Connection between quantum systems involving the fourth Painlevé transcendent and \(k\)-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial (Q2814206)
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scientific article; zbMATH DE number 6595451
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Connection between quantum systems involving the fourth Painlevé transcendent and \(k\)-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial |
scientific article; zbMATH DE number 6595451 |
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20 June 2016
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fourth Painlevé transcendent
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\(k\)-step rational extensions of the harmonic oscillator
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Connection between quantum systems involving the fourth Painlevé transcendent and \(k\)-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial (English)
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In this paper the authors discuss the connection between quantum systems involving rational solutions (related to generalized Hermite and Okamoto polynomials) of the fourth Painlevé equation and one- and two-step rational extensions of the harmonic oscillator. A particular case of this connection had been mentioned in recent papers, and this previous observation is here explicitly demonstrated and clarified.
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