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

(2012) JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 45(27).- 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.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-2966797

- author
- Elchin Jafarov UGent and Joris Van der Jeugt UGent
- organization
- alternative title
- A finite oscillator model related to sl(2 vertical bar 1)
- year
- 2012
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- LIE SUPERALGEBRA SL(2|1), QUANTIZATION, Krawtchouk polynomials, REPRESENTATIONS, FINITE 1-DIMENSIONAL OSCILLATOR
- journal title
- JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- J. Phys. A-Math. Theor.
- volume
- 45
- issue
- 27
- article_number
- 275301
- pages
- 16 pages
- Web of Science type
- Article
- Web of Science id
- 000305973600011
- JCR category
- PHYSICS, MATHEMATICAL
- JCR impact factor
- 1.766 (2012)
- JCR rank
- 13/55 (2012)
- JCR quartile
- 1 (2012)
- ISSN
- 1751-8113
- DOI
- 10.1088/1751-8113/45/27/275301
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
*I have transferred the copyright for this publication to the publisher*- id
- 2966797
- handle
- http://hdl.handle.net/1854/LU-2966797
- date created
- 2012-08-02 09:15:05
- date last changed
- 2012-08-08 13:38:50

@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 {\textlangle} p {\textlangle} 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}, keyword = {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}, }

- Chicago
- 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). - APA
- Jafarov, Elchin, & Van der Jeugt, J. (2012). A finite oscillator model related to sl(2|1).
*JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*,*45*(27). - 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).
- MLA
- Jafarov, Elchin, and Joris Van der Jeugt. “A Finite Oscillator Model Related to Sl(2|1).”
*JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*45.27 (2012): n. pag. Print.