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

Elchin Jafarov UGent and Joris Van der Jeugt UGent (2012) 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.
author
organization
alternative title
A finite oscillator model related to sl(2 vertical bar 1)
year
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
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
2016-12-21 15:41:36
```@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.