A finite quantum oscillator model related to special sets of Racah polynomials
- Author
- Roy Oste (UGent) and Joris Van der Jeugt (UGent)
- Organization
- Abstract
- In [R. Oste and J. Van der Jeugt, arXiv: 1507.01821 [math-ph]] we classified all pairs of recurrence relations in which two (dual) Hahn polynomials with different parameters appear. Such pairs are referred to as (dual) Hahn doubles, and the same technique was then applied to obtain all Racah doubles. We now consider a special case concerning the doubles related to Racah polynomials. This gives rise to an interesting class of two-diagonal matrices with closed form expressions for the eigenvalues. Just as it was the case for (dual) Hahn doubles, the resulting two-diagonal matrix can be used to construct a finite oscillator model. We discuss some properties of this oscillator model, give its (discrete) position wavefunctions explicitly, and illustrate their behavior by means of some plots.
- Keywords
- Finite oscillator models, Racah polynomial, 2-DIMENSIONAL OSCILLATOR
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8530611
- MLA
- Oste, Roy, and Joris Van der Jeugt. “A Finite Quantum Oscillator Model Related to Special Sets of Racah Polynomials.” PHYSICS OF ATOMIC NUCLEI, vol. 80, no. 4, 2017, pp. 786–93, doi:10.1134/S1063778817040196.
- APA
- Oste, R., & Van der Jeugt, J. (2017). A finite quantum oscillator model related to special sets of Racah polynomials. PHYSICS OF ATOMIC NUCLEI, 80(4), 786–793. https://doi.org/10.1134/S1063778817040196
- Chicago author-date
- Oste, Roy, and Joris Van der Jeugt. 2017. “A Finite Quantum Oscillator Model Related to Special Sets of Racah Polynomials.” PHYSICS OF ATOMIC NUCLEI 80 (4): 786–93. https://doi.org/10.1134/S1063778817040196.
- Chicago author-date (all authors)
- Oste, Roy, and Joris Van der Jeugt. 2017. “A Finite Quantum Oscillator Model Related to Special Sets of Racah Polynomials.” PHYSICS OF ATOMIC NUCLEI 80 (4): 786–793. doi:10.1134/S1063778817040196.
- Vancouver
- 1.Oste R, Van der Jeugt J. A finite quantum oscillator model related to special sets of Racah polynomials. PHYSICS OF ATOMIC NUCLEI. 2017;80(4):786–93.
- IEEE
- [1]R. Oste and J. Van der Jeugt, “A finite quantum oscillator model related to special sets of Racah polynomials,” PHYSICS OF ATOMIC NUCLEI, vol. 80, no. 4, pp. 786–793, 2017.
@article{8530611,
abstract = {{In [R. Oste and J. Van der Jeugt, arXiv: 1507.01821 [math-ph]] we classified all pairs of recurrence relations in which two (dual) Hahn polynomials with different parameters appear. Such pairs are referred to as (dual) Hahn doubles, and the same technique was then applied to obtain all Racah doubles. We now consider a special case concerning the doubles related to Racah polynomials. This gives rise to an interesting class of two-diagonal matrices with closed form expressions for the eigenvalues. Just as it was the case for (dual) Hahn doubles, the resulting two-diagonal matrix can be used to construct a finite oscillator model. We discuss some properties of this oscillator model, give its (discrete) position wavefunctions explicitly, and illustrate their behavior by means of some plots.}},
author = {{Oste, Roy and Van der Jeugt, Joris}},
issn = {{1063-7788}},
journal = {{PHYSICS OF ATOMIC NUCLEI}},
keywords = {{Finite oscillator models,Racah polynomial,2-DIMENSIONAL OSCILLATOR}},
language = {{eng}},
number = {{4}},
pages = {{786--793}},
title = {{A finite quantum oscillator model related to special sets of Racah polynomials}},
url = {{http://doi.org/10.1134/S1063778817040196}},
volume = {{80}},
year = {{2017}},
}
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