Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator

DOI10.1134/S0040577919090083zbMath1436.81041MaRDI QIDQ2174632

Vadim V. Borzov, E. V. Damaskinskiĭ

Publication date: 21 April 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

orthogonal polynomialsJacobi matrixgeneralized Chebyshev polynomialclassical Chebyshev polynomialgeneralized Chebyshev oscillator

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Best approximation, Chebyshev systems (41A50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (2)

Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator ⋮ Calculation of the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials

Cites Work

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• \(N\)-symmetric Chebyshev polynomials in a composite model of a generalized oscillator
• On orthogonal polynomials with perturbed recurrence relations
• When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
• Special linear combinations of orthogonal polynomials
• Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials
• On the dimensions of oscillator algebras induced by orthogonal polynomials
• Orthogonal polynomials and generalized oscillator algebras
• Orthogonality of quasi-orthogonal polynomials
• A point interaction for the discrete Schrödinger operator and generalized Chebyshev polynomials

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