Email this article Local Perturbation of the Discrete Schrödinger Operator and a Generalized Chebyshev Oscillator
- Authors: Borzov V.V.1, Damaskinsky E.V.2
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Affiliations:
- Bonch-Bruevich St. Petersburg State University of Telecommunications
- Institute of Defence Technical Engineering
- Issue: Vol 200, No 3 (2019)
- Pages: 1348-1359
- Section: Article
- URL: https://journals.rcsi.science/0040-5779/article/view/172457
- DOI: https://doi.org/10.1134/S0040577919090083
- ID: 172457
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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.
About the authors
V. V. Borzov
Bonch-Bruevich St. Petersburg State University of Telecommunications
Author for correspondence.
Email: borzov.vadim@yandex.ru
Russian Federation, St. Petersburg
E. V. Damaskinsky
Institute of Defence Technical Engineering
Author for correspondence.
Email: evd@pdmi.ras.ru
Russian Federation, St. Petersburg
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