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A finite oscillator model with equidistant position spectrum based on an extension of $\mathfrak{su}(2)$
- Source :
- J. Phys. A: Math. Theor. 49 175204 (2016)
- Publication Year :
- 2016
-
Abstract
- We consider an extension of the real Lie algebra $\mathfrak{su}(2)$ by introducing a parity operator $P$ and a parameter $c$. This extended algebra is isomorphic to the Bannai-Ito algebra with two parameters equal to zero. For this algebra we classify all unitary finite-dimensional representations and show their relation with known representations of $\mathfrak{su}(2)$. Moreover, we present a model for a one-dimensional finite oscillator based on the odd-dimensional representations of this algebra. For this model, the spectrum of the position operator is equidistant and coincides with the spectrum of the known $\mathfrak{su}(2)$ oscillator. In particular the spectrum is independent of the parameter $c$ while the discrete position wavefunctions, which are given in terms of certain dual Hahn polynomials, do depend on this parameter.<br />Comment: This is a preprint of a paper whose final and definite form is in Journal of Physics A: Mathematical and Theoretical
- Subjects :
- Mathematical Physics
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Phys. A: Math. Theor. 49 175204 (2016)
- Publication Type :
- Report
- Accession number :
- edsarx.1612.07692
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/1751-8113/49/17/175204