Abstract
We discuss the conditions under which a special linear transformation of the classical Chebyshev polynomials (of the second kind) generate a class of polynomials related to “local perturbations” of the coefficients of a discrete Schrödinger equation. These polynomials are called generalized Chebyshev polynomials. We answer this question for the simplest class of “local perturbations” and describe a generalized Chebyshev oscillator corresponding to generalized Chebyshev polynomials.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 3, pp. 494–506, September, 2019.
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Borzov, V.V., Damaskinsky, E.V. Local Perturbation of the Discrete Schrödinger Operator and a Generalized Chebyshev Oscillator. Theor Math Phys 200, 1348–1359 (2019). https://doi.org/10.1134/S0040577919090083
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DOI: https://doi.org/10.1134/S0040577919090083