Advanced search
2 files | 758.16 KB Add to list

A finite oscillator model related to sl(2|1)

Elchin Jafarov (UGent) and Joris Van der Jeugt (UGent)
Author
Organization
Abstract
We investigate a new model for the finite one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). In this setting, it is natural to present the position and momentum operators of the oscillator as odd elements of the Lie superalgebra. The model involves a parameter p (0 < p < 1) and an integer representation label j. In the (2 j + 1)-dimensional representations W-j of sl(2|1), the Hamiltonian has the usual equidistant spectrum. The spectrum of the position operator is discrete and turns out to be of the form +/-root k, where k = 0, 1, ... , j. We construct the discrete position wavefunctions, which are given in terms of certain Krawtchouk polynomials. These wavefunctions have appealing properties, as can already be seen from their plots. The model is sufficiently simple in the sense that the corresponding discrete Fourier transform (relating position wavefunctions to momentum wavefunctions) can be constructed explicitly.
Keywords
LIE SUPERALGEBRA SL(2|1), QUANTIZATION, Krawtchouk polynomials, REPRESENTATIONS, FINITE 1-DIMENSIONAL OSCILLATOR

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 452.71 KB
  • sl21oscillator2.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 305.44 KB

Citation

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

MLA
Jafarov, Elchin, and Joris Van der Jeugt. “A Finite Oscillator Model Related to Sl(2|1).” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 45, no. 27, 2012, doi:10.1088/1751-8113/45/27/275301.
APA
Jafarov, E., & Van der Jeugt, J. (2012). A finite oscillator model related to sl(2|1). JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(27). https://doi.org/10.1088/1751-8113/45/27/275301
Chicago author-date
Jafarov, Elchin, and Joris Van der Jeugt. 2012. “A Finite Oscillator Model Related to Sl(2|1).” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45 (27). https://doi.org/10.1088/1751-8113/45/27/275301.
Chicago author-date (all authors)
Jafarov, Elchin, and Joris Van der Jeugt. 2012. “A Finite Oscillator Model Related to Sl(2|1).” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45 (27). doi:10.1088/1751-8113/45/27/275301.
Vancouver
1.
Jafarov E, Van der Jeugt J. A finite oscillator model related to sl(2|1). JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2012;45(27).
IEEE
[1]
E. Jafarov and J. Van der Jeugt, “A finite oscillator model related to sl(2|1),” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 45, no. 27, 2012.
@article{2966797,
  abstract     = {{We investigate a new model for the finite one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). In this setting, it is natural to present the position and momentum operators of the oscillator as odd elements of the Lie superalgebra. The model involves a parameter p (0 < p < 1) and an integer representation label j. In the (2 j + 1)-dimensional representations W-j of sl(2|1), the Hamiltonian has the usual equidistant spectrum. The spectrum of the position operator is discrete and turns out to be of the form +/-root k, where k = 0, 1, ... , j. We construct the discrete position wavefunctions, which are given in terms of certain Krawtchouk polynomials. These wavefunctions have appealing properties, as can already be seen from their plots. The model is sufficiently simple in the sense that the corresponding discrete Fourier transform (relating position wavefunctions to momentum wavefunctions) can be constructed explicitly.}},
  articleno    = {{275301}},
  author       = {{Jafarov, Elchin and Van der Jeugt, Joris}},
  issn         = {{1751-8113}},
  journal      = {{JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}},
  keywords     = {{LIE SUPERALGEBRA SL(2|1),QUANTIZATION,Krawtchouk polynomials,REPRESENTATIONS,FINITE 1-DIMENSIONAL OSCILLATOR}},
  language     = {{eng}},
  number       = {{27}},
  pages        = {{16}},
  title        = {{A finite oscillator model related to sl(2|1)}},
  url          = {{http://dx.doi.org/10.1088/1751-8113/45/27/275301}},
  volume       = {{45}},
  year         = {{2012}},
}

Altmetric
View in Altmetric
Web of Science
Times cited: