The su(2)α Hahn oscillator and a discrete FourierHahn transform
 Author
 Elchin Jafarov (UGent) , Nedialka Stoilova (UGent) and Joris Van der Jeugt (UGent)
 Organization
 Abstract
 We define the quadratic algebra su(2)(alpha) which is a oneparameter deformation of the Lie algebra su(2) extended by a parity operator. The odddimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2)(alpha). We investigate a model of the finite onedimensional harmonic oscillator based upon this algebra su(2)(alpha). It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this socalled discrete FourierHahn transform is computed explicitly. The matrix of this discrete FourierHahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform.
 Keywords
 Hahn polynomials, Lie algebra deformation, Finite oscillator models
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU1917306
 Chicago
 Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. 2011. “The Su(2)α Hahn Oscillator and a Discrete FourierHahn Transform.” Journal of Physics Amathematical and Theoretical 44 (35).
 APA
 Jafarov, Elchin, Stoilova, N., & Van der Jeugt, J. (2011). The su(2)α Hahn oscillator and a discrete FourierHahn transform. JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL, 44(35).
 Vancouver
 1.Jafarov E, Stoilova N, Van der Jeugt J. The su(2)α Hahn oscillator and a discrete FourierHahn transform. JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 2011;44(35).
 MLA
 Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. “The Su(2)α Hahn Oscillator and a Discrete FourierHahn Transform.” JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL 44.35 (2011): n. pag. Print.
@article{1917306, abstract = {We define the quadratic algebra su(2)(alpha) which is a oneparameter deformation of the Lie algebra su(2) extended by a parity operator. The odddimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2)(alpha). We investigate a model of the finite onedimensional harmonic oscillator based upon this algebra su(2)(alpha). It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this socalled discrete FourierHahn transform is computed explicitly. The matrix of this discrete FourierHahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform.}, articleno = {355205}, author = {Jafarov, Elchin and Stoilova, Nedialka and Van der Jeugt, Joris}, issn = {17518113}, journal = {JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL}, keyword = {Hahn polynomials,Lie algebra deformation,Finite oscillator models}, language = {eng}, number = {35}, pages = {18}, title = {The su(2)\ensuremath{\alpha} Hahn oscillator and a discrete FourierHahn transform}, url = {http://dx.doi.org/10.1088/17518113/44/35/355205}, volume = {44}, year = {2011}, }
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