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The u(2)α and su(2)α Hahn harmonic oscillators

(2013) BULGARIAN JOURNAL OF PHYSICS. 40(2). p.115-120
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Organization
Abstract
New models for the finite one-dimensional harmonic oscillator are proposed based upon the algebras u(2)_alpha and su(2)_alpha. These algebras are deformations of the Lie algebras u(2) and su(2) extended by a parity operator, with deformation parameter alpha. Classes of irreducible unitary representations of u(2)_alpha and su(2)_alpha are constructed. It turns out that in these models the spectrum of the position operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials.
Keywords
Hahn polynomials, finite quantum oscillators

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Citation

Please use this url to cite or link to this publication:

MLA
Jafarov, EI, et al. “The u(2)α and Su(2)α Hahn Harmonic Oscillators.” BULGARIAN JOURNAL OF PHYSICS, vol. 40, no. 2, 2013, pp. 115–20.
APA
Jafarov, E., Stoilova, N., & Van der Jeugt, J. (2013). The u(2)α and su(2)α Hahn harmonic oscillators. BULGARIAN JOURNAL OF PHYSICS, 40(2), 115–120.
Chicago author-date
Jafarov, EI, NI Stoilova, and Joris Van der Jeugt. 2013. “The u(2)α and Su(2)α Hahn Harmonic Oscillators.” BULGARIAN JOURNAL OF PHYSICS 40 (2): 115–20.
Chicago author-date (all authors)
Jafarov, EI, NI Stoilova, and Joris Van der Jeugt. 2013. “The u(2)α and Su(2)α Hahn Harmonic Oscillators.” BULGARIAN JOURNAL OF PHYSICS 40 (2): 115–120.
Vancouver
1.
Jafarov E, Stoilova N, Van der Jeugt J. The u(2)α and su(2)α Hahn harmonic oscillators. BULGARIAN JOURNAL OF PHYSICS. 2013;40(2):115–20.
IEEE
[1]
E. Jafarov, N. Stoilova, and J. Van der Jeugt, “The u(2)α and su(2)α Hahn harmonic oscillators,” BULGARIAN JOURNAL OF PHYSICS, vol. 40, no. 2, pp. 115–120, 2013.
@article{4208620,
  abstract     = {{New models for the finite one-dimensional harmonic oscillator are proposed based upon the algebras u(2)_alpha  and su(2)_alpha. These algebras are deformations of the Lie algebras u(2) and su(2) extended by a parity operator, with deformation parameter alpha. Classes of irreducible unitary representations of u(2)_alpha  and su(2)_alpha are constructed. It turns out that in these models the spectrum of the position operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials.}},
  author       = {{Jafarov, EI and Stoilova, NI and Van der Jeugt, Joris}},
  issn         = {{1310-0157}},
  journal      = {{BULGARIAN JOURNAL OF PHYSICS}},
  keywords     = {{Hahn polynomials,finite quantum oscillators}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{115--120}},
  title        = {{The u(2)α and su(2)α Hahn harmonic oscillators}},
  url          = {{http://www.bjp-bg.com/paper.php?id=648}},
  volume       = {{40}},
  year         = {{2013}},
}