = {Jafarov, Elchin and Stoilova, Nedialka and Van der Jeugt, Joris},
  issn         = {1815-0659},
  journal      = {SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS},
  keyword      = {Meixner-Pollaczek polynomial,continuous dual Hahn polynomial,oscillator model,deformed algebra su(1\_1),FINITE 2-DIMENSIONAL OSCILLATOR,GROUP THEORETIC INTERPRETATIONS,ORTHOGONAL POLYNOMIALS,REPRESENTATIONS,OPERATORS,LIE},
  language     = {eng},
  pages        = {15},
  title        = {Deformed su (1,1) algebra as a model for quantum oscillators},
  url          = {http://dx.doi.org/10.3842/SIGMA.2012.025},
  volume       = {8},
  year         = {2012},
}
Chicago
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. 2012. “Deformed Su (1,1) Algebra as a Model for Quantum Oscillators.” Symmetry Integrability and Geometry-methods and Applications 8.
APA
Jafarov, Elchin, Stoilova, N., & Van der Jeugt, J. (2012). Deformed su (1,1) algebra as a model for quantum oscillators. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 8.
Vancouver
1.
Jafarov E, Stoilova N, Van der Jeugt J. Deformed su (1,1) algebra as a model for quantum oscillators. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 2012;8.
MLA
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. “Deformed Su (1,1) Algebra as a Model for Quantum Oscillators.” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 8 (2012): n. pag. Print.