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Entanglement Theory Quantum Correlations

A finite quantum oscillator model related to special sets of Racah polynomials

arXiv
Authors: Roy Oste, Joris Van der Jeugt

Year

2016

Paper ID

41633

Status

Preprint

Abstract Read

~2 min

Abstract Words

121

Citations

N/A

Abstract

In Oste and Van der Jeugt, SIGMA, 12 (2016) 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 behaviour by means of some plots.

Why This Paper Matters

  • This paper contributes to the Entanglement Theory & Quantum Correlations research area in the Quantum Articles archive.
  • It adds a 2016 reference point for readers tracking recent quantum research.
  • In Oste and Van der Jeugt, SIGMA, 12 (2016) we classified all pairs of recurrence relations in which two (dual) Hahn polynomials with different parameters appear.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1612.07700 [2] arXiv https://arxiv.org/abs/1612.07700 [3] Publisher https://arxiv.org/abs/1612.07700

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