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Finite oscillator models: the Hahn oscillator

Elchin Jafarov UGent, Nedialka Stoilova UGent and Joris Van der Jeugt UGent (2011) JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 44(26).
abstract
A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra u(2)(alpha). This algebra is a deformation of the Lie algebra u(2) extended by a parity operator, with the deformation parameter alpha. A class of irreducible unitary representations of u(2)(alpha) is constructed. In the finite oscillator model, the (discrete) spectrum of the position operator is determined, and the position wavefunctions are shown to be dual Hahn polynomials. Plots of these discrete wavefunctions display interesting properties, similar to those of the parabose oscillator. We show indeed that in the limit, when the dimension of the representations goes to infinity, the discrete wavefunctions tend to the continuous wavefunctions of the parabose oscillator.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
SYSTEMS, QUANTIZATION, SPACE, 2-DIMENSIONAL OSCILLATOR, quantum oscillator, finite quantum physics, Hahn polynomial
journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
J. Phys. A-Math. Theor.
volume
44
issue
26
article number
265203
pages
15 pages
Web of Science type
Article
Web of Science id
000291305900007
JCR category
PHYSICS, MATHEMATICAL
JCR impact factor
1.564 (2011)
JCR rank
16/55 (2011)
JCR quartile
2 (2011)
ISSN
1751-8113
DOI
10.1088/1751-8113/44/26/265203
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1266613
handle
http://hdl.handle.net/1854/LU-1266613
date created
2011-06-17 08:48:21
date last changed
2016-12-21 15:42:40
@article{1266613,
  abstract     = {A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra u(2)(alpha). This algebra is a deformation of the Lie algebra u(2) extended by a parity operator, with the deformation parameter alpha. A class of irreducible unitary representations of u(2)(alpha) is constructed. In the finite oscillator model, the (discrete) spectrum of the position operator is determined, and the position wavefunctions are shown to be dual Hahn polynomials. Plots of these discrete wavefunctions display interesting properties, similar to those of the parabose oscillator. We show indeed that in the limit, when the dimension of the representations goes to infinity, the discrete wavefunctions tend to the continuous wavefunctions of the parabose oscillator.},
  articleno    = {265203},
  author       = {Jafarov, Elchin and Stoilova, Nedialka and Van der Jeugt, Joris},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  keyword      = {SYSTEMS,QUANTIZATION,SPACE,2-DIMENSIONAL OSCILLATOR,quantum oscillator,finite quantum physics,Hahn polynomial},
  language     = {eng},
  number       = {26},
  pages        = {15},
  title        = {Finite oscillator models: the Hahn oscillator},
  url          = {http://dx.doi.org/10.1088/1751-8113/44/26/265203},
  volume       = {44},
  year         = {2011},
}

Chicago
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. 2011. “Finite Oscillator Models: The Hahn Oscillator.” Journal of Physics A-mathematical and Theoretical 44 (26).
APA
Jafarov, Elchin, Stoilova, N., & Van der Jeugt, J. (2011). Finite oscillator models: the Hahn oscillator. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44(26).
Vancouver
1.
Jafarov E, Stoilova N, Van der Jeugt J. Finite oscillator models: the Hahn oscillator. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2011;44(26).
MLA
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. “Finite Oscillator Models: The Hahn Oscillator.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 44.26 (2011): n. pag. Print.