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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations Quantum State Preparation Representation

Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations

arXiv
Authors: Satoru Odake, Ryu Sasaki

Year

2010

Paper ID

9060

Status

Preprint

Abstract Read

~2 min

Abstract Words

78

Citations

N/A

Abstract

An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009. Darboux-Crum transformations intertwining the discrete quantum mechanical systems of the original and the exceptional polynomials play an important role. Infinitely many continuous Hahn polynomials are derived in the same manner. The present method provides a simple proof of the shape invariance of these systems as in the corresponding cases of the exceptional Laguerre and Jacobi polynomials.

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  • An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1004.0544 [2] arXiv https://arxiv.org/abs/1004.0544 [3] Publisher https://arxiv.org/abs/1004.0544

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