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Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions

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  • Kravchenko, Vladislav V.

Abstract

A new representation for solutions of the one-dimensional Schrödinger equation −u″+q(x)u=ω2u is obtained in the form of a series possessing the following attractive feature. The truncation error is ω-independent for all ω∈R. For the coefficients of the series simple recurrent integration formulas are obtained which make the new representation applicable for computation.

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  • Kravchenko, Vladislav V., 2018. "Construction of a transmutation for the one-dimensional Schrödinger operator and a representation for solutions," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 75-81.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:75-81
    DOI: 10.1016/j.amc.2018.01.037
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    References listed on IDEAS

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    1. Kravchenko, Vladislav V. & Navarro, Luis J. & Torba, Sergii M., 2017. "Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 173-192.
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    Cited by:

    1. Khmelnytskaya, Kira V. & Kravchenko, Vladislav V. & Torba, Sergii M., 2019. "A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 274-281.

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